## Monday, 21 May 2018

### On This Day in Math - May 21

Whoever ... proves his point
and demonstrates the prime truth geometrically
should be believed by all the world,
for there we are captured
~Albrecht Durer

The 141st day of the year; 141 is the first non-trivial palindrome appearing in the decimal expansion of Pi, appearing immediately after the decimal point, 3.14159. Tanya Khovanova, Number Gossip

141 is the second n to give a prime Cullen number (of the form n*2n + 1). Cullen numbers were first studied by Fr. James Cullen in 1905. (That prime is 393050634124102232869567034555427371542904833,

141 is the number of lattice paths from (0,0) to (6,6) using steps (2,0), (0,2), (1,1).

EVENTS

1728 The term "mathematical expectation, "l'espérance mathématique," with its modern meaning is found in a letter by Gabriel Cramer to Nicholas Bernoulli.
The first use in English seems to be in A. de Morgan's Essay on Probabilities (1838, p. 97), "The balance is the average required, and is known by the name of the mathematical expectation." (OED). *Jeff Miller, Earliest Known Uses of Some of the Words of Mathematics

1819 the first bicycle in the U.S. was seen in New York City. Such bicycle velocipedes or "swift walkers" had been imported that same year. Shortly thereafter, on 19 Aug 1819, the city's Common Council passed a law to "prevent the use of velocipedes in the public places and on the sidewalks of the city of New York."**TIS (Skateborders take note, you are not the first to be banned from the sidewalks)

1908 Glenn (Hammond) Curtiss was a pioneer in the development of U.S. aviation whose aircraft were widely used during World War I. That the Wrights made the first powered flights has generally been accepted, but the achievements of Curtiss spanned several decades and took the airplane from its wood, fabric and wire beginnings to the forerunners of modern transport aircraft. Curtiss made his first flight on his 30th birthday, 21 May 1908, in White Wing, a design of the Aerial Experiment Association, a group led by Alexander Graham Bell. White Wing was the first plane in America to be controlled by ailerons instead of the wing-warping used by the Wrights. It was also the first plane on wheels in the U.S. *TIS (See 1878 Birth below)

1901 the first U.S. State motor car legislation was an act to regulate the speed of motor vehicle, passed in Connecticut. A limit was established of 12 mph within city limits and 15 mph outside, which were higher than the 8 mph city and 12mph country speeds in the bill as originally presented. Also, the car driver was required to reduce speed upon meeting or passing a horse-drawn vehicle, and if necessary, to stop to avoid frightening the horse.*TIS

This last part about meeting (or passing) a horse, with or without cart, is still essentially the law in England and Ireland.

1916 Daylight Saving Time was introduced in Britain as a war-time measure to save fuel. The idea began when a London builder, William Willett, presented a scheme of shifting the clock to better use the hours of daylight in summer. He campaigned and published a brochure on the subject in 1907 (in which his proposal was to adjust the clocks in four weekly adjustments of 10-mins). When Parliament did consider a Daylight Saving Bill, to implement a seasonal one-hour change, it failed for lack of support. However, a little more than a year after his death after his death, the idea was finally adopted during WW I for wartime fuel savings. Now most of the countries in the northern hemisphere use a form of daylight saving time. *TIS

1932 Amelia Earhart ﬂew alone across the Atlantic, being the ﬁrst woman to do so. *VFR

1952 IBM Announces Model 701, "Defense Calculator.":
IBM announced its 701 machine and by doing so emphasized its commitment to innovation in electronic computing. The company's first computer designed for scientific computations. The IBM 701 had an electrostatic storage tube memory and kept information on magnetic tape. The company eventually sold 19 of the machines -- more than expected -- to the government and large companies and universities for complex research.*CHM

BIRTHS

429 B.C. Plato born in Athens. He died on the same date in 348 B.C. [Muller] [Should it be 427 B.C.?] *VFR

1471 Albrecht Durer, (21 May 1471 – 6 April 1528) German painter and engraver. Mathematicians are fond of his etching Melancholia for it contains the magic square. Oldstyle numerals are used in the two center squares to emphacize the year that this etching was done by Durer. There is still debate about the shape of the solid in the foreground of the picture. *TIS He also published a book on geometric constructions (1525) using a straight-edge and compass. Although designed to enable artists better represent a natural three-dimensional scene on a canvas, Dürer included careful proofs to establish the validity of the constructions. In this respect, it could be regarded as the oldest surviving text on applied mathematics. He also wrote on the proportions of the human body. *TIS  At a blog by Richard Elwes I found out that Durer was also was one of the first to create a fractal image. In reference to some snowflake fractals at walking randomly he writes,  "It was Dürer who first discovered them, in the second volume of his work Underweysung der Messung (‘Instruction in measurement’) in 1525 (almost 400 years before the discovery of the Koch snowflake)."  He also let me know that "Durer had a hand in the invention of nets, and the rediscovery of Archimedan solids." Thanks Richard. The Renaissance Mathematicus pointed out in his blog that Durer's geometry book was the first true math book printed in the German language.

A close up of the magic square

1792 Gustave-Gaspard Coriolis  (21 May 1792 – 19 September 1843) French engineer and mathematician who first described the Coriolis force, an effect of motion on a rotating body, of paramount importance to meteorology, ballistics, and oceanography. Whereas pressure differences tend to push winds in straight paths, winds follow curved paths across the Earth. In 1835, Coriolis first gave a mathematical description of the effect, giving his name to the Coriolis force. While air begins flowing from high to low pressure, the Earth rotates under it, thus making the wind appear to follow a curved path. In the Northern Hemisphere, the wind turns to the right of its direction of motion. In the Southern Hemisphere, it turns to the left. The Coriolis force is zero at the equator. *TIS

My high-school science teacher told me that the Coriolis effect explains why bathtubs in the Northern Hemisphere drain in a clockwise swirl ... John Cook explains that is a science myth.

