## Monday 18 September 2023

### On This Day in Math - September 18

Lisez Euler, lisez Euler, c'est notre maître à tous.

—~Pierre-Simon Laplace

The 261st Day of the Year
261 = 15^2 + 6^2. It is also 45^2 - 42^2 and 131^2 - 130^2

261 is the number of possible unfolded tesseract patterns. (Charles Howard Hinton coined the term tesseract  (4-dimensional "cube").  He is also the inventor of the baseball  pitching gun.) (see Baseball and the Fourth Dimension)

If you draw diagonals in a 16 sided polygon, it is possible to dissect it into 7 quadrilaterals.  There are 261 unique  ways to  make this dissection.

261 is the only three digit number n, for which 2^n - n is prime. *Prime Curios

261 is divisible by 9, the sum of its digits, so it is a Joy-Giver (Harshad) number.

261 Fearless, a non-profit organization started by Kathrine Switzer, who in 1967 wore bib number 261 when she became the first woman to run the Boston Marathon as a numbered entrant. *Wikipedia

This should  have been the Day of the Year in 2021, as that's the base five representation for 261(2021)

A bracelet with 261 Blue beads and 3 Red beads can be ordered in 261 different ways.

261 = 4^4 + 4^1 + 4^0

My conjecture:  There is no square that is made up of five Pythagorean triangles with a side shorter than 261, as shown  *HT to @simon_gregg

EVENTS

1820 André Marie AMPÈRE describes electromagnetic effect.  On 11 September 1820 he heard of H. C. Ørsted's discovery that a magnetic needle is acted on by a voltaic current. Only a week later, on 18 September, Ampère presented a paper to the Academy containing a much more complete exposition of that and kindred phenomena. On the same day, Ampère also demonstrated before the Academy that parallel wires carrying currents attract or repel each other, depending on whether currents are in the same (attraction) or in opposite directions (repulsion). This laid the foundation of electrodynamics.*Wik.

Two of Ampère’s experimental set-ups to demonstrate electromagnetism, engraving, in Annales de chimie et de la physique, vol. 15, 1820 (Linda Hall Library)

In 1830, B&O locomotive Tom Thumb, the first locomotive built in America, lost in a 14-km race with a horse due to a boiler leak.*TIS

Peter Cooper, an American inventor and industrialist, first came on the engineering scene in 1830, when he assembled from spare parts a locomotive that he called Tom Thumb, and on behalf of which he challenged a horse-drawn rail car to a race, which took place on Aug. 28, 1830 . Tom Thumb lost the race due to mechanical problems, but he won the marathon, since the locomotive’s superiority was evident, and the Baltimore and Ohio Railroad decided to put their money on steam locomotives.  Their rapid expansion enabled them to buy iron rails from Cooper's iron works in Maryland, which was the whole idea behind Tom Thumb in the first place.  In the early 20th century, the Bureau of Public Roads (now the Federal Highway Administration) commissioned a painting of the race by their staff artist Carl Rakeman (as well as a hundred other events in highway and rail history).  The original Tom Thumb does not survive, but in 1927 the Baltimore and Ohio Railroad commissioned a replica as best they could (there are no images of the original) and it is a popular attraction in their Museum in Baltimore .

1846  Le Verrier transmits his most famous achievement, his prediction of the existence of the then unknown planet Neptune, using only mathematics and astronomical observations of the known planet Uranus. Encouraged by physicist Arago Director of the Paris Observatory, Le Verrier was intensely engaged for months in complex calculations to explain small but systematic discrepancies between Uranus's observed orbit and the one predicted from the laws of gravity of Newton. At the same time, but unknown to Le Verrier, similar calculations were made by John Couch Adams in England. Le Verrier announced his final predicted position for Uranus's unseen perturbing planet publicly to the French Academy on 31 August 1846, two days before Adams's final solution, which turned out to be 12° off the mark, was privately mailed to the Royal Greenwich Observatory. Le Verrier transmitted his own prediction by 18 September letter to Johann Galle of the Berlin Observatory. The letter arrived five days later, and the planet was found with the Berlin Fraunhofer refractor that same evening, 23 September 1846, by Galle and Heinrich d'Arrest within 1° of the predicted location near the boundary between Capricorn and Aquarius.*Wik

Excerpt from the Hora XXI sky chart of the Berlin Science Academy completed by Carl Bremiker. The predicted location (square) and the observed location (circle) were noted in pencil, allegedly by Galle, but at some time after the discovery.

