## Wednesday, 17 August 2016

### On This Day in Math - August 17

Base eight is just like base ten, really… if you're missing two fingers!
~Tom Lehrer, "New Math"

The 230th day of the year; 230 is the first number such that it and the next number are both sphenic numbers, the product of three distinct primes (230 = 2*5*23 and 231 = 3*7*11). *Prime Curios (can there be three consecutive numbers that are the product of three (or n) distinct primes

Their are 230 possible crystal shapes that can tile space (this counts the chiral reflections as separate). This is the analogy of the better known 17 "wallpaper groups" which tile the plane. Interestingly, both were proved by the same man, Evgraf Fedorov, in 1891. He did the plane problem the hard way, he proved the case for space first, then worked backwards to the plane.

EVENTS
1585 The Roanoak Colony in Virginia (to later become known as the "lost" colony) was founded on this day by Sir Walter Raleigh's agents, led by Ralph Lane. If you don't know why that is on a math page, read more here.

1655 William Oughtred writes to John Wallis to praise his methods in "Arithmetica Infinitorum" . It was received too late to be included in the first edition, but was included in the 1695 second edition.  *The Arithmetics of Infinitesimals, J. Stedall, pg 11

1762 The Board of Longitude Grants £500 to Christopher Irwin for his marine chair. Marine chairs, despite often having been ignored by modern scholars in favor of the chronometer and lunar-distance approaches to estimating longitude, reappeared throughout the history of the British Commissioners of the Longitude. Christopher Irwin of Ireland generated a lot of national and international interest in the late 1750s and early 1760s with his design. The Board funded the finishing and sea trial of it, granting him £500 on 17 August 1762. Nevil Maskelyne considered the chair alongside the lunar-distance method and one of John Harrison's longitude timekeepers on his 1763 trip to Barbados. (Maskelyne, who in 1765 would become Astronomer Royal and a Commissioner of Longitude, reported that the invention was useless. *Cambridge Digital Library

1771 Joseph Priestley sets out to test the rejuvenating effect of mint growing in a sealed container. He placed a candle in the covered glass and let it burn out in the presence of the mint. Ten days later he would return to the experiment and relight the candle and found, "it burned perfectly well in it." *Steven Johnson, The Invention of Air

1811 “Having to conduct my grandson through his course of mathematics, I have resumed the study with great avidity. It was ever my favorite one. We have no theories there, no uncertainties remain on the mind; all is demonstration and satisfaction.” So wrote Thomas Jefferson (1743– 1826) to Benjamin Rush. Taken from The Writings of Thomas Jefferson, edited by A. A. Lipscomb, vol. 13 (1903), p. 75, as quoted from Cajori, Mathematics in Liberal Education, p. 109, which is a collection of interesting quotations on the value of mathematics.  The following year, his 70th, Jefferson describes his early affection for mathematics in a letter to William Duane "When I was young, mathematics was the passion of my life." *John Fauval, lecture at Univ of Va.

1825 A royal decree granted Niels Henrik Abel, then 23, sufficient funds for a year’s travel in France and Germany. *VFR

1877 Asaph Hall discovered Phobos, inner satellite of Mars. The two moons of Mars, Phobos and Deimos, were found when American astronomer Hall identified them after a long search, although their existence had been a source of speculation before. The possibility of Martian moons had been speculated long before Hall's discovery. The astronomer Johannes Kepler (1571–1630) even predicted their number correctly, although with faulty logic: he wrote that since Jupiter had four known moons and Earth had one, it was only natural that Mars should have two.
Perhaps inspired by Kepler (and quoting Kepler's third law), Jonathan Swift's satire Gulliver's Travels (1726) refers to two moons in Part 3, Chapter 3 (the "Voyage to Laputa"), in which the astronomers of Laputa are described as having discovered two satellites of Mars orbiting at distances of 3 and 5 Martian diameters, and periods of 10 and 21.5 hours, respectively. The actual orbital distances and periods of Phobos and Deimos of 1.4 and 3.5 Martian diameters, and 7.6 and 30.3 hours, respectively.
Hall discovered Deimos on August 12, 1877 at about 07:48 UTC and Phobos on August 18, 1877, at the US Naval Observatory in Washington, D.C., at about 09:14 GMT (contemporary sources, using the pre-1925 astronomical convention that began the day at noon, give the time of discovery as August 11, 14:40 and August 17 16:06 Washington mean time respectively)*Wik
In the words of Asaph Hall, "Of the various names that have been proposed for these satellites, I have chosen those suggested by Mr Madan of Eton, England, viz: Deimos for the outer satellite; Phobos for the inner satellite. These are generally the names of the horses that draw the chariot of Mars. "