1839 Nils Christofer Dunér (21 May 1839; 10 Nov 1914 at age 75) Swedish astronomer who studied the rotational period of the Sun. Although his PhD thesis had been theoretical (the orbit of asteroid Panopea), Dunér mostly worked as an observer. The most outstanding observing astronomer in Swedish 19th century astronomy, he is mostly known for his introduction of new astrophysical techniques. In 1867-75, he made 2679 micrometer measurements of 445 double and multiple stars. After publishing his catalogue of double star measurements in 1876, Dunér turned to spectroscopy, at first specializing in the spectra of red stars. Later, by measuring the Doppler shift of the spectral lines of light from the approaching and receding edges of the sun, he made the significant discovery that the rotational period differs from about 25.5 days near the Sun's equator but up to 38.5 days near the Sun's poles. His career spanned over almost 50 years, from classical astronomy to astrophysics. *TIS

1847 Antonio Favaro, (21 May, 1847 - ? 1922) Professor of Projective Geometry at Padua, editor of  the works of Galileo after a labor of thirty years.

1858 Édouard (-Jean-Baptiste) Goursat - (21 May 1858 – 25 November 1936) French mathematician and theorist whose contribution to the theory of functions, pseudo- and hyperelliptic integrals, and differential equations influenced the French school of mathematics. The Cauchy-Goursat theorem states the integral of a function round a simple closed contour is zero if the function is analytic inside the contour. Cauchy had established the theorem with the added condition that the derivative of the function was continuous. In 1891, he wrote Leçons sur l'intégration des équations aux dérivées partielles du premier ordre. Goursat's best known work is Cours d'analyse mathématique (1900-10) which introduced many new analysis concepts. *Wik

1878 Glenn (Hammond) Curtiss (May 21, 1878 – July 23, 1930) was a pioneer in the development of U.S. aviation.. (see 1908 in Events above)

1923 Armand Borel (21 May 1923 –11 August 2003) was a Swiss mathematician, born in La Chaux-de-Fonds, and was a permanent professor at the Institute for Advanced Study in Princeton, New Jersey, United States from 1957 to 1993. He worked in algebraic topology, in the theory of Lie groups, and was one of the creators of the contemporary theory of linear algebraic groups. *Wik

1958 Curtis Tracy McMullen (21 May 1958- ) is Professor of Mathematics at Harvard University. He was awarded the Fields Medal in 1998 for his work in complex dynamics, hyperbolic geometry and Teichmüller theory.
McMullen graduated as valedictorian in 1980 from Williams College and obtained his Ph.D. in 1985 from Harvard University, supervised by Dennis Sullivan. He held post-doctoral positions at the Massachusetts Institute of Technology, the Mathematical Sciences Research Institute, and the Institute for Advanced Study, after which he was on the faculty at Princeton University (1987–1990) and the University of California, Berkeley (1990–1997), before joining Harvard in 1997. He received the Salem Prize in 1991 and was elected to the National Academy of Sciences in 2007.
McMullen also has given a proof that backgammon ends with probability one*Wik

DEATHS

1670 Niccolò Zucchi (December 6, 1586 – May 21, 1670) Italian astronomer who, in approximately 1616, designed one of the earliest reflecting telescopes, antedating those of James Gregory and Sir Isaac Newton. A professor at the Jesuit College in Rome, Zucchi developed an interest in astronomy from a meeting with Johannes Kepler. With this telescope Zucchi discovered the belts of the planet Jupiter (1630) and examined the spots on Mars (1640). He also demonstrated (in 1652) that phosphors generate rather than store light. His book Optica philosophia experimentalis et ratione a fundamentis constituta (1652-56) inspired Gregory and Newton to build improved telescopes. *TIS

1686 Otto von Guericke (originally spelled Gericke) (November 20, 1602 – May 11, 1686 (Julian calendar); November 30, 1602 – May 21, 1686 (Gregorian calendar)) was a German scientist, inventor, and politician. He is best remembered for his invention of the Magdeburg hemispheres, popularized in the writings of Caspar Schott. His major scientific achievements were the establishment of the physics of vacuums, the discovery of an experimental method for clearly demonstrating electrostatic repulsion, and his advocacy of the reality of "action at a distance" and of "absolute space". *Wik

1825 William Nicholson (13 December 1753 – 21 May 1815) was a renowned English chemist and writer on "natural philosophy" and chemistry, as well as a translator, journalist, publisher, scientist, inventor, patent agent and civil engineer.
In 1797 he began to publish and contribute to the Journal of Natural Philosophy, Chemistry and the Arts, generally known as Nicholson's Journal, the earliest monthly scientific work of its kind in Great Britain— the publication continued until 1814. The journal included the first comprehensive descriptions of aerodynamics with George Cayley's "On Aerial Navigation", which inspired the Wright brothers a hundred years later. In May 1800 he with Anthony Carlisle discovered electrolysis, the decomposition of water into hydrogen and oxygen by voltaic current. The two were then appointed to a chemical investigation committee of the new Royal Institution. But his own interests shortly turned elsewhere.
Besides considerable contributions to the Philosophical Transactions, Nicholson wrote translations of Fourcroy's Chemistry (1787) and Chaptal's Chemistry (1788), First Principles of Chemistry (1788) and a Chemical Dictionary (1795); he also edited the British Encyclopaedia, or Dictionary of Arts and Sciences (6 vols., London, 1809).
Nicholson died in Bloomsbury at the age of 61 on 21 May 1815. *Wik