1948 Alan Turing writes to Jack Good and mentions, "Chess machine designed by Champ and myself..". *Turing Archive

BIRTHS

1752 Adrien-Marie Legendre (18 Sep 1752; 10 Jan 1833) French mathematician who contributed to number theory, celestial mechanics and elliptic functions. In 1794, he was put in charge of the French government's department that was standardizing French weights and measures. In 1813, he took over as head of the Bureau des Longitudes upon the death of Lagrange, its former chief. It was in a paper on celestial mechanics concerning the motion of planets (1784) that he first introduced the Legendre Polynomials. His provided outstanding work on elliptic functions (1786), and his classic treatise on the theory of numbers (1798) and also worked on the method of least squares. *TIS

1819 Jean Bernard Léon Foucault (18 Sep 1819; 11 Feb 1868) French physicist whose Foucault Pendulum experimentally proved that the Earth rotates on its axis (6 Jan 1851). Using a long pendulum with a heavy bob, he showed its plane rotated at a rate related to Earth's angular velocity and the latitude of the site. He studied medicine and physics and became an assistant at the Paris Observatory (1855). He invented an accurate test of a lens for chromatic and spherical aberrations. Working with Fizeau, and also independently, he made accurate measurements of the absolute velocity of light. In 1850, Foucault showed that light travels slower in water than in air. He also built a gyroscope (1852), the Foucault's prism (1857) and made improvements for mirrors of reflecting telescopes. *TIS (a brief biography of Foucault is here)

1839 John Aitken (18 Sep 1839; 14 Nov 1919) Scottish physicist and meteorologist who, through a series of experiments and observations in which he used apparatus of his own design, elucidated the crucial role that microscopic particles, now called Aitken nuclei, play in the condensation of atmospheric water vapour in clouds and fogs. Ill health prevented Aitken from holding any official position; he worked instead in the laboratory in his home in Falkirk. Much of his work was published in the journals of the Royal Society of Edinburgh, of which he was a member.*TIS

1854 Sir Richard Tetley Glazebrookb(18 Sep 1854; 15 Dec 1935) English physicist who was the first director of the UK National Physical Laboratory, from 1 Jan 1900 until his retirement in Sep 1919. At first, the laboratory's income depended on much routine, commercial testing, but Glazebrook championed fundamental, industrially oriented research. With support from individual donors, buildings were added for electrical work, metrology, and engineering. Data useful to the shipbuilding industry was collected in pioneering experimental work on models of ships made possible by a tank funded by Alfred Yarrow (1908). From 1909, laboratory began work benefitting the embryonic aeronautics industry, at the request of the secretary of state for war. The lab to contributed substantially to military needs during WW I *TIS

1907 Edwin Mattison McMillan (Sep 18, 1907 - September 7, 1991) McMillan was an American physicist and Nobel laureate credited with being the first-ever to produce a transuranium element, neptunium. For this, he shared the Nobel Prize in Chemistry with Glenn Seaborg in 1951.
McMillan and his colleagues discovered the elements neptunium (Np) and plutonium (Pu), the two elements following uranium (U) in the periodic table. Their names were inspired by the position of the planets in the solar system - Neptune is beyond Uranus and Pluto (before being declassified as a planet) is beyond Neptune. *http://www.rsc.org/

Three Nobel Prize winners (left to right): Edwin McMillan, Emilio Segre, Glenn Seaborg, photograph, 1959 (nara.getarchive.net) *Linda Hall Library

 *Linda Hall org

1863 William Henry Metzler (18 Sept 1863, 18 April 1943) was a Canadian mathematician who graduated from Toronto University and taught at Syracuse University and Albany Teachers Training College, both in New York State. He published papers on the theory of matrices and determinants, several of them in the Proceedings of the EMS. *SAU

1926 James Cooley, (September 18, 1926 - ) co-creator of the fast Fourier transform, was born. Working with John Tukey, Cooley in 1965 worked out a vast improvement to a common mathematical algorithm called the Fourier transform. Although the algorithm had been useful in computing, its complexity required too much time. While working at IBM, Cooley built on Tukey's ideas for a swifter version. *CHM