1896 Mrs. Bridget Driscoll of Croydon, Surrey, became the 1st pedestrian in Britain to die after being hit by a car. Mrs Driscoll, a 44 year old housewife, who was traveling from Old Town, Croydon to a folk-dancing display in Crystal Palace, was hit by a demonstration car traveling at 4mph (according to the driver, Arthur Edsel) . She died within minutes of receiving a head injury.
At her inquest, Coroner William Percy Morrison said he hoped that "such a thing would never happen again" and was the first to apply the term ‘accident’ to violence caused by speed. Coroners across the country have followed his example ever since. *Road Safety Center Cardiff.

1934 Dunham Jackson personalizes a book. Harold Bacon recalls that Jackson was an inspired writer of limericks. When Bacon purchased Jackson's "The Theory of Approximations" he took it to Jackson's office and requested he sign it, suggesting a limerick. Without any visible prethought Jackson wrote on the flyleaf:
There was a young fellow named Bacon
Whose judgement of books was mistaken
In a moment too rash
He relinquished some cash
And his faith in the Author was shaken
August 17, 1934
*Steven Krantz, Mathematical Apocrypha Redux
Harold M Bacon was a long-serving calculus professor at Stanford where a teaching award in his name has been created since his death in 1992.

1941 When Herbert Robbins saw the proof sheet of the title page of What is Mathematics? with only the name Richard Courant on it, his ﬁrst reaction was “My god, the man’s a crook.” Realizing that a quiet meeting on their co-authorship of the book would be impossible, Robbins wrote Courant on this date that, while the custom might be different in Europe, in this country the junior author did receive credit. Courant backed down, and so today we know this lovely book as one by Courant and Robbins. For the two sides of this story see Constance Reid, Courant in Gottingen and New York. The Story of an Improbable Mathematician (Springer 1976), 223– 226 and 230–232 as well as “An interview with Herbert Robbins,” The College Mathematics Journal, 15(1984), 4–6. *VFR

1966 Launch of Pioneer 7, American solar satellite. Studied prominences and solar atmosphere. *NSEC

BIRTHS
1601 Pierre de Fermat (17 Aug 1601; 12 Jan 1665) French mathematician, often called the founder of the modern theory of numbers. Together with Rene Descartes, Fermat was one of the two leading mathematicians of the first half of the 17th century. He anticipated differential calculus with his method of finding the greatest and least ordinates of curved lines. He proposed the famous Fermat's Last Theorem while studying the work of the ancient Greek mathematician Diophantus. He wrote in pencil in the margin, "I have discovered a truly remarkable proof which this margin is too small to contain," that when the Pythagorean theorem is altered to read an + bn = cn, the new equation cannot be solved in integers for any value of n > 2 . *TIS