1826 Georg von Reichenbach (July 21, 1771 – May 21, 1826) German maker of astronomical instruments who introduced the meridian, or transit, circle, (above) a specially designed telescope for measuring both the time when a celestial body is directly over the meridian (the longitude of the instrument) and the angle of the body at meridian passage. By 1796 he was engaged in the construction of a dividing engine, a machine used to mark off equal intervals accurately, usually on precision instruments. *TIS

1848 Pierre Laurent Wantzel (June 5, 1814 in Paris – May 21, 1848 in Paris) was a French mathematician who proved that several ancient geometric problems were impossible to solve using only compass and straightedge. In a paper from 1837,( "Recherches sur les moyens de reconnaître si un Problème de Géométrie peut se résoudre avec la règle et le compas". Journal de Mathématiques Pures et Appliquées) he proved that the problems of
1. doubling the cube
2. trisecting the angle and
3. constructing a regular polygon whose number of sides is not the product of a power of two and any number of distinct Fermat primes (i.e. that does not fulfill the same conditions proven to be sufficient by Carl Friedrich Gauss) the solution to which had been sought for thousands of years, particularly by the ancient Greeks, were all impossible to solve if one uses only compass and straightedge. *Wik

1911 Williamina Paton Stevens Fleming (15 May 1857 - 21 May 1911 at age 53) was a Scottish-American astronomer (née Stevens) who pioneered in the classification of stellar spectra and the first to discover stars called "white dwarfs." She emigrated to Boston at age 21. Prof. Edward Pickering, director of the Harvard Observatory first employed Fleming as a maid, but in 1881 hired her to do clerical work and some mathematical calculations at the Observatory. She further proved capable of doing science. After devising her system of classifying stars by their spectra, she cataloged over 10,000 stars within the next nine years. Her duties were expanded and she was put in charge of dozens of young women hired to do mathematical computations (as now done by computers).*TIS

1953 Ernst Friedrich Ferdinand Zermelo (July 27, 1871 – May 21, 1953) was a German mathematician, whose work has major implications for the foundations of mathematics and hence on philosophy. He is known for his role in developing Zermelo–Fraenkel axiomatic set theory and his proof of the well-ordering theorem.*Wik

1957 Aleksandr Ivanovich Nekrasov (9 Dec 1883 in Moscow, Russia - 21 May 1957 in Moscow, Russia) Nekrasov published important work on the theory of waves, the theory of whirlpools, the theory of jet streams and gas dynamics. He also investigated mathematical questions which were related to these applications, in particular writing important works on non-linear integral equations. In fact his deep understanding of mathematical analysis as developed by mathematicians such as Goursat enabled him to succeed in solving a whole range of concrete problems. *SAU

1958 Wilhelm Süss (7 March 1895 - 21 May 1958) was a German mathematician. He was born in Frankfurt, Germany and died in Freiburg im Breisgau, Germany. He was founder and first director of the Mathematical Research Institute of Oberwolfach.*Wik

1964 James Franck (26 Aug 1882; 21 May 1964) German-born American physicist who shared the Nobel Prize for Physics in 1925 with Gustav Hertz for research on the excitation and ionization of atoms by electron bombardment that verified the quantized nature of energy transfer.*TIS
In 1933, after the Nazis came to power, Franck, being a Jew, decided to leave his post in Germany and continued his research in the United States, first at Johns Hopkins University in Baltimore and then, after a year in Denmark, in Chicago. It was there that he became involved in the Manhattan Project during World War II; he was Director of the Chemistry Division of the Metallurgical Laboratory[5] at the University of Chicago. He was also the chairman of the Committee on Political and Social Problems regarding the atomic bomb; the committee consisted of himself and other scientists at the Met Lab, including Donald J. Hughes, J. J. Nickson, Eugene Rabinowitch, Glenn T. Seaborg, J. C. Stearns and Leó Szilárd. The committee is best known for the compilation of the Franck Report, finished on 11 June 1945, which recommended not to use the atomic bombs on the Japanese cities, based on the problems resulting from such a military application.
When Nazi Germany invaded Denmark in World War II, the Hungarian chemist George de Hevesy dissolved the gold Nobel Prizes of Max von Laue and James Franck in aqua regia to prevent the Nazis from stealing them. He placed the resulting solution on a shelf in his laboratory at the Niels Bohr Institute. After the war, he returned to find the solution undisturbed and precipitated the gold out of the acid. The Nobel Society then recast the Nobel Prizes using the original gold.*Wik

1973 Grigore Constantin Moisil (10 January 1906 in Tulcea, Romania – 21 May 1973 in Ottawa, Canada) was a Romanian mathematician, computer pioneer, and member of the Romanian Academy. His research was mainly in the fields of mathematical logic, (Łukasiewicz-Moisil algebra), Algebraic logic, MV-algebra, algebra and differential equations. He is viewed as the father of computer science in Romania. *Wik

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

## Sunday, 20 May 2018

### White Rabbit Mathematics, Extended

***I first wrote most of this post in 2008, but today an event reminded me of it, and so I thought I would add on to this old, but still interesting post with an additional interesting connection.

One of the things that amazes me, and I think most people who are attracted to math, is the mysterious way that different parts of math come together in unexpected ways. I tried to explain this to someone once using a literary analogy..."It is as if you were reading along in some great drama, or trying to understand the message in some grand poem, and suddenly the White Rabbit from Alice in Wonderland comes running through muttering, "Oh dear! Oh dear! I shall be too late!"
It is not the White Rabbit you see in math, but the effect is the same. Euler must have felt that feeling after he struggled to find the value of the series $\frac{1}{1^2} + \frac{1}{2^2} + \frac{1}{3^2}+ ...$.. and finds that it turns out to be $\frac{\pi^2}{6}$. Wait.... Pi is the ratio of the circumference to the diameter of a circle, but there are no circles in the sum of the squares of the reciprocals of the integers; and yet, there it is, the mathematical white rabbit coming seemingly from nowhere. Certainly none of the many mathematicians of great repute who had worked on the problem found (or expected) Pi to appear.

