## Sunday, 26 March 2017

### On This Day in Math - March 26

 “Have you seen the world go around?"

Every human activity, good or bad, except mathematics, must come to an end.
~Paul Erdos

The 85th day of the year; 85 is the largest number for which the sum of 12 + 22+32+42+...+n2= 1+2+3+4+.... +M for some n,M, can you find that M?   85 is the largest such n, with a total of 208,335; but can you find some solutions n,M that are smaller? (Reminder for students, the sums of first n consecutive squares are called pyramidal numbers, the sums of the first n integers are called triangular numbers.)

and a bonus I found at the Prime Curios web site, (8511 - 85)/11 ± 1 are twin primes. (too cool)

85 is the second smallest n such that n, n+1 and n+2 are products of two primes. (called pronic, or oblong numbers) *Don S McDonald

There are 85 five-digit primes that begin with 85.

And 85 is the sum of consecutive integers, and the difference of their squares  $42+43= 43^2 - 42^2 = 85$, and can be expressed as the sum of two squares in two different ways, 92+ 2 2 = 72 + 62 =85

EVENTS

1619 Descartes reported (to Beekman) his ﬁrst glimpse of “an entirely new science, by which all problems that can be posed, concerning any kind of quantity, continuous or discrete, can be generally solved”  which was to become his analytic geometry (published 1637).
Descartes relies on the “single motions” of his “new types of compasses (often referred to by commentators as “proportional compasses”), which [he says] are no less exact and geometrical…than the common ones used to draw circles” in order to mark out a new class of problems that have legitimate geometrical solutions. He would apply them to to the problems of (1) dividing a given angle into any number of equal parts, (2) constructing the roots of three types of cubic equations, and (3) describing a conic section.
*Stanford Encyclopedia of Philosophy

1760 Guillaume le Gentil sailed from France planning to view the transit of Venus the following year from the east coast of India. Monsoons blew his ship off course, and on the day of the transit, he was becalmed in the Indian Ocean, unable to make any useful observations. Determined to redeem his expedition he books passage to India and builds an observatory to await the 1769 transit in Pondecherry. "The sky remained marvelously clear throughout May, only to cloud over on June 4, the morning of the transit, then clear again as soon as the transit was over."
His ordeal of a decade was not yet over. Stricken with dysentery he had to stay nine months more in India, and then booked passage on a Spanish warship. The ship lost its mast in a hurricane off the Cape of Good Hope, and finally limped into Cadiz. Le Gentil set out across the Pyrenees and returned to Paris after a total absence of eleven years, six months, and thirteen days, only to find that he had been presumed dead and his estate divided among his heirs. *Timothy Ferris, Coming of Age in the Milky Way (Thony Christie, The Renaissance Mathematicus, has a more detailed, and perhaps somewhat more accurate, version of Guillame's great adventure. See it here

1851 French Science reporter Terrien wrote in “le National, “Have you seen the world go around? Would you like to see it rotate? Go to the Parthenon on Thursday…the experiment devised by M. Leon Foucault is carried out there, in the presence of the public, under the finest conditions in the world.” *Amir D Aczel, Pendulum, pg 152
Foucault’s most famous pendulum . He suspended a 28 kg brass-coated lead bob with a 67 meter long wire from the dome of the Panthéon, Paris. The plane of the pendulum's swing rotated clockwise 11° per hour, making a full circle in 32.7 hours. *Wik

In 1859, Edmond Modeste Lescarbault, a French medical doctor and amateur astronomer, reported sighting a new planet in an orbit inside that of Mercury which he named Vulcan. He had seen a round black spot on the Sun with a transit time across the solar disk 4 hours 30 minutes. He sent this information and his calculations on the planet's movements to Jean LeVerrier, France's most famous astronomer. Le Verrier had already noticed that Mercury had deviated from its orbit. A gravitational pull from Vulcan would fit in nicely with what he was looking for. However, it was not consistently seen again and it is now believed to have been a "rogue asteroid" making a one-time pass close to the sun.*TIS (It was just pointed out to me by @Astroguyz,David Dickinson, that Leonard Nimoy, the actor who is best remembered for his role as the half-Vulcan character of Dr. Spock in the Star Trek series and films was also born on this day in 1931.)

1900 the Roentgen Society of the United States was organised a meeting of doctors from nine states held in Dr. Herber Robarts' office in St. Louis. Dr. Robarts was founder and editor of the American X-Ray Journal, and had been active in radiology since exposing his first X-ray plates in Feb 1896. Robarts was elected as president of the new society and and Dr. J. Rudis-Jicinsky as secretary. They arranged to hold the first annual meeting at the Grand Central Palace in New York City on 13-14 Dec 1900. In 1901, it was renamed as the Roentgen Society of America to include Canadians. It was reorganised at the next annual meeting on 10-11 Dec 1902 as the American Roentgen Ray Society.*TIS

1936 The 200" Hale mirror was SHIPPED, it had been cast in 1934. Still a great video: *David Dickinson ‏@Astroguyz
The 200-inch (5.1 m) Hale Telescope (f/3.3) was the world's largest effective telescope for 45 years (1948 - 1993). It is still a workhorse of modern astronomy. It is used nightly for a wide range of astronomical studies. On average the weather allows for at least some data collection about 290 nights a year. *Caltech Astronomy

1985 Alexander's Star is a puzzle similar to the Rubik's Cube, in the shape of a great dodecahedron.
Alexander's Star was invented by Adam Alexander, an American mathematician, in 1982. It was patented on 26 March 1985, with US patent number 4,506,891, and sold by the Ideal Toy Company. It came in two varieties: painted surfaces or stickers. Since the design of the puzzle practically forces the stickers to peel with continual use, the painted variety is likely a later edition.
*Wik

1994, A picture was released showing the first moon discovered to be in orbit around an asteroid. The potato-shaped asteroid Ida and its newly-discovered moon, Dactyl was imaged by NASA's Galileo spacecraft, about 14 minutes before its closest approach to the asteroid on 28 Aug 1993. Ida appears to be about about 36 miles long and 14 miles wide. It shows numerous craters, including many degraded craters, indicating Ida's surface is older than previously thought. The tiny moon is about one mile (1.5-km) across. The names are derived from the Dactyli, a group of mythological beings who lived on Mount Ida, where the infant Zeus was hidden (and raised, in some accounts) by the nymph Ida and protected by the Dactyli.

2010 Crocheting Adventures with Hyperbolic Planes by Dr Daina Taimina has won the 2009 Diagram Prize, having received the majority of the public vote for the oddest titled book of the year at thebookseller.com. The first award was given in 1978 for Proceedings of the Second International Workshop on Nude Mice

BIRTHS
1516 Conrad Gessner (Konrad Gessner, Conrad Geßner, Conrad von Gesner, Conradus Gesnerus, Conrad Gesner; 26 March 1516 – 13 December 1565) was a Swiss naturalist and bibliographer. His five-volume Historiae animalium (1551–1558) is considered the beginning of modern zoology, and the flowering plant genus Gesneria (Gesneriaceae) is named after him. He is denoted by the author abbreviation Gesner when citing a botanical name. Gessner in 1551 was the first to describe adipose tissue; and in 1565 the first to document the pencil. *Wik See more at The Renaissance Mathematicus blog.

1753 Count Benjamin Thompson Rumford (26 Mar 1753, 21 Aug 1814) American-born British physicist, government administrator, and a founder of the Royal Institution of Great Britain, London. Because he was a Redcoat officer and an English spy during the American revolution, he moved into exile in England. Through his investigations of heat he became one of the first scientists to declare that heat is a form of motion rather than a material substance, as was popularly believed until the mid-19th century. Among his numerous scientific contributions are the development of a calorimeter and a photometer. He invented a double boiler, a kitchen stove and a drip coffee pot. *TIS

1773 Nathaniel Bowditch (26 Mar 1773, 16 Mar 1838 at age 65) Self-educated American mathematician and astronomer. He learned Latin to study Newton's Principia and later other languages to study mathematics in these languages. Between 1795 and 1799 he made four sea voyages and in 1802 he was in command of a merchant ship. He was author of the best book on navigation of his time, New American Practical Navigator (1802), and his translation (assisted by Benjamin Peirce) of Laplace's Mécanique céleste gave him an international reputation. Bowditch was the discoverer of the Bowditch curves (more often called Lisajous figures for their co-discoverer), which have important applications in astronomy and physics.*TIS Bowditch was a navigator on the Wilkes Expedition and an island in the Stork Archipelago in the South Pacific is named for him (and sometimes called Fakaofu) *TIS Nathaniel Bowditch acquired his knowledge of mathematics through self-study while apprenticed to a ship’s chandler. He is most noted for his translation of Laplace’s M´ecanique c´eleste. [DSB 2, 368] *VFR