DEATHS

1783 Leonhard Euler dies (15 Apr 1707, 18 Sep 1783) . After having discussed the topics of the day, the Montgolﬁers, and the discovery of Uranus, “He [Euler] ceased to calculate and to live,”according to the oft-quoted words of de Condorcet. *VFR   Swiss mathematician and physicist, one of the founders of pure mathematics. He not only made decisive and formative contributions to the subjects of geometry, calculus, mechanics, and number theory but also developed methods for solving problems in observational astronomy and demonstrated useful applications of mathematics in technology. At age 28, he blinded one eye by staring at the sun while working to invent a new way of measuring time. *TIS (Students who have not, should read Dunham's "Euler, The Master of us All")

1891 William Ferrel (born 29 Jan 1817, 18 Sep 1891) American meteorologist was an important contributor to the understanding of oceanic and atmospheric circulation. He was able to show the interrelation of the various forces upon the Earth 's surface, such as gravity, rotation and friction. Ferrel was first to mathematically demonstrate the influence of the Earth's rotation on the presence of high and low pressure belts encircling the Earth, and on the deflection of air and water currents. The latter was a derivative of the effect theorized by Gustave de Coriolis in 1835, and became known as Ferrel's law. Ferrel also considered the effect that the gravitational pull of the Sun and Moon might have on the Earth's rotation and concluded (without proof, but correctly) that the Earth's axis wobbles a bit. *TIS (A more complete biography is here)

1896 Armand Hippolyte Fizeau (23 Sep 1819, 18 Sep 1896) French physicist was the first to measure the speed of light successfully without using astronomical calculations (1849). Fizeau sent a narrow beam of light between gear teeth on the edge of a rotating wheel. The beam then traveled to a mirror 8 km/5 mi away and returned to the wheel where, if the spin were fast enough, a tooth would block the light. Knowing this time from the rotational speed of the wheel, and the mirror's distance, Fizeau directly measured the speed of light. He also found that light travels faster in air than in water, which confirmed the wave theory of light, and that the motion of a star affects the position of the lines in its spectrum. With Jean Foucault, he proved the wave nature of  the Sun's heat rays by showing their interference (1847). *TIS

1913 Samuel Roberts FRS (15 December 1827, Horncastle, Lincolnshire – 18 September 1913, London) was a British mathematician.
Roberts studied at Queen Elizabeth's Grammar School, Horncastle. He matriculated in 1845 at the University of London, where he earned in 1847 his bachelor's degree in mathematics and in 1849 his master's degree in mathematics and physics, as first in his class. Next he studied law and became a solicitor in 1853. After a few years of law practice he abandoned his law career and returned to mathematics, although he never had an academic position. He had his first mathematical paper published in 1848. In 1865 he was an important participant in the founding of the London Mathematical Society (LMS). From 1866 to 1892 he acted as legal counsel for LMS, from 1872 to 1880 he was the organization's treasurer, and from 1880 to 1882 its president. In 1896 he received the De Morgan Medal of the LMS. In 1878 he was elected FRS.
Roberts published papers in several fields of mathematics, including geometry, interpolation theory, and Diophantine equations.
Roberts and Pafnuty Chebyschev are jointly credited with the Roberts-Chebyshev theorem related to four-bar linkages *Wik

1967 Sir John Douglas Cockcroft (27 May 1897, 18 Sep 1967) British physicist, who shared (with Ernest T.S. Walton of Ireland) the 1951 Nobel Prize for Physics for pioneering the use of particle accelerators to study the atomic nucleus. Together, in 1929, they built an accelerator, the Cockcroft-Walton generator, that generated large numbers of particles at lower energies - the first atom-smasher. In 1932, they used it to disintegrate lithium atoms by bombarding them with protons, the first artificial nuclear reaction not utilizing radioactive substances. They conducted further research on the splitting of other atoms and established the importance of accelerators as a tool for nuclear research. Their accelerator design became one of the most useful in the world's laboratories. *TIS

1977 Paul Isaak Bernays (17 Oct 1888, 18 Sep 1977) Swiss mathematician and logician who is known for his attempts to develop a unified theory of mathematics. Bernays, influenced by Hilbert's thinking, believed that the whole structure of mathematics could be unified as a single coherent entity. In order to start this process it was necessary to devise a set of axioms on which such a complete theory could be based. He therefore attempted to put set theory on an axiomatic basis to avoid the paradoxes. Between 1937 and 1954 Bernays wrote a whole series of articles in the Journal of Symbolic Logic which attempted to achieve this goal. In 1958 Bernays published Axiomatic Set Theory in which he combined together his work on the axiomatisation of set theory. *TIS

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