The normal distribution is another example; De Moivre takes the binomial probability distribution for flipping a coin and generalizes it toward an infinite number of flips, and POW, the normal or bell-shaped curve that is ubiquitous in intro stats. And what happens? Right there in the middle, the height of the normal curve at Z=0 is .39894... No, NO, NO, NOT JUST .39894.. but the .39894... that is exactly equal to $\frac{1}{\sqrt{2 \pi}}$

Ok, so what brought this sudden rebirth of excitement about mathematical interrelationships? Well recently I came across a blog that referred to another blog that (as these things sometimes do) led me to a paper on just such a mathematical "white rabbit". The paper was about partitions of numbers as powers of two (1, 2, 4, 8, 16, etc..)
It began with a simple question, what is the number of ways to write a number n as a sum of powers of two if each value can be expressed no more than two times. For example, we could express 4 as 4, or as 2+2, or as 2 + 1 + 1 since each value is a power of two, and none appears more than twice. You couldn't use 1+1+1+1 since it appears more than twice. For n= 4 it turns out that the number of partitions, as shown above, is three. If we assume that there is one way to express zero, and one way to express one, and figure out the others we get a string like this

1, 1, 2, 1, 3, 2, 3, 1, 4, 3, 5, 2, 5, 3, 4, 1, 5, 4, 7,..
Ok, you don't see a white rabbit yet... but then someone ask you a different question. Is it possible to write out ALL the rational numbers in simplified form without repeating any of them. The answer is "Yes, of course, see the list above."
"What?", you ask, "How?", but there it is... The sequence of rational numbers is formed by taking each of the numbers to be the numerator, and using the number behind it to be the denominator. 1/1; 1/2; 2/1; 1/3; 3/2; ... and you never get a repeat, never get an unsimplified form, and you eventually get them ALL, the entire Infinite Set.....
No way you would expect that partitions of powers of two should give you the rational numbers in their entirety... there is (it would seem) nothing to relate the two questions... and yet... there it is. I think that is what makes math the most exciting area of study in the world.
Prove it you say? Nope, In truth I ain't man enough, but you can find the entire paper
Recounting the rationals, by Neil Calkin and Herb Wilf. Read their proof and Enjoy.

*** So today I was catching up on some old audio podcasts from "My Favorite Theorem," and Jordan Ellenberg   was explaining his choice of a special part of Fermat's Little Theorem, that for any prime p, $2^p \equiv 2 Mod p$.   (or in very primitive terms, if you divide 2p by p, you always get a remainder of 2.  I wondered why he found that so interesting, but then he hit me with, "you can discover at least that it’s true on your own, for instance by messing with Pascal’s Triangle, for example." And of course, in a moment I realized yes, Fermat's Little Theorem, at least this limited case, is elementary true by looking at the rows of Pascal's Triangle. The sum of all the elements of any row add up to a power of two, and the pth row has a sum of 2p. But look at some prime row.....

the 3rd has 1,3,3,1 ;

the fifth has 1,5,10,10,5, 1 ;

and the 7th has 1, 7, 21, 35, 35, 21, 7, 1....

In each row, all the entries are divisible by p, except the two ones. Scan the rest and you notice the same thing. And just importantly, you don't have to go very far to see an exception for the non-primes.

Math has those White Rabbits everywhere.

### On This Day in Math - May 20

Mathematicians are like Frenchmen:
whatever you say to them
they translate into their own language
and forthwith it is something entirely different.
-- Johann Wolfgang von Goethe (Maxims and Reflexions, 1829)

The 140th day of the year; 140 is the sum of the squares of the first seven positive integers. 12 + 22 + 32 + 42 + 52 + 62 + 72 = 140. *Prime Curios

140 is a repdigit in bases 13 (aa), 19(7,7), 27(5,5), 34(4,4), 69(2,2), and 139(1,1).

There are 140 x 1021 (140 followed by 21 zeroes) different configurations of the Rubik's Cube. *Cliff Pickover@pickover

140 is the character limit on Twitter (or was)

A. J. Meyl proved in 1878 that only three tetrahedral numbers are also perfect squares,The largest of these is T(48) =1402 = 19600:

T1 = 1² = 1
T2 = 2² = 4
T48 = 140² = 19600.

EVENTS

1570 Cartographer Abraham Ortelius issues Theatrum Orbis Terrarum, the first modern atlas. *RMAT

 * National Maritime Museum
1608 In a letter to Christopher Clavius, Croation mathematician Marino Ghetaldi says that with his latest parabolic mirror:-
... the sun melts not only lead, but silver.
Ghetaldi had traveled extensively throughout Europe visiting and studying with many of the great science minds, including Viete and Galileo. From Galileo he learned optics and produced a 66cm diameter parabolic mirror which is at the National Maritime Museum in London.
*SAU

1663 Robert Hooke was one of 98 persons who were declared members at a meeting of the Royal Society. He was admitted to society on 3 Jun 1663, and was peculiarly exempted of all payments. Before the Royal Society had been establish in 1660, Hooke was already distinguished for the invention of various astronomical instruments, and the air-pump he contrived for Charles Boyle (whom he had assisted for several years with chemical experiments at the Philosophical Society, Oxford). He invented a balance or pendulum spring (1656-58), one of the greatest improvements in the construction of timepieces. By 1662, he had been appointed curator of experiments to the Royal Society, and on 11 Jan 1664, awarded a salary of £30 per annum for life for that position.*TIS

1665 Newton's earliest use of dots, "pricked letters," to indicate velocities or fluxions is found on a leaf dated May 20, 1665; no facsimile reproduction of it has ever been made.' The earliest printed account of Newton's fluxional notation appeared from his pen in the Latin edition of Wallis' Algebra [Cajori, History of Mathematical Notations, vol. 2, p. 197] *VFR