1789 William C. Redfield (26 Mar 1789, 12 Feb 1857 at age 67) American meteorologist who observed the whirlwind character of tropical storms. Following a hurricane that struck New England on 3 Sep 1821, he noted that in central Connecticut trees had toppled toward the northwest, but in the opposite direction 80-km further west. He found that hurricanes are generated in a belt between the Equator and the tropics, then veer eastward when meeting westerly winds at about latitude 30ºN. In 1831, he published his evidence that storm winds whirl counterclockwise about a centre that moves in the normal direction of the prevailing winds. He also promoted railroads and steamships. He co-founded the American Association for the Advancement of Sciences and was president at its first meeting (Sep 1848).*TIS

1803 Sir John William Lubbock, (London, England, 26 March 1803 - Downe, Kent, England, 20 June 1865 )English astronomer and mathematician. He made a special study of tides and of the lunar theory and developed a method for calculating the orbits of comets and planets. In mathematics he applied the theory of probability to life insurance problems. He was a strong proponent of Continental mathematics and astronomy.
Lubbock, third Baron Lubbock, was born into a London banking family. After attending Eton, he moved to Trinity College, Cambridge, where he became a student of William Whewell.(it was at the request of Lubbock that Whewell created the term "biometry".) He excelled in mathematics and traveled to France and Italy to deepen his knowledge of the works of Pierre-Simon de Laplace and Joseph Lagrange. Entering his father’s banking firm as a junior partner, he devoted his free time to science.
Lubbock strongly supported Lord Brougham’s Society for the Diffusion of Useful Knowledge [SDUK], which produced scientific and technical works designed for the working class. His articles on tides for the Society’s publications resulted in a book, *An Elementary Treatise on the Tides, in 1839. *Biographical Encyclopedia of Astronomers

1821 Ernst Engel (26 Mar 1821, 8 Dec 1896) German statistician, the head of the Prussian Statistical Bureau (1860-82), known for the "Engel curve," or Engel's law, which states that the proportion of expenditure on food will fall as income rises, i.e. food is a necessary good. Engel's law applies to goods as a whole. Demand for food, clothing and shelter - and for most manufactured products - doesn't keep pace with increases in incomes. Engel curves are useful for separating the effect of income on demand from the effects of changes in relative prices. Engel also examined the relationship between the size of the Prussian rye harvest and the average price of rye over a number of years prior to 1860, probably the first empirical study of the relationship between price and supply. *TIS

1848 Konstantin Alekseevich Andreev (26 March 1848 in Moscow, Russia - 29 Oct 1921 Near Sevastopol, Crimea) Andreev is best known for his work on geometry, although he also made contributions to analysis. In the area of geometry he did major pieces of work on projective geometry. Let us note one particular piece of work for which he has not received the credit he deserves. Gram determinants were introduced by J P Gram in 1879 but Andreev invented them independently in the context of problems of expansion of functions into orthogonal series and the best quadratic approximation to functions. *SAU

1862 Philbert Maurice d'Ocagne (26 March 1862 in Paris, France - 23 Sept 1938 in Le Havre, France) In 1891 he began publishing papers on nomography, the topic for which he is most remembered today. Nomography consists in the construction of graduated graphic tables, nomograms, or charts, representing formulas or equations to be solved, the solutions of which were provided by inspection of the tables. An advertisement for a colloquium at the Edinburgh Mathematical Society gave the following description of d'Ocagne's course:
It is now generally recognised that for most purposes the nomographic methods are superior to the older graphical methods of calculation. The introduction of some nomographic teaching in British Universities (and schools, for much of it is not too hard for schoolboys) is much to be desired.
*SAU
Nomographs are still used in wide areas of science and technology. The book below is an excellent coverage of the history and modern usage.

1875 Max Abraham (26 Mar 1875, 16 Nov 1922) German physicist whose life work was almost all related to Maxwell's theory. The text he wrote was the standard work on electrodynamics in Germany for a long time. Throughout his life, he remained strongly opposed to Einstein's Theory of Relativity, objecting to its postulates which he felt were contrary to classical common sense. He further held that the experimental evidence did not support that theory. In 1902, he had developed a theory of the electron in which he held that an electron was a perfectly rigid sphere with a charge distributed evenly over its surface. He also believed in the ether theory, thought that future astronomical data would validate it, and thus relativity was not in fact a good description of the real world. *TIS

1902 Marion Gray (26 March 1902, 16 Sept 1979) graduated from Edinburgh University and then went to Bryn Mawr College in the USA. She completed her doctorate there and returned to posts at Edinburgh and Imperial College London. She returned to the USA and worked for AT&T for the rest of her career. The Gray graph is named after her.*SAU The Gray graph is an undirected bipartite graph with 54 vertices and 81 edges. It is a cubic graph: every vertex touches exactly three edges. The Gray graph is interesting as the first known example of a cubic graph having the algebraic property of being edge but not vertex transitive *Wik

1903 Patrick du Val (March 26, 1903–January 22, 1987) was a British mathematician, known for his work on algebraic geometry, differential geometry, and general relativity. The concept of Du Val singularity of an algebraic surface is named after him. Du Val's early work before becoming a research student was on relativity, including a paper on the De Sitter model of the universe and Grassmann's tensor calculus. His doctorate was on algebraic geometry and in his thesis he generalised a result of Schoute. He worked on algebraic surfaces and later in his career became interested in elliptic functions.*Wik

1908 Theodore Samuel Motzkin (26 March 1908–15 December 1970) was an Israeli-American mathematician. Motzkin received his Ph.D. in 1934 from the University of Basel under the supervision of Alexander Ostrowski.
He was appointed at UCLA in 1950 and worked there until retirement.
The Motzkin transposition theorem, Motzkin numbers and the Fourier–Motzkin elimination are named after him. Motzkin first developed the "double description" algorithm of polyhedral combinatorics and computational geometry.[3] He was the first to prove the existence of principal ideal domains that are not Euclidean domains.
The quote "complete disorder is impossible," describing Ramsey theory is attributed to him. *Wik

1913 Paul Erdös (26 Mar 1913; 20 Sep 1996 at age 83) Hungarian mathematician, who was one of the century's top math experts and pioneered the fields of number theory and combinatorics. The type of mathematics he worked on were beautiful problems that were simple to understand, but notoriously difficult to solve. At age 20, he discovered a proof for a classic theorem of number theory that states that there is always at least one prime number between any positive integer and its double. In the 1930s, he studied in England and moved to the USA by the late 1930s when his Jewish origins made a return to Hungary impossible. Affected by McCarthyism in the 1950s, he spent much of the next ten years in Israel. Writing his many hundreds of papers made him one of history's most prolific mathematicians. *TIS His forte is posing and solving problems. One of his customs is to offer cash prizes for problems he poses. These awards range from $5 to$10,000 depending on how difficult he judges them to be. Erdos has written over 1,000 research papers, more than any other mathematician. The previous record was held by Arthur Cayley, who wrote 927. [Gallian, Contemporary Abstract Algebra, p 378]*VFR
McGill University Professor Willy Moser, a friend and collaborator of Erdos, tells of the "trial" of hosting Erdos. Once when Erdos was staying with him, Moser set up five dinners for him with five of erdos' old friends. Moser's wife pointed out that after the many times he had visited these homes and never brought a gift, perhaps Moser should remind him to bring candy or flowers. When he suggested the idea to Erdos, he thought it was a great idea and asked Moser, "Would you pick me up five boxes of chocolates?"

1922 Guido Stampacchia (March 26, 1922 - April 27, 1978) was a 20th century mathematician. Stampacchia was active in research and teaching throughout his career. He made key contributions to a number of fields, including calculus of variation and differential equations. In 1967 Stampacchia was elected President of the Unione Matematica Italiana. It was about this time that his research efforts shifted toward the emerging field of variational inequalities, which he modeled after boundary value problems for partial differential equations.
Stampacchia accepted the position of Professor Mathematical Analysis at the University of Rome in 1968 and returned to Pisa in 1970. He suffered a serious heart attack in early 1978 and died of heart arrest on April 27 of that year *Wik

1938 Sir Anthony James (Tony) Leggett (26 March 1938, ), has been a Professor of Physics at the University of Illinois at Urbana-Champaign since 1983.
Professor Leggett is widely recognized as a world leader in the theory of low-temperature physics, and his pioneering work on superfluidity was recognized by the 2003 Nobel Prize in Physics. He has shaped the theoretical understanding of normal and superfluid helium liquids and strongly coupled superfluids. He set directions for research in the quantum physics of macroscopic dissipative systems and use of condensed systems to test the foundations of quantum mechanics. *Wik

DEATHS

1609 John Dee (13 July 1527– *SAU gives 26 March 1609 in Mortlake, London, England) was an English mathematician, astronomer, astrologer, occultist, navigator, imperialist[4] and consultant to Queen Elizabeth I. He devoted much of his life to the study of alchemy, divination and Hermetic philosophy.
Dee straddled the worlds of science and magic just as they were becoming distinguishable. One of the most learned men of his age, he had been invited to lecture on advanced algebra at the University of Paris while still in his early twenties. Dee was an ardent promoter of mathematics and a respected astronomer, as well as a leading expert in navigation, having trained many of those who would conduct England's voyages of discovery.
Simultaneously with these efforts, Dee immersed himself in the worlds of magic, astrology and Hermetic philosophy. He devoted much time and effort in the last thirty years or so of his life to attempting to commune with angels in order to learn the universal language of creation and bring about the pre-apocalyptic unity of mankind. A student of the Renaissance Neo-Platonism of Marsilio Ficino, Dee did not draw distinctions between his mathematical research and his investigations into Hermetic magic, angel summoning and divination. Instead he considered all of his activities to constitute different facets of the same quest: the search for a transcendent understanding of the divine forms which underlie the visible world, which Dee called "pure verities".
In his lifetime Dee amassed one of the largest libraries in England. His high status as a scholar also allowed him to play a role in Elizabethan politics. He served as an occasional adviser and tutor to Elizabeth I and nurtured relationships with her ministers Francis Walsingham and William Cecil. Dee also tutored and enjoyed patronage relationships with Sir Philip Sidney, his uncle Robert Dudley, 1st Earl of Leicester, and Edward Dyer. He also enjoyed patronage from Sir Christopher Hatton.*Wik
I have Woolley's book, and enjoyed it.