1936 Margaret Heafield Hamilton (August 17, 1936 - ) is a computer scientist, systems engineer and business owner. She was Director of the Software Engineering Division of the MIT Instrumentation Laboratory, which developed on-board flight software for the Apollo space program. In 1986, she became the founder and CEO of Hamilton Technologies, Inc. in Cambridge, Massachusetts. The company was developed around the Universal Systems Language based on her paradigm of Development Before the Fact (DBTF) for systems and software design.
In one of the critical moments of the Apollo 11 mission, Hamilton's team's work prevented an abort of the landing on the Moon. Among other things, Hamilton credits the Apollo Guidance Computer (AGC) together with its asynchronous executive as a foundation that provided the means for her to design systems software that included AGC error detection and recovery mechanisms such as the Display Interface Routines, the purpose of which was to warn the astronauts in case of an emergency, by interrupting the astronaut's normal mission sequence displays and replacing them with priority displays (e.g., the priority displays of the 1201 and 1202 alarms that took place during the Apollo 11 landing). Three minutes before the Lunar lander reached the Moon's surface, several computer alarms were triggered. The computer was overloaded with incoming data, because the rendezvous radar system (not necessary for landing) updated an involuntary counter in the computer, which stole cycles from the computer. Due to its robust architecture, the computer was able to keep running; the Apollo onboard flight software was developed using an asynchronous executive so that higher priority jobs (important for landing) could interrupt lower priority jobs.

Hamilton has published over 130 papers, proceedings, and reports concerned with the 60 projects and six major programs in which she has been involved. *Wik

1954 Ingrid Daubechies ( born 17 August 1954- ) is a Belgian physicist and mathematician. She is currently Professor in the mathematics and applied mathematics departments at Princeton University. In January 2011 she moved to Duke University as a Professor in mathematics. She is the first woman president of the International Mathematical Union (2011–2014). She is best known for her work with wavelets in image compression. In 2000 Daubechies became the first woman to receive the National Academy of Sciences Award in Mathematics, presented every 4 years for excellence in published mathematical research. The award honored her "for fundamental discoveries on wavelets and wavelet expansions and for her role in making wavelets methods a practical basic tool of applied mathematics."
In January 2005, Daubechies became just the third woman since 1924 to give the Josiah Willard Gibbs Lecture sponsored by the American Mathematical Society. Her talk was on "The Interplay Between Analysis and Algorithm."*Wik

DEATHS

1786 Death of Frederick the Great. Euler's interest in lotteries began at the latest in 1749 when he was commissioned by Frederick the Great to render an opinion on a proposed lottery. The first of two letters began 15 September 1749. A second series began on 17 August 1763.

1924 Pavel Samuilovich Urysohn, Pavel Uryson (February 3, 1898, Odessa – August 17, 1924, Batz-sur-Mer) is best known for his contributions in the theory of dimension, and for developing Urysohn's Metrization Theorem and Urysohn's Lemma, both of which are fundamental results in topology. His name is also commemorated in the term Menger-Urysohn dimension and in the term Urysohn integral equation. The modern definition of compactness was given by him and Pavel Alexandrov in 1923.*Wik

1927 (Erik) Ivar Fredholm (7 Apr 1866,17 Aug 1927) Swedish mathematician who founded modern integral equation theory. *TIS

1969 Otto Stern (17 Feb 1888; 17 Aug 1969 at age 81) German-American scientist and winner of the Nobel Prize for Physics in 1943 for his development of the molecular beam as a tool for studying the characteristics of molecules and for his measurement of the magnetic moment of the proton. *TIS

2004 Shizuo Kakutani August 28 1911, August 17 2004) was a Japanese-born American mathematician, best known for his eponymous fixed-point theorem.
The Kakutani fixed-point theorem is a generalization of Brouwer's fixed-point theorem, holding for generalized correspondences instead of functions. Its most important uses are in proving the existence of Nash equilibria in game theory, and the Arrow–Debreu–McKenzie model of general equilibrium theory.
Kakutani's other mathematical contributions include the Kakutani skyscraper, a concept in ergodic theory (a branch of mathematics that studies dynamical systems with an invariant measure and related problems). They also include his solution of the Poisson equation using the methods of stochastic analysis.
The Collatz (or 3n+1) conjecture is also known as the Kakutani conjecture. *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