1716 In a letter written to Leibniz, May 20, 1716, John Bernoulli discussed the equation:d2y/dx2 = 2y/x2
where the general solution when written in the form
y = x2/a + b2/3x
involves three cases: When b approaches zero the curves are parabolas; when a approaches infinity, they are hyperbolas; otherwise, they are of the third order. *John E. Sasser, HISTORY OF ORDINARY DIFFERENTIAL EQUATIONS THE FIRST HUNDRED YEARS

1875 The International Bureau of Weights and Measures established by the International Metric Convention, Sevres, France. The bureau is the repository for the “International Prototype Meter” and the “International Prototype Kilogram.” *SAU= St. Andrews Univ

And for your (in case you thought that 3D movie technology was new, file)
In 1901, Claude Grivolas, one of Pathe's main shareholders in Paris, France, invented a projector that produced three-dimensional pictures.*TIS

1927 At 7:40 a.m., Charles Lindbergh took off from Roosevelt Field in Long Island, N.Y., aboard the "Spirit of St. Louis" monoplane on his historic first solo flight across the Atlantic Ocean. He arrived in France thirty-three and one-half hours later. *TIS

1930 The Institute for Advanced Study incorporated. Two and a half years later Albert Einstein and Oswald Veblen were appointed the ﬁrst professors. [Goldstein, The Computer from Pascal to von Neumann, p. 77]*VFR

In 1956, the first hydrogen fusion bomb (H-bomb) to be dropped from an airplane exploded over Namu Atoll at the northwest edge of the Bikini Atoll. The fireball was four miles in diameter. It was designated as "Cherokee," as part of "Operation Redwing."*TIS

1961 France issued a stamp honoring Charles Coulomb (1736–1806) [Scott #B 352].

1968 A team of six high school students from Upstate New York went to London to participate in the Fourth British Mathematical Olympiad. This was the ﬁrst time a team from the U.S. participated in an international mathematical competition. [The College Mathematics Journal, 16 (1985), p. 331] *VFR

1975 Norway issued a stamp for the centenary of the International Meter Convention in Paris. It pictures Ole Jacob Broch (1818– 1889), the ﬁrst director of the International Bureau of Weights and Measures. [Scott #655] *VFR At least ten other countries issued stamps to commemorate the same event, including Bulgaria, Romania, France, the Soviet Union..... but not the USA. (see 1975 below for another)

1975 Sweden issued a stamp picturing a metric tape measure to honor the centenary of the International Meter Convention in Paris. [Scott #1121] *VFR

1990 the Hubble Space Telescope sent its first photograph from space, an image of a double star 1,260 light years away. *TIS

2012 Solar Eclipse, A total of 154 U.S. national parks will provide views of the eclipse, from partial to full annularity. Many western parks will offer solar observing as a ranger-led program or host a solar party with the help of local amateur astronomy clubs.

Poster advertising viewing the eclipse from Glen Canyon National Recreation Area. Poster © Tyler Nordgren.

2063 99 year old Johnny Depp rolls down red-carpet in wheel-chair for opening of Pirates of the Caribbean sequel #42, “Sun City Pirates”.

BIRTHS

1782 William Emerson (14 May 1701 – 20 May 1782), English mathematician, was born at Hurworth, near Darlington, where his father, Dudley Emerson, also a mathematician, taught a school. William himself had a small estate in Weardale called Castle Gate situated not far from Eastgate where he would repair to work throughout the Summer on projects as disparate as stonemasonry and watchmaking. Unsuccessful as a teacher, he devoted himself entirely to studious retirement. Possessed of remarkable energy and forthrightness of speech, Emerson published many works which are singularly free from errata.
He was early influence in the life of Jeremiah Fenwicke Dixon, of Mason-Dixon fame.

In The Principles of Mechanics (1754) he shows a wind-powered vehicle in which the vertically mounted propeller gives direct power to the front wheels via a system of cogs. In mechanics he never advanced a proposition which he had not previously tested in practice, nor published an invention without first proving its effects by a model. He was skilled in the science of music, the theory of sounds, and the ancient and modern scales; but he never attained any excellence as a performer. He died on 20 May 1782 at his native village, where his gravestone bears epitaphs in Latin and Hebrew.

Emerson dressed in old clothes and his manners were uncouth. He wore his shirt back to front and his legs wrapped in sacking so as not to scorch them as he sat over the fire. He declined an offer to become FRS because it would cost too much after all the expense of farthing candles he had been put to in the course of his life of study. Emerson rode regularly into Darlington on a horse like Don Quixote's, led by a hired small boy. In old age, plagued by the stone, he would alternately pray and curse, wishing his soul 'could shake off the rags of mortality without such a clitter-me-clatter.' *Wik

1825 George Phillips Bond ((May 20, 1825 {sometimes given 1826} – February 17, 1865) Astronomer who made the first photograph of a double star, discovered a number of comets, and with his father discovered Hyperion, the eight moon of Saturn.*TIS

1861 Henry Seely White (May 20, 1861 - May 20, 1943) worked on invariant theory, the geometry of curves and surfaces, algebraic curves and twisted curves. *SAU He matriculated at Wesleyan University in Connecticut and graduated with honors in 1882 at the age of twenty-one. White excelled at Wesleyan in astronomy, ethics, Latin, logic, mathematics, and philosophy. At the university, John Monroe Van Vleck taught White mathematics and astronomy. Later, Van Vleck persuaded White to continue to study mathematics at the graduate level.[1] Subsequently, White studied at the University of Göttingen under Klein, and received his doctorate in 1891.
White was Mathematics Department Chair at Northwestern University. He left Northwestern to be near his ill mother and became Chairman of the Mathematics Department at Vassar College. He "attributed his interest in geometry both to his work at Wesleyan and Goettingen and to summers spent working on his grandfather’s farm."[2] His particular interests were in the fields of the geometry of curves and surfaces (Curves, Differential geometry of surfaces), algebraic planes and twisted curves (Algebraic Geometry, Algebraic curves, Twisted curves), homeomorphic sets of lines in a plane (line coordinates), the theory of invariants, relativity in mechanics, and correspondences.
In 1915 Seely was elected a Fellow of the United States National Academy of Sciences. Northwestern conferred upon him an LL.D. in the same year. At the time of its 100th anniversary in 1932, Wesleyan conferred upon him an D.Sc. *Wik
Died on his birthday in 1943