1797 James Hutton (3 June 1726 in Edinburgh, Scotland - 26 March 1797 in Edinburgh, Scotland) geologist who initiated the principle of uniformitarianism with his Theory of the Earth (1785). He asserted that geological processes examined in the present time explain the formation of older rocks. John Playfair effectively championed Hutton's theory. Hutton, in effect, was the founder of modern geology, replacing a belief in the role of a biblical flood forming the Earth's crust. He introduced an understanding of the action of great heat beneath the Earth's crust in fusing sedimentary rocks, and the elevation of land forms from levels below the ocean to high land in a cyclical process. He established the igneous origin of granite (1788). He also had early thoughts on the evolution of animal forms and meterology. *TIS

1914 John S Mackay (22 Oct 1843 in Auchencairn near Kirkudbright, Kirkcudbrightshire, Scotland - 26 March 1914 in Edinburgh, Scotland)graduated from St Andrews University and taught at Perth Academy and Edinburgh Academy. He was a founder member of the EMS and became the first President in 1883 and an honorary member in 1894. He published numerous papers on Geometry in the EMS Proceedings.*SAU

1933 József Kürschák (14 March 1864 – 26 March 1933) was a Hungarian mathematician noted for his work on trigonometry and for his creation of the theory of valuations. He proved that every valued field can be embedded into a complete valued field which is algebraically closed. In 1918 he proved that the sum of reciprocals of consecutive natural numbers is never an integer. Extending Hilbert's argument, he proved that everything that can be constructed using a ruler and a compass, can be constructed by using a ruler and the ability of copying a fixed segment. He was elected a member of the Hungarian Academy of Sciences in 1897. *Wik

1974 Edward Uhler Condon (March 2, 1902 – March 26, 1974) was a distinguished American nuclear physicist, a pioneer in quantum mechanics, and a participant in the development of radar and nuclear weapons during World War II as part of the Manhattan Project. The Franck–Condon principle and the Slater–Condon rules are named after him.
He was the director of the National Bureau of Standards (now NIST) from 1945 to 1951. In 1946, Condon was president of the American Physical Society, and in 1953 was president of the American Association for the Advancement of Science.
During the McCarthy period, when efforts were being made to root out communist sympathizers in the United States, Edward Condon was a target of the House Un-American Activities Committee on the grounds that he was a 'follower' of a 'new revolutionary movement', quantum mechanics; Condon defended himself with a famous commitment to physics and science.
Condon became widely known in 1968 as principal author of the Condon Report, an official review funded by the United States Air Force that concluded that unidentified flying objects (UFOs) have prosaic explanations. The lunar crater Condon is named for him.
Years later, Carl Sagan reported how Condon described one encounter with a loyalty review board. A board member stated his concern: "Dr. Condon, it says here that you have been at the forefront of a revolutionary movement in physics called...quantum mechanics. It strikes this hearing that if you could be at the forefront of one revolutionary movement...you could be at the forefront of another". Condon said he replied: "I believe in Archimedes' Principle, formulated in the third century B.C. I believe in Kepler's laws of planetary motion, discovered in the seventeenth century. I believe in Newton's laws...." and continued with a catalog of scientists from earlier centuries, including the Bernoulli, Fourier, Ampère, Boltzmann, and Maxwell.[35] He once said privately: "I join every organization that seems to have noble goals. I don't ask whether it contains Communists".*Wik

1996 Hewlett-Packard Co-Founder David Packard Dies:
Hewlett-Packard Company co-founder David Packard dies after several weeks of illness. With fellow Stanford graduate Bill Hewlett, Packard founded Hewlett-Packard in a Palo Alto garage in 1938, spurring the development of what has come to be known as Silicon Valley. The company's first product was an oscillator, eight of which Disney used in its groundbreaking film ""Fantasia."" Since then, HP has made a name in personal computers, laser printers, calculators, accessories, and test equipment.*CHM

1966 Anna Johnson Pell Wheeler (5 May 1883 in Calliope (now Hawarden), Iowa, USA - 26 March 1966 in Bryn Mawr, Pennsylvania, USA) In 1899 she entered the University of South Dakota where she showed great promise in mathematics. The professor of mathematics, Alexander Pell, recognised her talents and helped persuade Anna Johnson that she should follow a career in mathematics. She received an A.B. degree in 1903.
After winning a scholarship to study for her master's degrees at the University of Iowa, she was awarded the degree for a thesis The extension of Galois theory to linear differential equations in 1904. A second master's degree from Radcliffe was awarded in 1905 and she remained there to study under Bôcher and Osgood.
Anna Johnson was awarded the Alice Freeman Palmer Fellowship from Wellesley College to study for a year at Göttingen University. There she attended lectures by Hilbert, Klein, Minkowski, Herglotz and Schwarzschild. She worked for her doctorate at Göttingen. While there Alexander Pell, her former mathematics professor came to Göttingen so that they could marry.
After returning to the United States, where her husband was by now Dean of Engineering, she taught courses in the theory of functions and differential equations. In 1908 Anna Pell returned to Göttingen where she completed the work for her doctorate but, after a disagreement with Hilbert, she returned to Chicago, where her husband was now on the university staff, without the degree being awarded.
At Chicago she became a student of Eliakim Moore and received her Ph.D. in 1909, her thesis Biorthogonal Systems of Functions with Applications to the Theory of Integral Equations being the one written originally at Göttingen. From 1911 Anna Pell taught at Mount Holyoke College and then at Bryn Mawr from 1918. Anna Pell's husband Alexander, who was 25 years older than she was, died in 1920. In 1924 Anna Pell became head of mathematics when Scott retired, becoming a full professor in 1925.
After a short second marriage to Arthur Wheeler, during which time they lived at Princeton and she taught only part-time, her second husband died in 1932. After this Anna Wheeler returned to full time work at Bryn Mawr where Emmy Noether joined her in 1933. However Emmy Noether died in 1935. The period from 1920 until 1935 certainly must have been one with much unhappiness for Anna Wheeler since during those years her father, mother, two husbands and close friend and colleague Emmy Noether died. Anna Wheeler remained at Bryn Mawr until her retirement in 1948.
The direction of Anna Wheeler's work was much influenced by Hilbert. Under his guidance she worked on integral equations studying infinite dimensional linear spaces. This work was done in the days when functional analysis was in its infancy and much of her work has lessened in importance as it became part of the more general theory.
Perhaps the most important honour she received was becoming the first woman to give the Colloquium Lectures at the American Mathematical Society meetings in 1927.
*SAU

Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbel

## Saturday, 25 March 2017

### On This Day in Math - March 25

Mathematics, however, is, as it were, its own explanation; this, although it may seem hard to accept, is nevertheless true, for the recognition that a fact is so is the cause upon which we base the proof.
~Girolamo Cardano

The 84th day of the year, with nine points equally placed around a circle there are 84 different triangles using three of these points as vertices. Are any of them right triangles?

84 is the only number that is spelled with ten letters that are all different.

Litttle is known of the life of Diophantus, but this problem, supposedly on his tomb, will reveal his age.
**If you get stuck, I posted the answer at the bottom of the blog.

Keith numbers are much rarer than the primes, with only 84 Keith numbers with digits.
Here is a Numberphile video explaining Keith numbers.

A hepteract is a seven-dimensional hypercube with 84 penteract 5-faces.