1874 Friedrich Moritz Hartogs (20 May 1874, Brussels–18 August 1943, Munich) was a German-Jewish mathematician, known for work on set theory and foundational results on several complex variables. *Wik

1901 Machgielis (Max) Euwe (last name is pronounced [ˈøːwə]) (May 20, 1901 – November 26, 1981) was a Dutch chess Grandmaster, mathematician, and author. He was the fifth player to become World Chess Champion (1935–37). Euwe also served as President of FIDE, the World Chess Federation, from 1970 to 1978. *Wik

1901 Hannes Olof Gösta Alfvén (born 30 May 1908 in Norrköping, Sweden; died 2 April 1995 in Djursholm, Sweden) was a Swedish electrical engineer, plasma physicist and winner of the 1970 Nobel Prize in Physics for his work on magnetohydrodynamics (MHD). He described the class of MHD waves now known as Alfvén waves. He was originally trained as an electrical power engineer and later moved to research and teaching in the fields of plasma physics and electrical engineering. Alfvén made many contributions to plasma physics, including theories describing the behavior of aurorae, the Van Allen radiation belts, the effect of magnetic storms on the Earth's magnetic field, the terrestrial magnetosphere, and the dynamics of plasmas in the Milky Way galaxy.*Wik

1913 William Redington Hewlett (20 May 1913; Ann Arbor, Michigan - 12 Jan 2001 at age 87) was an American electrical engineer who co-founded the Hewlett-Packard Company, a leading manufacturer computers, computer printers, and analytic and measuring equipment. In 1939, he formed a partnership known as Hewlett-Packard Company with David Packard, a friend and Stanford classmate. (The order of their names was determined by a coin toss.) HP's first product was an audio oscillator based on a design developed by Hewlett when he was in graduate school. Eight were sold to Walt Disney for Fantasia. Lesser-known early products were: bowling alley foul-line indicator, automatic urinal flusher, weight-loss shock machine. The company began with $538 intial capital, and its first production facility was a small garage in Palo Alto. *TIS DEATHS 1798 Erland Bring (19 August 1736 – 20 May 1798) was a Swedish mathemaician who made contributions to the algebraic solution of equations.*SAU At Lund he wrote eight volumes of mathematical work in the fields of algebra, geometry, analysis and astronomy, including Meletemata quaedam mathematematica circa transformationem aequationum algebraicarum (1786). This work describes Bring's contribution to the algebraic solution of equations. *Wik 1943 Henry Seely White, died on his birthday. (see 1861 above) 1947 Philipp Eduard Anton von Lenard (7 June 1862 – 20 May 1947), was a German physicist and the winner of the Nobel Prize for Physics in 1905 for his research on cathode rays and the discovery of many of their properties. He was a nationalist and anti-Semite; as an active proponent of the Nazi ideology, he had supported Adolf Hitler in the 1920s and was an important role model for the "Deutsche Physik" movement during the Nazi period. Lenard is remembered today as a strong German nationalist who despised "English physics", which he considered to have stolen its ideas from Germany. He joined the National Socialist Party before it became politically necessary or popular to do so. During the Nazi regime, he was the outspoken proponent of the idea that Germany should rely on "Deutsche Physik" and ignore what he considered the fallacious and deliberately misleading ideas of "Jewish physics", by which he meant chiefly the theories of Albert Einstein, including "the Jewish fraud" of relativity. An advisor to Adolf Hitler, Lenard became Chief of Aryan physics under the Nazis. *Wik 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 ## Saturday, 19 May 2018 ### On This Day in Math - May 19  "Big Mac", the beautiful Mackinaw Bridge We [he and Halmos] share a philosophy about linear algebra: we think basis-free, we write basis-free, but when the chips are down we close the office door and compute with matrices like fury. Irving Kaplansky honoring Paul Halmos The 139th day of the year; 139 and 149 are the first consecutive primes differing by 10. 139 = 9*8+7*6+5*4+3*2-1 *Prime Curios 139 is the sum of five consecutive prime numbers( 19+ 23+ 29 +31+ 37) 139 is also a Happy number, if you square the digits and add, then continue to repeat with each result, you will eventually come to the number one. 139 ---- 91----- 82 ------ 68---- 100 ----- 1 (The earliest I have ever found this term was in an article in The Arithmetic Teacher, Feb 1974. "Happiness is some Intriguing numbers" by Billie Earl Sparks of George Peabody College in Nashville, Tn. Does anyone know of an earlier usage?" EVENTS 1662 Samuel Pepys, Secretary of the Navy Board inspects the new Mint in the Tower of London, but will not be allowed to see the ultra secret "edging" machines that engraved an inscription into the edge of the coins to safeguard against the common practice of "clipping" that was common. It was one of the first "milled" currencies in the world. 1673 Leeuwenhoek's first letter to the Royal Society, is published in Philosophical Transactions number 94, "A Specimen of Some Observations Made by a Microscope, Contrived by M. Leewenhoeck in Holland, Lately Communicated by Dr. Regnerus de Graaf." Over the rest of his life, the Society would publish 116 articles containing excerpts from 113 letters. *lensonleeuwenhoek In 1910, the Earth passed through the tail of Halley's Comet, the most intimate contact between the Earth and any comet in recorded history. The event was anticipated with dire predictions. Since a few years earlier, astronomers had found the poisonous gas cyanogen in a comet, it was surmised that if Earth passed through the comet's tail everyone would die. Astronomers explained that the gas molecules within the tail were so tenuous that absolutely no ill effects would be noticed. Nevertheless, ignorance bred opportunists selling "comet pills" to the panicked portion of the public to counter the effects of the cyanogen gas. On 20 May, after Earth had passed through the tail, everyone was still alive - with or without taking pills! *TIS New York Times coverage is HALLEY’S COMET BRUSHES EARTH WITH ITS TAIL (banner headline of the newspaper); 350 American astronomers keep vigil; Reactions of fear and prayer repeated; All night services held in many churches; 1881 dire prophecies recalled by comet scare. 1979 In the Chicago Sun-Times W. F. Buckley wrote “The Rasmussen Report estimates there will be one melt down every 20,000 reactor-years, and one fatality (from cancer) every 50 reactor-years. Conjoin these data (20,000 divided by 50) and you get the ﬁgure of 400 deaths per year.” Quoted from the “Hows that again department,” AMM 90 (1983), p 220.*VFR 1825 Faraday isolates benzine. In 1825, Faraday started work on a sample of oil that had been sent to him for analysis by the Portable Oil Company of London. He subjected this oil to fractional distillation, a process that proved to be extremely difficult, and it took him some time to resolve the oil into its pure components. By repeated fractional distillation followed by selective fractional freezing, each stage monitored by analysis, he produced a fairly pure sample of what he called bicarburet of hydrogen. Faraday’s notebook records these procedures, which he carried out on 18 and 19 May 1825. Auguste Laurent suggested the name benzene. *Jennifer Wilson, Celebrating Michael Faraday’s Discovery of Benzene, Ambix,Volume 59, Issue 3 2006 Apple 'Cube' Shop Opens in Big Apple, NY City: Apple Computer opened its second retail store in New York City. The 20,000-square foot store is situated in the underground concourse of the General Motors building at 767 Fifth Avenue. New Yorkers stood on line for hours in order to be among the first to enter. Open 24-hours a day, the shop is visible at street level through a 32-foot glass cube. It cost$9 million and was designed by Apple’s CEO Steve Jobs.*CHM