EVENTS
1539 Tartaglia tells Cardano about his method of solving cubic equations and Cardano signs an oath to keep the method secret, according to Tartaglia. *B L van der Waerden, History of Algebra
"Scipio Ferro of Bologna well-nigh thirty years ago discovered this rule and handed it on to Antonio Maria Fior of Venice, whose contest with Niccolo Tartaglia of Brescia gave Niccolo

occasion to discover it. He [Tartaglia] gave it to me in response to my entreaties, though withholding the demonstration. Armed with this assistance, I sought out its demonstration in [various] forms. This was very difficult." Cardano in Ars Magna (Basel, 1545)

1655 Christiaan Huygens was the first to discover a moon of Saturn, when he viewed Titan (the largest and easiest to see) on 25 Mar 1655. However, the moon wasn't named until almost two centuries later when Sir John Herschel, discoverer of Uranus, assigned names to the seven moons of Saturn that were known at that time. Saturn's largest moon was named simply "Titan," since the word means "one that is great in size, importance, or achievement." *TIS

1792 D’Alembert wrote: “I would like to see our friend Condorcet, who assuredly has great talent and wisdom, express himself in another manner.” Reading Condorcet’s mathematical works is a thankless task, for the notation is inconsistent, the expression of ideas often imprecise and obscure, and the proofs labored. Perhaps this helps explain why he is not a well known mathematician. [DSB 3, 384]*VFR

1822 Gauss reveals plans to contact aliens: Gauss wrote of the heliotrope's potential (an instrument invented by Gauss in 1821 that uses a mirror to reflect sunlight over great distances) as a celestial signaling device in a March 25, 1822 letter to Heinrich Olbers, by which he reveals a belief and interest in finding a method to contact extraterrestrial life: "With 100 separate mirrors, each of 16 square feet, used conjointly, one would be able to send good heliotrope-light to the moon.... This would be a discovery even greater than that of America, if we could get in touch with our neighbors on the moon."
Some have suggested Gauss may have also proposed the constructing an immense right triangle and three squares on the surface of the earth to signal to aliens from the Moon or Mars. See more on that story here.*Wik

In 1857, Frederick Laggenheim took the first photograph of a solar eclipse. This is often reported but seems not to be the first. I found a note on Wikipedia that "The first correctly-exposed photograph of the solar corona was made during the total phase of the solar eclipse of 28 July 1851 by a local daguerreotypist named Berkowski at the Royal Observatory in Königsberg, Prussia (now Kalinigrad in Russia). Berkowski, whose first name was never published, observed at the Royal Observatory. A small 6-cm refracting telescope was attached to the 15.8-cm Fraunhofer heliometer and a 84-second exposure was taken shortly after the beginning of totality. *Wik

In 1903, The Times newspaper reported that the French physicist, Pierre Curie assisted by Marie Curie, communicated to the Academy of Sciences that the recently discovered Radium “possesses the extraordinary property of continuously emitting heat, without combustion, without chemical change of any kind, and without any change to its molecular structure, which remains spectroscopically identical after many months of continuous emission of heat ... such that the pure Radium salt would melt more than its own weight of ice every hour ... A small tube containing Radium, if kept in contact with the skin for some hours ... produces an open sore, by destroying the epidermis and the true skin beneath ... and cause the death of living things whose nerve centres do not lie deep enough to be shielded from their influence.” *TIS

1992 Excel 4.0 Spreadsheet Software Released: Microsoft Corporation releases its Excel 4.0 spreadsheet program. Excel was one in a long line of practical applications that Microsoft and other companies developed for personal computers, making them more appealing to home and office users. The earliest commercial computerized spreadsheet was VisiCalc, written by Ed Frankston and Dan Bricklin and released for the Apple II personal computer in 1979.*CHM

BIRTHS
1538 Christopher Clavius (March 25, 1538 – February 6, 1612) was a German Jesuit mathematician and astronomer who was the main architect of the modern Gregorian calendar. In his last years he was probably the most respected astronomer in Europe and his textbooks were used for astronomical education for over fifty years in Europe and even in more remote lands (on account of being used by missionaries). As an astronomer Clavius held strictly to the geocentric model of the solar system, in which all the heavens rotate about the Earth. Though he opposed the heliocentric model of Copernicus, he recognized problems with the orthodox model. He was treated with great respect by Galileo, who visited him in 1611 and discussed the new observations being made with the telescope; Clavius had by that time accepted the new discoveries as genuine, though he retained doubts about the reality of the mountains on the Moon. Later, a large crater on the Moon was named in his honour.*Wik
Called the Euclid of the sixteenth-century, born in the German town of Bamberg, the see of the prince-bishop of Franconia. He was also the leader of the Gregorian calendar reform. Perhaps his greatest contribution was as an educational reformer.
In his Astrolabium (Rome,1593) he uses a dot to separate whole numbers from decimal fractions, but it would be 20 more years before the decimal point would be widely accepted. Carl Boyer mentions "the Jesuit friend of Kepler" who was the first to use the decimal point with a clear idea of its significance. In the same work, Clavius originated a way of dividing a scale for precise measurements. His idea was adopted by Vernier 42 years later.
In his Algebra (Rome, 1608) Clavius was the first to use parenthesis to express aggregation and the first to use a symbol for an unknown quantity. Other innovations were also seen in the symbols attributed to him by Florian Cajori such as the radical sign, plus and minus signs.

Clavius proposed a proof that there can be no more than three dimensions in geometry, based on the fact that only three concurrent lines can be drawn from a point so that they are mutually perpendicular. He discovered and proved a theorem for a regular polygon with an odd number of sides which two centuries later enabled Carl Friedrich Gauss to construct a 17-sided polygon by ruler and compass.
In hisTriangula sphaerica (Mainz 1611) Clavius summarized all contemporary knowledge of plane and spherical trigonometry. His prostlaphaeresis , the grandparent of logarithms, relied on the sine of the sum and differences of numbers. In this way he was able to substitute addition and subtraction for multiplication, by solving the identity with which we are familiar today: 2 sin x sin y = cos(x-y)-cos(x+y). D. E. Smith gives the details of the proof and emphasizes the impact Clavius' work had on the discovery of logarithms. Smith also underlines the modesty of Clavius in generously giving to one of his contemporaries more credit than is due for his own prostlaphaeresis . *Joseph MacDonnell, S.J., Fairfield Univ webpage
Some really nice detail about Clavius is at Renaissance Mathematicus

1798 Christoph Gudermann (March 25, 1798, September 25, 1852) was born in Vienenburg. He was the son of a school teacher and became a teacher himself after studying at the University of Göttingen, where his advisor was Karl Friedrich Gauss. He began his teaching career in Kleve and then transferred to a school in Münster.
He is most known today for being the teacher of Karl Weierstrass, who took Gudermann's course in elliptic functions, 1839–1840, the first to be taught in any institute. Weierstrass was greatly influenced by this course, which marked the direction of his own research.
Gudermann originated the concept of uniform convergence, in an 1838 paper on elliptic functions, but only observed it informally, neither formalizing it nor using it in his proofs. Instead, Weierstrass elaborated and applied uniform convergence.
His researches into spherical geometry and special functions focused on particular cases, so that he did not receive the credit given to those who published more general works. The Gudermannian function, or hyperbolic amplitude, is named after him.Gudermann died in Münster. *Wik

1833 (Henry Charles) Fleeming Jenkin (25 Mar 1833; 12 Jun 1885 at age 52) British engineer noted for his work in establishing units of electrical measurement. After earning an M.A. (1851), he worked for the next 10 years with engineering firms engaged in the design and manufacture of submarine telegraph cables and equipment for laying them. In 1861 his friend William Thomson (later Lord Kelvin) procured Jenkin's appointment as reporter for the Committee of Electrical Standards of the British Association for the Advancement of Science. He helped compile and publish reports that established the ohm as the absolute unit of electrical resistance and described methods for precise resistance measurements. *TIS

1859 Samuil Shatunovsky (25 March 1859 – 27 March 1929) was a Russian mathematician. focused on several topics in mathematical analysis and algebra, such as group theory, number theory and geometry. Independently from Hilbert, he developed a similar axiomatic theory and applied it in geometry, algebra, Galois theory and analysis. However, most of his activity was devoted to teaching at Odessa University and writing associated books and study materials.*Wik

1865 Pierre-Ernest Weiss (25 Mar 1865, 24 Oct 1940) French physicist who investigated magnetism and determined the Weiss magneton unit of magnetic moment. Weiss's chief work was on ferromagnetism. Hypothesizing a molecular magnetic field acting on individual atomic magnetic moments, he was able to construct mathematical descriptions of ferromagnetic behaviour, including an explanation of such magnetocaloric phenomena as the Curie point. His theory succeeded also in predicting a discontinuity in the specific heat of a ferromagnetic substance at the Curie point and suggested that spontaneous magnetization could occur in such materials; the latter phenomenon was later found to occur in very small regions known as Weiss domains. His major published work was Le magnetisme ( 1926).*TIS

1923 Kenneth Linn Franklin (25 Mar 1923, ) American astronomer who discovered that the giant planet Jupiter emits radio waves (1955). Dr. Bernard F. Burke and Franklin, astronomers at the Carnegie Institution in Washington, were scanning the sky for radio waves from galaxies. By chance, they found a radio signal that resembled short bursts of static, similar to interference by lightning on home radios. After weeks of study, finding the signals were periodic, four minutes earlier each day, they pin-pointed Jupiter as the source. Never before had radio sounds from a planet in our solar system been detected. Later it was discovered that the radio waves were circularly polarized, so a magnetic field was involved.*TIS

1939 Richard Alfred Tapia (March 25, 1939 - ) is a renowned American mathematician and champion of under-represented minorities in the sciences. In recognition of his broad contributions, in 2005, Tapia was named "University Professor" at Rice University in Houston, Texas, the University's highest academic title. The honor has been bestowed on only six professors in Rice's ninety-nine year history. On September 28, 2011, President Barack Obama announced that Tapia was among twelve scientists to be awarded the National Medal of Science, the top award the United States offers its researchers. Tapia is currently the Maxfield and Oshman Professor of Engineering; Associate Director of Graduate Studies, Office of Research and Graduate Studies; and Director of the Center for Excellence and Equity in Education at Rice University.
Tapia's mathematical research is focused on mathematical optimization and iterative methods for nonlinear problems. His current research is in the area of algorithms for constrained optimization and interior point methods for linear and nonlinear programming.*Wik

DEATHS
1818 Caspar Wessel (8 Jun 174525 Mar 1818 at age 72) was a Norwegian mathematician who invented a geometric way of representing complex numbers which pre-dated Argand. *SAU
His fundamental paper, Om directionens analytiske betegning, was published in 1799 by the Royal Danish Academy of Sciences and Letters. Since it was in Danish, it passed almost unnoticed, and the same results were later independently found by Argand and Gauss.
One of the more prominent ideas presented in "On the Analytical Representation of Direction" was that of vectors. Even though this wasn't Wessel's main intention with the publication, he felt that a geometrical concept of numbers, with length and direction, was needed. Wessel's approach on addition was: "Two straight lines are added if we unite them in such a way that the second line begins where the first one ends and then pass a straight line from the first to the last point of the united lines. This line is the sum of the united lines". This is the same idea as used today when summing vectors. Wessel's priority to the idea of a complex number as a point in the complex plane is today universally recognized. His paper was re-issued in French translation in 1899, and in English in 1999 as On the analytic representation of direction (ed. J. Lützen et al.).*Wik

1995 James S(amuel) Coleman (12 May 1926, 25 Mar 1995 at age 68) was a U.S. sociologist, a pioneer in mathematical sociology whose studies strongly influenced education policy. In the early 1950s, he was as a chemical engineer with Eastman-Kodak Co. in Rochester, N.Y. He then changed direction, fascinated with sociology and social problems. In 1966, he presented a report to the U.S. Congress which concluded that poor black children did better academically in integrated, middle-class schools. His findings provided the sociological underpinnings for widespread busing of students to achieve racial balance in schools. In 1975, Coleman rescinded his support of busing, concluding that it had encouraged the deterioration of public schools by encouraging white flight to avoid integration. (We can never control the law of unintended consequences)*TIS

* Diophantus died at 84, why else would I have it on the 84th day of the year?

Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell

## Friday, 24 March 2017

### On This day in Math - March 24

 Harrison H1

But mathematics is the sister, as well as the servant, of the arts and is touched by the same madness and genius.
~Marston Morse

The 83rd day of the year; 83 is the smallest prime number which is the sum of a prime number of consecutive prime numbers in a prime number of different ways, i.e., 23 + 29 + 31 = 11 + 13 + 17 + 19 + 23. *Prime Curios (Whew! say that three times in a hurry)

The smallest prime with a digit sum of 83 is 3999998999.
83 is the smallest prime whose square, 6889, is a strobogrammatic number. (you can rotate it 180 degrees and it reads the same)

83 is The number of permutations of the 10 distinct digits taken 9 at a time that are perfect squares. These range from 101242 = 102495376 to 303842 = 923187456.*Prime Curios

EVENTS
1789 Throughout his life, Jefferson was avid to keep up with the mathematical world, and to spread knowledge about it to others. How deeply he explored mathematics depended obviously on what else was happening in his life at the time, but he was always keen to pass on what he had learned to his correspondents. Staying in Paris in 1789 he was eager to pass on information about the latest work by Lagrange In a letter to Harvard President Joseph Willard on March 24, 1789 he writes, "A very remarkeable work is the 'Mechanique Analytique' of La Grange in 4to. He is allowed to be the greatest mathematician now living, and his personal worth is equal to his science. The object of his work is to reduce all the principles of Mechanics to the single one of the Equilibrium, and to give a simple formula applicable to them all. The subject is treated in the Algebraic method, without diagrams to assist the conception. My present occupation not permitting me to read any thing which requires a long and undisturbed attention, I am not able to give you the character of this work from my own examination. It has been received with great approbation in Europe." *John Fauval, Lecture at Univ of Va.
Good book about Jefferson's Scientific interests and contributons:

1899 Ren´e Louis Baire defended his doctoral thesis on the theory of functions of a real variable. He was inﬂuential in introducing transﬁnite set theory into analysis. *VFR

1930 Planet X  was officially named Pluto on March 24, 1930:  On the nights of Jan 23 and 30th of January, 1930, Tombaugh found a planet in the images that he thought was the Planet X. "The discovery made front page news around the world. The Lowell Observatory, who had the right to name the new object, received over 1000 suggestions, from "Atlas" to "Zymal". Tombaugh urged Slipher to suggest a name for the new object quickly before someone else did. Name suggestions poured in from all over the world. Constance Lowell proposed Zeus, then Lowell, and finally her own first name. These suggestions were disregarded.
The name "Pluto" was proposed by Venetia Burney (later Venetia Phair), an eleven-year-old schoolgirl in Oxford, England. Venetia was interested in classical mythology as well as astronomy, and considered the name, one of the alternate names of Hades, the Greek god of the Underworld, appropriate for such a presumably dark and cold world. She suggested it in a conversation with her grandfather Falconer Madan, a former librarian of Oxford University's Bodleian Library. Madan passed the name to Professor Herbert Hall Turner, who then cabled it to colleagues in America. *Wik

1959 TI Demonstrates Integrated Circuit Invented by Jack Kilby:
Texas Instruments demonstrates the first integrated circuit. Its inventor, Jack Kilby (b. Nov 8, 1923), created the device to prove that resistors and capacitors could exist on the same piece of semiconductor material. His circuit consisted of a sliver of germanium with five components linked by wires. It was Fairchild's Robert Noyce, however, who filed for a patent within months of Kilby and who made the IC a commercially-viable technology. Both men are credited as co-inventors of the IC.*CHM

BIRTHS

1693 John Harrison (24 Mar 1693; 24 Mar 1776 at age 83)
English horologist who invented the first practical marine chronometer, which enabled navigators to compute accurately their longitude at sea. He was prompted to begin this work after a huge reward was offered by the British government for new navigational tools to avoid further disasters at sea. John Harrison took on the scientific and academic establishment of his time and won the longitude prize through extraordinary mechanical insight, talent and determination. *TIS [The Dictionary of Scientific Biographies  shows an uncertainty in the date of birth as 24 Mar(?) 1693.] See deaths below for notes on a popular biography.

1809 Joseph Liouville   (24 Mar 1809, 8 Sep 1882) French mathematician who discovered transcendental numbers (those which are not the roots of algebraic equations having rational coefficients), and that there are infinitely many of them. He also did work in real and complex analysis, number theory, and differential geometry. His name is remembered in the Sturm-Liouville theory of differential equations that generalizes Joseph Fourier's ideas, and are important in mathematical physics. He studied celestial mechanics. Liouville founded in 1836, and edited for nearly four decades, the Journal de Mathématique which remains a leading French mathematical publication. He edited and published (1843) the manuscripts left behind upon the untimely death of Evariste Galois 22 years earlier.*TIS Liouville was one of Lord Kelvin's mathematical heroes, and he once stopped a lecture in Glascow to ask his students, "Do you know what a mathematician is?" He then wrote on the blackboard the equation

and, pointing to the board stated, A mathematician is one to whom that  is as obvious as twice two are four is to you.  Liouville was a  mathematician." *Walter Gratzer, Eurekas and Euphorias, pg 21

1835 Josef Stefan (24 Mar 1835, 7 Jan 1893) Austrian physicist who proposed a law of radiation (1879) stating that the amount of energy radiated per second from a black body is proportional to the fourth power of its absolute temperature. (A black body is a theoretical object that absorbs all radiation that falls on it.) This law is known as Stefan's law or the Stefan-Bolzmann law. He also studied electricity, the kinetic theory of gases and hydrodynamics.*TIS

1848 Jules Tannery (March 24, 1848 – December 11, 1910) was a French mathematician who notably studied under Charles Hermite and was the PhD advisor of Jacques Hadamard.
He discovered a surface of the fourth order of which all the geodesic lines are algebraic. He was not an inventor, however, but essentially a critic and methodologist. He once remarked, "Mathematicians are so used to their symbols and have so much fun playing with them, that it is sometimes necessary to take their toys away from them in order to oblige them to think."
He notably influenced Paul Painlevé, Jules Drach, and Émile Borel to take up science.
His efforts were mainly directed to the study of the mathematical foundations and of the philosophical ideas implied in mathematical thinking.*Wik

1892 Harold Calvin Marston Morse (24 March 1892 in Waterville, Maine, USA - 22 June 1977 in Princeton, New Jersey, USA) developed variational theory in the large with applications to equilibrium problems in mathematical physics, a theory which is now called Morse theory and forms a vital role in global analysis*SAU