BIRTHS

1682 Mei Juecheng (19 May 1681 in Xuangcheng, now Xuanzhou City, Anhui province, China - 20 Nov 1763 in China) published Chishui yizhen (Pearls recovered from the Red River). This contained the infinite series expansion for sin(x) which was discovered by James Gregory and Isaac Newton. In fact the Jesuit missionary Pierre Jartoux (1669-1720) (known in China as Du Demei) introduced the infinite series for the sine into China in 1701 and it was known there by the name 'formula of Master Du'.*SAU

1832 Edmond Bour (19 May 1832 in Gray, Haute-Saône, France - 9 March 1866 in Paris, France)Bour made many significant contributions to analysis, algebra, geometry and applied mechanics despite his early death from an incurable disease. His remarkable achievements were cut short at the age of 33 and as a consequence Bour is hardly known in the history of mathematics whereas one feels that if he had been given the chance to continue his outstanding work he would today be remembered as one of the major figures in the subject. *SAU

1862 Gino Benedetto Loria (19 May 1862 in Mantua, Italy -30 Jan 1954 in Genoa, Italy) In his day, Loria was arguably the pre-eminent historian of mathematics in Italy. A full professor of higher geometry at the University of Genoa beginning in 1891, Loria wrote the history of mathematics as a mathematician writing for other mathematicians. He emphasised this approach repeatedly in his works. For instance, in the introduction to his 'Storia delle matematiche dall'alba della civilità al tramonto del secolo XIX' (History of Mathematics from the Dawn of Civilisation to the End of the 19th Century), he stated that general history of mathematics was written "by a mathematician for mathematicians". *SAU

1918 Abraham Pais (19 May 1918 - 28 Jul 2000 at age 82) Dutch-American physicist and science historian whose research became the building blocks of the theory of elemental particles. He wrote Subtle Is the Lord: The Science and Life of Albert Einstein, which is considered the definitive Einstein biography. In Holland, his Ph.D. in physics was awarded on 9 Jul 1941, five days before a Nazi deadline banning Jews from receiving degrees. Later, during WW II, while in hiding to evade the Gestapo, he worked out ideas in quantum electrodynamics that he later shared when working with Niels Bohr (Jan - Aug 1946). In Sep 1946, he went to the U.S. to work with Robert Oppenheimer at Princeton, where Pais contributed to the foundations of the modern theory of particle physics. *TIS
"To make a discovery is not necessarily the same as to understand a discovery. "

1919 Georgii Dmitrievic Suvorov (19 May 1919 in Saratov, Russia - 12 Oct 1984 in Donetske, Ukraine) Suvorov made major contributions to the theory of functions. He worked, in particular, on the theory of topological and metric mappings on 2-dimensional space. Another area on which Suvorov worked was the theory of conformal mappings and quasi-formal mappings. His results in this area, mostly from the late 1960s when he was at Donetsk, are of particular significance. He extended Lavrentev's results in this area, in particular Lavrentev's stability and differentiability theorems, to more general classes of transformations. One of the many innovations in Suvorov's work was new methods which he introduced to help in the understanding of metric properties of mappings with bounded Dirichlet integral. *SAU