1893 Walter Baade (24 Mar 1893; 25 Jun 1960 at age 67) German-American astronomer who, with Fritz Zwicky, proposed that supernovae could produce cosmic rays and neutron stars (1934), and Baade made extensive studies of the Crab Nebula and its central star. During WW II blackouts of the Los Angeles area Baade used the 100-inch Hooker telescope to resolve stars in the central region of the Andromeda Galaxy for the first time. This led to his definition of two stellar populations, to the realization that there were two kinds of Cepheid variable stars, and from there to a doubling of the assumed scale of the universe. Baade and Rudolph Minkowski identified and took spectrograms of optical counterparts of many of the first-discovered radio sources, including Cygnus A and Cassiopeia A. *TIS

1941 Joseph H. Taylor Jr. (24 Mar 1941,   )American radio astronomer and physicist who, with Russell A. Hulse, was the corecipient of the 1993 Nobel Prize for Physics for their joint discovery of the first binary pulsar (1974). This unique phenomenon, two stars orbiting each other - one of them giving off regular radio-frequency "beeps" - has been important as a deep space proving ground for Einstein's general theory of relativity. Their research group at Princeton used the 1,000 foot radio telescope at Arecibo, Puerto Rico, the largest and most sensitive in the world for catching radio waves from space. *TIS

1948 Alice Chang (24 March 1948 in Ci-an, China)is a Chinese American mathematician specializing in aspects of mathematical analysis ranging from harmonic analysis and partial differential equations to differential geometry. She is a professor of mathematics and chair of the department at Princeton University.*Wik Her husband Paul Yang works on a.o. differential geometry -currently Princeton U. (HT to C L O ‏@cldm_ish)

DEATHS
1776 John Harrison (24 Mar 1693; 24 Mar 1776 at age 83)
English horologist who invented the first practical marine chronometer, which enabled navigators to compute accurately their longitude at sea. He was prompted to begin this work after a huge reward was offered by the British government for new navigational tools to avoid further disasters at sea. John Harrison took on the scientific and academic establishment of his time and won the longitude prize through extraordinary mechanical insight, talent and determination. *TIS
Dava Sobel's book, below, is a fun read, but it is important to point out that historians of science often find it less than satisfactory.  Here is one clip from Rebekah Higgitt, an excellent young science historian at the Univ of Kent and former Curator of History of Science and Technology at the National Maritime Museum and the Royal Observatory, Greenwich. "Sobel’s book is well-done but greatly simplified journalistic history, in which she unashamedly creates a story by identifying heroes and villains, and by making astronomy and timekeeping rival rather than complementary methods for finding longitude. It has annoyed professional historians of science because it plays to some of the ‘sins’ of our field, typified by the notion of the “lone genius”, and causes angst because our preferred version of history is always richer and more complex," In a personal note she wrote, [The book] "Unfairly & inaccurately creates a villain (Maskleyne) as a foil."

1956 Christine Mary Hamill (July 24, 1923 – March 24, 1956) was an English mathematician who specialized in group theory and finite geometry. After receiving her Ph.D. at the University of Cambridge in 1951, she was appointed to a lectureship in the University of Sheffield and later was appointed lecturer in the University College, Ibadan, Nigeria.*Wik

1956 Sir Edmund Taylor Whittaker (24 Oct 1873; March 24 1956) English mathematician who made pioneering contributions to the area of the special functions, which is of particular interest in mathematical physics. Whittaker is best known work is in analysis, in particular numerical analysis, but he also worked on celestial mechanics and the history of applied mathematics and physics. He wrote papers on algebraic functions and automorphic functions. His results in partial differential equations (described as most sensational by Watson) included a general solution of the Laplace equation in three dimensions in a particular form and the solution of the wave equation. On the applied side of mathematics he was interested in relativity theory and he also worked on electromagnetic theory. *TIS

1962 Auguste Antoine Piccard (28 January 1884 – 24 March 1962) was a Swiss physicist, inventor and explorer. Piccard and his twin brother Jean Felix were born in Basel, Switzerland. Showing an intense interest in science as a child, he attended the Swiss Federal Institute of Technology (ETH) in Zurich, and became a professor of physics in Brussels at the Free University of Brussels in 1922, the same year his son Jacques Piccard was born. He was a member of the Solvay Congress of 1922, 1924, 1927, 1930 and 1933.
In 1930, an interest in ballooning, and a curiosity about the upper atmosphere led him to design a spherical, pressurized aluminum gondola that would allow ascent to great altitude without requiring a pressure suit. Supported by the Belgian Fonds National de la Recherche Scientifique (FNRS) Piccard constructed his gondola.
An important motivation for his research in the upper atmosphere were measurements of cosmic radiation, which were supposed to give experimental evidence for the theories of Albert Einstein, whom Piccard knew from the Solvay conferences and who was a fellow alumnus of ETH.
On May 27, 1931, Auguste Piccard and Paul Kipfer took off from Augsburg, Germany, and reached a record altitude of 15,781 m (51,775 ft). (FAI Record File Number 10634) During this flight, Piccard was able to gather substantial data on the upper atmosphere, as well as measure cosmic rays. On 18 August 1932, launched from Dübendorf, Switzerland, Piccard and Max Cosyns made a second record-breaking ascent to 16,201 m (53,153 ft). (FAI Record File Number 6590) He ultimately made a total of twenty-seven balloon flights, setting a final record of 23,000 m (75,459 ft).
In the mid-1930s, Piccard's interests shifted when he realized that a modification of his high altitude balloon cockpit would allow descent into the deep ocean. By 1937, he had designed the bathyscaphe, a small steel gondola built to withstand great external pressure. Construction began, but was interrupted by the outbreak of World War II. Resuming work in 1945, he completed the bubble-shaped cockpit that maintained normal air pressure for a person inside the capsule even as the water pressure outside increased to over 46 MPa (6,700 psi). Above the heavy steel capsule, a large flotation tank was attached and filled with a low density liquid for buoyancy. Liquids are relatively incompressible and can provide buoyancy that does not change as the pressure increases. And so, the huge tank was filled with gasoline, not as a fuel, but as flotation. To make the now floating craft sink, tons of iron were attached to the float with a release mechanism to allow resurfacing. This craft was named FNRS-2 and made a number of unmanned dives in 1948 before being given to the French Navy in 1950. There, it was redesigned, and in 1954, it took a man safely down 4,176 m (13,701 ft).
Piccard was the inspiration for Professor Cuthbert Calculus in The Adventures of Tintin by Belgian cartoonist Hergé. Piccard held a teaching appointment in Brussels where Hergé spotted his unmistakable figure in the street.
Gene Roddenberry named Captain Jean-Luc Picard in Star Trek after one or both of the twin brothers Auguste and Jean Felix Piccard, and derived Jean-Luc Picard from their names. *Wik

1995 (Noël) Joseph (Terence Montgomery) Needham (9 Dec 1900, 24 Mar 1995 at age 94)was an English biochemist, embryologist, and historian of science who wrote and edited the landmark history Science and Civilization in China, a remarkable multivolume study of nearly every branch of Chinese medicine, science, and technology over some 25 centuries. As head of the British Scientific Mission in China (1942-46) he worked to assure adequate liaison between Chinese scientists and technologists and their colleagues in the West. As an historian of science and technology he wanted to break through the parochial, Europe-centred views of most of his colleagues by disclosing the achievements of traditional China and the contributions made by China leading up to the scientific revolution. *TIS

1976 Francis Dominic Murnaghan (4 Aug 1893 in Omagh, Co. Tyrone, Ireland- 24 March 1976 in Baltimore, Maryland, USA) was an Irish mathematician, former head of the mathematics department at Johns Hopkins University. His name is attached to developments in group theory and mathematics applied to continuum mechanics (Murnaghan and Birch–Murnaghan equations of state).*SAU

Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell

## Thursday, 23 March 2017

### On This Day in Math - March 23

 Interior of Iranian Mosque *Cliff Pickover@pickover

Science does not have a moral dimension. It is like a knife. If you give it to a surgeon or a murderer, each will use it differently.
~Wernher von Braun

The 82nd day of the year; 82 is the sum of the 10th(8+2) prime and the 16th(8x2) prime. It is the smallest number with this property.  Can you find the next?

82 is a happy number. Take the sum of the square of the digits, repeat on the result, and you eventually arrive at 1.