1927 Serge Lang  (May 19, 1927 – September 12, 2005) was a French-born mathematician who spent most of his life in the USA. He is best-known for his outstanding undergraduate text-books.*SAU He was a member of the Bourbaki group. Lang was born in Paris in 1927, and moved with his family to California as a teenager, where he graduated in 1943 from Beverly Hills High School. He subsequently graduated from the California Institute of Technology in 1946, and received a doctorate from Princeton University in 1951. He held faculty positions at the University of Chicago and Columbia University (from 1955, leaving in 1971 in a dispute). At the time of his death he was professor emeritus of mathematics at Yale University. *Wik

1930 Rudolf (Rudy) Emil Kálmán (May 19, 1930 - ) is a Hungarian-American electrical engineer, mathematical system theorist, and college professor, who was educated in the United States, and has done most of his work there. He is currently a retired professor from three different institutes of technology and universities. He is most noted for his co-invention and development of the Kalman filter, a mathematical formulation that is widely used in control systems, avionics, and outer space manned and unmanned vehicles. For this work, U.S. President Barack Obama awarded Kálmán with the National Medal of Science on October 7, 2009. *Wik

DEATHS

804 Alcuin of York,(730s or 740s – 19 May 804) was an English scholar, ecclesiastic, poet and teacher from York, Northumbria. He was born around 735 and became the student of Archbishop Ecgbert at York. At the invitation of Charlemagne, he became a leading scholar and teacher at the Carolingian court, where he remained a figure in the 780s and 790s. He wrote many theological and dogmatic treatises, as well as a few grammatical works and a number of poems. He was made Abbot of Saint Martin's at Tours in 796, where he remained until his death. "The most learned man anywhere to be found" according to Einhard's Life of Charlemagne, he is considered among the most important architects of the Carolingian Renaissance. Among his pupils were many of the dominant intellectuals of the Carolingian era. *Wik
He was born in 735, the year Bede died. As minister of education under Charlemagne, he attempted to reorganize the educational system by popularizing the study of the seven liberal arts and encouraging the study of mathematics as an aid in determining the date of Easter. He wrote the ﬁrst book of mathematical recreations, Propositiones ad acuendis juvenas (Problems for Sharpening the Minds of Youths), which contained 53 mathematical puzzles, including: A wolf, a goat, and a cabbage must be moved across a river in a boat holding only one besides the ferryman. How must he carry them across so that the goat shall not eat the cabbage, nor the wolf the goat? *VFR (Singmaster asserts this is the first example of a river-crossing problem)

1731 Francis Maseres (15 December 1731 – 19 May 1824) was an English lawyer. He is known as attorney general of the Province of Quebec, judge, mathematician, historian, member of the Royal Society, and cursitor baron of the exchequer. *Wik Maseres wrote many mathematical works which show a complete lack of creative ability. He rejected negative numbers and that part of algebra which is not arithmetic, despite writing 150 years after Viète and Harriot. It is probable that Maseres rejected all mathematics which he could not understand. *SAU

1881 Rev U Jessee Kniseley (March 14, 1838 - May 19, 1881) was born in New Philadelphia, Ohio March 14 1838 He was a self made man and in a very great measure self educated. The degree of MA was conferred on him by Marietta College and that of PhD by Wittenberg College in which latter institution he had formerly been a classical and theological student. He also attended Jefferson College Pa but was not a graduate of any college. He was chosen President and Professor of Mathematics of Luther College, an institution of ephemeral existence. Rev Dr Knisely was a Lutheran preacher of marked ability and great eloquence and for fourteen years previous to his death he was the loved pastor of the church of that denomination at Newcomerstown. He was a very fine mathematician and excelled especially in the solution of algebraic and geometrical problems The elegant solution of a Diophantine problem on pp 105 and 106 of the Mathematical Visitor Vol I No 4 and of the celebrated Malfatti's Problem pp 189 and 190 of No 6 are admirable samples of his superior skill in these departments of analysis. Rev Dr Knisely was also a master of language and the author of several works. Copies of his Parser's Manual and Arithmetical Questions for the Recreation of the Teacher and the Discipline of the Pupil are possessed by the writer. It is stated in the Tuscarawas Chroical from which the substance of a portion of this notice is taken that he was also author of Kniseley's Arithmetic and Mrs Knisely states that he had in preparation a work on the Carculus, but of these works the writer knows nothing. His last work was the revision of Ray's Higher Arithmetic and the Key which he completed but a short time before his death. He died May 19, 1881 at the age of 43 years 2 months and 5 days The disease that caused his death was a general prostration of the nervous system. *Artemas Martin, Mathematical Visitor January 1882

1942 Sir Joseph Larmor (11 July 1857 Magheragall, County Antrim, Ireland – 19 May 1942 Holywood, County Down, Northern Ireland) Irish physicist, the first to calculate the rate at which energy is radiated by an accelerated electron, and the first to explain the splitting of spectrum lines by a magnetic field. His theories were based on the belief that matter consists entirely of electric particles moving in the ether. His elaborate mathematical electrical theory of the late 1890s included the "electron" as a rotational strain (a sort of twist) in the ether. But Larmor's theory did not describe the electron as a part of the atom. Many physicists envisioned both material particles and electromagnetic forces as structures and strains in that hypothetical fluid. *TIS

1979 Ralph Duncan James (1909 Liverpool, England – 19 May 1979 Salt Spring Island, British Columbia, Canada) was an English and Canadian mathematician working on number theory and analysis. *Wik James contributed in a major way towards the development of mathematics in North America. He was Editor-in-Chief of the American Mathematical Monthly from 1957 to 1962. For many years he was on the Editorial Boards of the Canadian Journal of Mathematics and of the Pacific Journal of Mathematics. He also served as President of the Canadian Mathematical Society (then called the Canadian Mathematical Congress) from 1961 to 1963. In fact all the previous presidents had served terms of four years, but James felt that this was too long a period to hold the position so it was reduced to a two year term. He served two terms on the Council of the American Mathematical Society. *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