82 is the number of different ways you can arrange 6 regular hexagons by joining their adjacent sides:

82 can be written as :
The sum of Fibonacci numbers, 82 = 1 + 5 + 21 + 55
The sum of consecutive integers, 82= 19 + 20 + 21 + 22

EVENTS
4BC A lunar eclipse may have coincided with the death of one of the most notorious kings of all time. Historian Flavius Josephus notes that an eclipse of the Moon preceded the death of the biblical king Herod. Three eclipses fit the bill as occurring in the right time frame and being visible from the Middle East, but the favorite contender is the March 23, 4 B.C. rising total lunar eclipse that may have marked the demise of Herod.*12 Famous Eclipses in History

In 1840, Englishman J.W. Draper took the first successful photo of the full Moon. He made a daguerreotype, a precursor of the modern photograph.*TIS The photo from this night was destroyed in a fire in a New York University. The one at right is one he took three days later, and displayed at the New York Lyceum on April 13, 1840.
Daguerre himself is believed to be the first person to take a photograph of the moon, using his daguerreotype process, on January 2, 1839. Unfortunately, in March of that same year, his entire laboratory burnt to the ground, destroying all his written records and much of his early experimental work–and that historical image of the moon. *lightsinthedark *APS.org
Appropriately, it was an astronomer who coined the term photography in 1839, when Johann Heinrich von Madler combined “photo” (from the Greek word for “light”) and “graphy” (“to write”).

1857 The Otis Elevator Company completes the first commercial passenger elevator installation at a five-story department store, the E. V . Haughwout Company at Broadway and Broome Street in what is now New York City’s SoHo district. After very slow sales the company's first few years, Otis decided to make a dramatic demonstration at the New York Crystal Palace, a grand exhibition hall built for the 1853 Worlds Fair.
Perched on a hoisting platform high above the crowd at New York’s Crystal Palace, a pragmatic mechanic (Otis himself, it seems) shocked the crowd when he dramatically cut the only rope suspending the platform on which he was standing. The platform dropped a few inches, but then came to a stop. His revolutionary new safety brake had worked, stopping the platform from crashing to the ground. “All safe, gentlemen!” the man proclaimed.
Otis’ demonstration had the desired effect. He sold seven elevators that year, and 15 the next. *Wired, HT Rick Brutti@Rbrutti

1881 J J Sylvester writes to Arthur Cayley to announce, "I believe that I have proved Gordan's Theorem, and can assign a superior limit to the number of fundamental invariants." His proof was founded on the prospect that a certain sequence increased without bound. By October he knew that it did not.

1920 When Professor Johann Palisan of the University of Vienna discovered an asteroid on this date, he chose to name it after Herbert Hoover, who would later become the President of the USA. As head of the American Relief Administration, after WWI, Hoover organized shipments of food for millions of starving people in Central Europe. In Finnish it is common to use the word “hoover” with the meaning, “to help”. (at least it was, can someone tell me if this is still so) It seems strange that today most history books in his home country preserve his name in the term “Hooverville’s” for hobo camps and shanty towns where displaced peoples lived during the American Great Depression. *Wik

In 1950, the U.N. World Meteorological Organization was established. *TIS The World Meteorological Organization (WMO) is a specialized agency of the United Nations. It is the UN system's authoritative voice on the state and behaviour of the Earth's atmosphere, its interaction with the oceans, the climate it produces and the resulting distribution of water resources. *WMO webpage

1981 The March 23 issue carried the first mention of Rubik's Cube in Time Magazine. *Mark Longridge, A Rubik's Cube Chronology
Rubik had begun distribution in Hungary in 1977, and by early 1979 Mathematical Intelligencer carried an introduction in of "The Hungarian Magic Cube" by David Singmaster with the note, "A new mathematical toy has been slowly becoming available in western Europe and is becoming more popular than the Soma Cube, Instant Insanity, and may well surpass the popularity of Mastermind or Sam Loyd's Fifteen puzzle."

In 1989, fusion at room temperature was claimed by Martin Fleischmann and Stan Pons, two Utah electrochemists. They believed they had sustained a controlled nuclear fusion reaction in a bench-top fusion percolator made up of two electrodes with heavy water which generated up to 100 per cent more energy than they put in. There were sporadic sightings of excess heat, which Fleischmann said cannot be accounted for by chemistry alone. However, the idea of cold fusion was discredited because leading scientists were unable to replicate the work and found no hallmarks of nuclear processes, especially none of the subatomic particles called neutrons. Their tantalizing promise of a limitless supply of cheap energy were invalid.*TIS

2012 Sonia Kovalevsky Day.. "Her birthday is January 15, but today gets to be her day. Cathy O'Neil (aka Mathbabe) started Sonia Kovalevsky Day at Barnard College in 2006, and it sounds like it's been going strong ever since." *Sue VanHattum at MathMama Writes blog.

BIRTHS
1709 Hans Ulrich Grubenmann (23 Mar 1709; 24 Jan 1783 at age 73)  Swiss carpenter, who with his brother Johannes, built a bridge (1758) over the Limmat River at the town of Wettingen, near Zürich, that is believed to be the first timber bridge to employ a true arch in its design. The brothers' ingenious combination of the arch and truss principles made it possible to construct bridges longer and better than ever before. They constructed churches as well as other bridges. *TIS

1754 (Jurij)Georg Freiherr von Vega (23 Mar 1754 in Zagorica, Ljubljana, Slovenia - 26 Sept 1802 in Vienna, Austria) wrote about artillery but he is best remembered for his tables of logarithms and trigonometric functions. Vega calculated π to 140 places, a record which stood for over 50 years. This appears in a paper which he published in 1789.
In September 1802 Vega was reported missing. A search was unsuccessful until his body was found in the Danube near Vienna. The official cause of death was an accident but many suspect that he was murdered. *SAU

1795 Bernt Michael Holmboe (23 March 1795 – 28 March 1850) was a Norwegian mathematician. Holmboe was hired as a mathematics teacher at the Christiania Cathedral School in 1818, where he met the future renowned mathematician Niels Henrik Abel. Holmboe's lasting impact on mathematics worldwide has been said to be his tutoring of Abel, both in school and privately. The two became friends and remained so until Abel's early death. Holmboe moved to the Royal Frederick University in 1826, where he worked until his own death in 1850.
Holmboe's significant impact on mathematics in the fledgling Norway was his textbook in two volumes for secondary schools. It was widely used, but faced competition from Christopher Hansteen's alternative offering, sparking what may have been Norway's first debate about school textbooks. *Wik

1827 Pierre Simon, Marquis de Laplace (23 Mar 1749, 5 Mar 1827 at age 78) was a French mathematician, physicist, statistician and astronomer known for his mathematical analysis of the stability of the solar system (1773), alleviating Isaac Newton's concerns about perturbations between planets. He took an exact approach to science. He developed an explanation of surface tension of a liquid in terms of inter-molecular attractions, investigated capillary action and the speed of sound. He assisted Antoine Lavoisier (1783) investigating specific heat and heats of combustion, initiating the science of thermochemistry. He believed the solar system formed from a collapsing nebula. He contributed to the mathematics of probability and calculus, in which a differential equation is known by his name, and was involved in establishing the metric system.*TIS His last words were, “What we know is very slight; what we don’t know is immense.” *Eves, Mathematical Circles Revisited, 319◦

1829 Norman Robert Pogson (23 Mar 1829; 23 Jun 1891 at age 62) English astronomer who devised the magnitude scale of the brightness of stars (1850) now in use. He divided the classical scale in which a first magnitude star is one hundred times brighter than a sixth magnitude star using five integer steps. Each step represents a fifth-root of 100 (about 2.512) increase in brightness. The Sun's magnitude on this scale is -26.91, whereby negative numbers denote objects brighter than first magnitude. Sirius is magnitude -1.58, Aldebaran is 1 and the faintest star detected is 30. His interest in astronomy began in his youth; by age 18 he had calculated orbits for two comets. He discovered 8 asteroids, 21 new variable stars and compiled a massive star catalogue. In 1860 he moved to India for the remainder of his life's work.*TIS

1837 Richard Anthony Proctor (23 Mar 1837, 12 Sep 1888) English astronomer who first suggested (1873) that meteor impacts caused lunar craters, rather than volcanic action. He studied the motion of stars, their distribution, and their relation to the nebulae. In 1867 he prepared a map of the surface of Mars on which he named continents, seas, bays and straits (in the same manner that Riccioli used on his map of the moon). However, he did not perceive "canals" on the surface, which later Schiaparelli identified. Proctor participated in expeditions of 1874 and 1882 to observe the transit of Venus. He was very successful popularizing astronomy by his writings in books, periodicals, and lectures he gave as far abroad as Australia and America (where he stayed after 1881).*TIS

1855 Franklin H(enry) Giddings (23 Mar 1855; 11 Jun 1931 at age 76) American sociologist, one of the first in the United States to turn sociology from a branch of philosophy into a research science dependent on statistics. He was noted for his doctrine of the "consciousness of kind," which he derived from Adam Smith's conception of "sympathy," or shared moral reactions. His explanation of social phenomena was based this doctrine - his theory that each person has an innate sense of belonging to particular social groups. He encouraged statistical studies in sociology. *TIS

1862 Eduard Study (23 March 1862 in Coburg, Germany - 6 Jan 1930 in Bonn, Germany)Study became a leader in the geometry of complex numbers. He reformulated, independently of Severi, the fundamental principles of enumerative geometry due to Schubert. He also worked on invariant theory helping to develop a symbolic notation. In 1923 he published important work on real and complex algebras of low dimension publishing these results. Study's contribution is summarized by W Burau as follows, "... Study demonstrated what he considered to be a thorough treatment of a problem. ... With Corrado Segre, Study was one of the leading pioneers in the geometry of complex numbers. ... Adept in the methods of invariant theory ... Study, employing the identities of the theory, sought to demonstrate that geometric theorems are independent of coordinates. ... Study was the first to investigate systematically all algebras possessing up to four generators over R and C. "
Other areas which Study worked on were straight lines in elliptic space, with his student at Bonn J L Coolidge, and he simplified the method of differential operators. In 1903 he published Geometrie der Dynamen which considered euclidean kinematics and the mechanics of rigid bodies. *SAU

1882 Amalie Emmy Noether (23 Mar 1882; 14 Apr 1935 at age 53) German mathematician best known for her contributions to abstract algebra, in particular, her study of chain conditions on ideals of rings. In theoretical physics, she produced Noether's Theorem, which proves a relationship between symmetries in physics and conservation principles. This basic result in the general theory of relativity was praised by Einstein. It was her work in the theory of invariants which led to formulations for several concepts of Einstein's general theory of relativity. For her obituary in The New York Times, Albert Einstein wrote: “Fraulein Noether was the most significant mathematical genius thus far produced since the higher education of women began. *TIS Someone once described her as the daughter of the mathematician Max Noether. To this Edumund Landau replied “Max Noether was the father of Emmy Noether. Emmy is the origin of coordinates in the Noether family.” *H. Eves, Introduction to the History of Mathematics
Emmy Noether’s house in Erlangen is in a blog at The Renaissance Mathematicus

1897 John Lighton Synge (March 23, 1897–March 30, 1995) was an Irish mathematician and physicist. Synge made outstanding contributions to different fields of work including classical mechanics, general mechanics and geometrical optics, gas dynamics, hydrodynamics, elasticity, electrical networks, mathematical methods, differential geometry, and Einstein's theory of relativity. He studied an extensive range of mathematical physics problems, but his best known work revolved around using geometrical methods in general relativity.
He was one of the first physicists to seriously study the interior of a black hole, and is sometimes credited with anticipating the discovery of the structure of the Schwarzschild vacuum (a black hole).
He also created the game of Vish in which players compete to find circularity (vicious circles) in dictionary definitions. *Wik

1907 Hassler Whitney (March 23, 1907 – May 10, 1989) was an American mathematician. He was one of the founders of singularity theory, and did foundational work in manifolds, embeddings, immersions, and characteristic classes. *SAU

1912 Wernher Magnus Maximilian von Braun (23 Mar 1912; 16 Jun 1977 at age 65) was a German-American rocket engineer who was one of the most important developers of rockets and their evolution to applications in space exploration. His interest began as a teenager in Germany, and during WW II he led the development of the deadly V–2 ballistic missile for the Nazis (which role remains controversial). After war, he was taken to use his knowledge to produce rockets for the U.S. Army. In 1960, he transferred to the newly formed NASA and became director of Marshall Space Flight Center and chief architect of the Saturn V launch vehicle used to put men on the moon. His contributions include the Explorer satellites; Jupiter, Pershing, Redstone and Saturn rockets, and Skylab. *TIS "My experiences with science led me to God. They challenge science to prove the existence of God. But must we really light a candle to see the sun? "

1928 Computer Pioneer Jean Sammet Is Born :
Jean Sammet, an early pioneer of computing, is born in New York. Sammet attended Mount Holyoke College and the University of Illinois, where she launched a teaching career. Trained in math, she moved into industry in 1961, developing the language FORMAC at IBM. The language was the first commonly used language for manipulating non-numeric algebraic expressions. She also wrote one of the classic histories of programming languages in her book, "Programming Languages: History and Fundamentals." *CHM

DEATHS
1924 Thomas Corwin Mendenhall (4 Oct 1841, 23 Mar 1924 at age 82) American physicist and meteorologist who was the first to propose the use of a ring pendulum for measuring absolute gravity. From 1889 to 1894 he served both as Director of the U.S. Coast and Geodetic Survey and also Superintendent of the U.S. Standard Weights and Measures where he oversaw the shift in the fundamental standards of the U.S. from the English yard and pound to the international meter and kilogram. Mendenhall devised a quarter second's pendulum for gravity measurements and instituted improvements in the measurement of base lines with wire tapes, in the construction of instruments for precise leveling and in the methods used in triangulation and gravity work, and developed a comprehensive plan for the study of terrestrial magnetism. *TIS

1945 Sir (William) Napier Shaw (4 Mar 1854; 23 Mar 1945 at age 90) was an English meteorologist who applied his training in mathematics. He studied the upper atmosphere, using instruments carried by kites and high-altitude balloons. He measured (1906) the movement of air in two anti-cyclones, finding descent rates of 350 and 450 metres per day. He calculated the reduction in pressure due to a certain depression to correspond to the removal of two million million tons of air. He introduced the millibar unit for measurement of air pressure (1000 millibar = 1 bar = 1 standard atmosphere) and the tephigram to illustrate the temperature of a vertical profile of the atmosphere. He also co-authored an early work on atmospheric polluiton, The Smoke Problem of Great Cities (1925).*TIS

1946 Gilbert Newton Lewis (23 Oct 1875, 23 Mar 1946 at age 70) American chemist who collaborated with Irving Langmuir in developing an atomic theory. He developed a theory of valency, which introduced the covalent bond (c. 1916), whereby a chemical combination is made between two atoms by the sharing of a pair of electrons, one contributed from each atom. This was part of his more general octet theory, published in Valence and the Structure of Atoms and Molecules (1923). Lewis visualized the electrons in an atom as being arranged in concentric cubes. The sharing of these electrons he illustrated in the Lewis dot diagrams familiar to chemistry students. He generalized the concept of acids and bases now known as Lewis acids and Lewis bases. *TIS

Max Mason (26 Oct 1877; 23 Mar 1961) American mathematical physicist, educator, and science administrator. During World War I he invented several devices for submarine detection - several generations of the Navy's "M," or multiple-tube, passive submarine sensors. This apparatus focused sound to ascertain its source. To determine the direction from which the sound came, the operator needed only to seek the maximum output on his earphones by turning a dial. The final device had a range of 3 miles. Mason's special interest and contributions lay in mathematics (differential equations, calculus of variations), physics (electromagnetic theory), invention (acoustical compensators, submarine-detection devices), and the administration of universities and foundations. *TIS

1963 Thoralf Skolem,(23 May 1887 in Sandsvaer, Buskerud, Norway - 23 March 1963 in Oslo, Norway) number theorist and logician. At the International Congress of Mathematicians in Cambridge in 1950 he said “We ought not to regard all that is written in the traditional textbooks as something sacred.” It was this attitude that earlier allowed him to discover that the real numbers could have countable models, a fact known as Skolem’s paradox. *Wik This Norwegian logician was the ﬁrst to introduce non-standard models of the natural numbers. *VFR

1979 Ivo Lah (AKA Ivan Lah; September 5, 1896 Štrukljeva vas near Cerknica, Austria-Hungary, now Slovenia,– March 23, 1979, Ljubljana, SFR Yugoslavia, now Slovenia) was a Slovenian mathematician and actuary, best known for his discovery of the Lah numbers in 1955. His scientific bibliography contains about 120 items covering a wide spectrum of topics from Mathematics to Statistics, Demographics, etc. For instance one can find 10 items in Maths Reviews, and 19 items in Zentralblatt für Mathematik. His most important mathematical result, published in 1955, is the so-called "Lah identity" where he shows how the rising powers can be expressed in terms of falling powers. The reviewer of his paper was a leading combinatorialist of that time, John Riordan. *Wik Unsigned Lah numbers have an interesting meaning in combinatorics: they count the number of ways a set of n elements can be partitioned into k nonempty linearly ordered subsets. Lah numbers are related to Stirling numbers.*Wik

1981 Beatrice Muriel Hill Tinsley (27 January 1941 – 23 March 1981) was a British-born New Zealand astronomer and cosmologist whose research made fundamental contributions to the astronomical understanding of how galaxies evolve, grow and die.
Tinsley completed pioneering theoretical studies of how populations of stars age and affect the observable qualities of galaxies. She also collaborated on basic research into models investigating whether the universe is closed or open. Her galaxy models led to the first approximation of what protogalaxies should look like.
In 1974 she received the American Astronomical Society's Annie J. Cannon Award in Astronomy, awarded for "outstanding research and promise for future research by a postdoctoral woman researcher", in recognition of her work on galaxy evolution.
In 1977, Tinsley, with Richard Larson of Yale, organized a conference on 'The Evolution of Galaxies and Stellar Populations'.
Shortly after, in 1978, she became the first female professor of astronomy at Yale University. Her last scientific paper, submitted to the Astrophysical Journal ten days before her death, was published posthumously that November, without revision. *Wik

2007 Paul Joseph Cohen (2 April 1934 in Long Branch, New Jersey, USA- 23 March 2007 in Palo Alto, California, USA) Cohen used a technique called forcing to prove the independence in set theory of the axiom of choice and of the generalized continuum hypothesis. *SAU

Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell