## Wednesday 10 May 2023

### On this Day in Math - May 10

Nature is not embarrassed by difficulties of analysis.

~Augustin Fresnel

The 130th day of the year; 130 is the sum of the factorials of the first five terms of the Fibonacci sequence.
Did you know that any four terms of the Fibonacci sequence will give you a Pythagorean triangle? If we use 3, 5, 8, 13 you can get 3+13 = 39, 2*5*8 = 80, and 3*8 + 5 * 13 = 89, and {39, 80, 89} is a Pythagorean Right triangle with an area of 1560 (which is 3 * 5 * 8 * 13) Which makes it a Heronian triangle. First observed by Charles W. Raine in 1948. For more on this Pythagonacci connection

130 is the sum of the squares of the divisors of 10, ( $1^2 + 2^2 + 5^2 + 10^2 = 130$
130 is also the only number equal to the sum of the squares of its first 4 divisors: 130 = 1^2 + 2^2 + 5^2 + 10^2.*Prime Curios

This is the 46th day of the year that is the sum of two squares.It is the sum of two squares in two different ways. 130 = 11² + 3² = 9² + 7².

Haven't mentioned the hexgonal numbers much this year so far, but 130 is the largest number that cannot be written as the  sum of four hexagonal numbers.
Hexagonal numbers are given by the formula H(n) = n(2n-1), and produce the sequence 1, 6, 15, 28, 45, 66, 91... (can you find  numbers that ARE the sum of four )  (All the even perfect numbers are in that sequence..)

EVENTS

1741 d'Alembert is (finally) accepted to the French Academy of Sciences.  He had applied five times since March 1 of the  same year.  He was accepted as an adjunct associate astronomer at the age of 24. *Thomas L. Hankins, Jean d'Alembert: science and the Englightenment; pg 25

1752 Thomas-François Dalibard of France conducted Franklin's experiment using a 40-foot (some say 50 ft) (12 m)-tall iron rod instead of a kite, and he extracted electrical sparks from a cloud. Based on his observations, Franklin had proposed an experiment with an elevated rod or wire to "draw down the electric fire" from a cloud, with the experimenter standing in the protection of an enclosure similar to a soldier's sentry box.
Before Franklin could put his proposal into practice, D'Alibard performed his experiment in Paris. One week later, M. Delor repeated the experiment in Paris, followed in July by an Englishman, John Canton. But one unfortunate physicist did not fare so well. Georg Wilhelm Reichmann attempted to reproduce the experiment, according to Franklin's instructions, standing inside a room. A glowing ball of charge traveled down the string, jumped to his forehead and killed him instantly - providing history with the first documented example of ball lightning in the process.
As for Franklin, he was apparently unaware of these other experiments when he undertook his own version during a thunderstorm in June 1752, on the outskirts of Philadelphia. Unlike Reichmann, he quite sensibly stood under a shed roof to ensure he was holding a dry, non-conducting portion of the kite string.*AMERICAN PHYSICAL SOCIETY News

1760 Euler writes the tenth of his Letters to a German Princess.  This one on the "Compression of the air. " .  "The explanation of sound, which I have had the honor of presenting to you Highness, leads me forward to..." (The Euler Archive)

1810 Friedrich Wilhelm Bessel was summoned by the King of Prussia to be Professor of Astronomy at the University at Konigsburg and to supervise the construction of an Observatory, becoming its first Director. In 1819 he developed and published Fourier series, three years before Fourier! In 1824, he first systematically studied the Bessel functions. In 1838, he made the first observation of a stellar parallax, hence of a stellar distance, of 61 Cygni, about 11 light-years away. Its parallax is less than .3" (or .3' ??) of arc – the aberration due to the Earth's motion is about 40'. He had started working on this about thirty years previously. Henderson, 1839, and Struve, 1840, made independent measurements of a stellar parallax.

1831 Everiste Galois was arrested, following a banquet, of about 200 young republicans, that he actively attended.*VFR (SEE MAY 9)

1845  The Spitalfields Mathematical Society  This mathematical society was founded in 1717 by Joseph Middleton who taught mathematics to sailors who required mathematical skills for navigating. It met in a public house, the Monmouth's Head, in Spitalfields which is a district just outside the east side of the city of London. The 'Mathematical Society', as it called itself, moved its meeting place a number of time over the following years but remaining in Spitalfields. In 1725 it moved to the White Horse in Wheeler Street, then in 1735 to the Ben Johnson's Head in Woodseer Street.

Dozens of these societies were formed in the early 18th century and contributed to the learning of many tradespeople, and the financial sustenance of many mathematicians of the period.  Thomas Simpson was an early member of the Spitalfields Mathematical Society, being one of 49 members in 1736Simpson was the most distinguished of a group of itinerant lecturers who taught in the London coffee houses. This may seems strange but in fact at this time coffee houses were sometimes called the Penny Universities because of the cheap education they provided. They would charge an entrance fee of one penny and then while customers drank coffee they could listen to lectures. Different coffee houses catered to specific interests such as art, business, law and mathematics. For example De Moivre used Slaughter's Coffee House in St Martin's Lane as a base during these years, and William Jones, who was a friend of Simpson, was able to make a living lecturing in coffee houses such as Child's Coffee House in St Paul's Churchyard.

The actual death date of the society is not known to me, but the Society wrote to the Royal Astronomical Society who responded on 10 May 1845:-

A meeting of the Council of the Royal Astronomical Society took place yesterday, and I brought forward the suggestions contained in your recent letters to me relating to the venerable Mathematical Society of London, and the Council were unanimous in regretting that this ancient Society of 130 years standing should be on the eve of dissolution and decline. The members of the Council were also, I believe, unanimous that if the nineteen surviving members of the Mathematical Society should in their liberality and public spirit wish to keep the mathematical and astronomical and philosophical portions of their library together, and should kindly and considerately offer to present it to the Royal Astronomical Society, that the Council of the latter would not only be grateful to them for this act of judicious benevolence, but would be willing to elect all the members of the Mathematical Society members for life of the Royal Astronomical Society.

*Assorted notes but much from *SAU, McTutor, Wik

1869 the first transcontinental railroad to run West out of Chicago was completed, running to Promontory, Utah. Amidst a crowd of dignitaries and workers, with the engines No. 119 and Jupiter practically touching noses, the Central Pacific and Union Pacific railroads were joined together. Telegraph operators transmitting to both coasts transmit the blows of the hammer as they fall on a golden spike. The nation listened as west and east came together in undivided union. *TIS

1898 Dewar becomes the first person to liquefy Hydrogen, working in the basement laboratory of the Ri with only a few assistants. *Royal Institution web page

1899 Parker Brothers put out Instant Insanity in 1967. But the puzzle itself was much older. Here's a patent filed on May 10, 1899 (issued April 3, 1900) by F.A. Schossow for a game that would be sold as the Katzenjammer Puzzle.  *Dave Richeson

1910 Florence Nightingale was presented with the badge of honour of the Norwegian Red Cross Society. *VictorianWeb   She would die a few months later on13 August 1910

1925 John T. Scopes was given a preliminary hearing before three judges. He had been arrested and charged under a new Tennessee's state law, the Butler act, which prohibited the teaching of Darwin's theory of evolution in public schools. Scopes had agreed to participate in a challenge to that law, with the support of local leaders in Dayton, Tennessee, and the American Civil Liberties Union. A few weeks later, at what became known as the Scope's Monkey Trial, he was found guilty and fined \$100. Although upon appeal the fine was ruled excessive and over-ruled, the state law itself was not found unconstitutional. Thereafter, the law was not enforced, but it was not repealed until 1967.*TIS (The state of Tennessee still seems to be struggling with this issue, 2011)

1933 Kurt Schutte, the last of Hilbert’s sixty-nine doctoral students, defends his dissertation on logic. For the full list see Hilbert’s Gesammelte Abhandlungen, vol. 3, pp. 431–433. *VFR

In 1949, the first planetarium in the U.S. owned by a university opened at the University of Chapel Hill, North Carolina. The Morehead Planetarium, one of the largest in the U.S., was the gift of John Motley Morehead III (1870-1965), class of 1891. The Morehead Building, erected at the north end of the campus, included the 68-ft dome, 300-seat Star Theater with a Zeiss Model II Star Projector. Morehead was an industrialist and chemist who commercially developed production of calcium carbide, basic to manufacturing acetylene gas, which led to the founding of Union Carbide Corporation. As the U.S. space program began, the planetarium provided important celestial navigation training for U.S. astronauts in the Mercury program.*TIS  A beautiful visit, take the kids.

1960 Triton ended her 84 day, 36,014 mile circumnavigation of the globe, the ﬁrst by a submerged submarine. The ship generally followed the path of the ﬁrst round the world voyager, Magellan. [Navy Facts, 181, 204] *VFR (Magellan's circumnavigation took three years, On August 10, 1519 to September 6, 1522. Of the 237 men who set out on five ships, only 18 completed the circumnavigation and managed to return to Spain in 1522.  As far as I know the Triton had no casualties.)

2012 National Abacus Day in Japan. Today is National Abacus Day in Japan. By manipulating beads, the user of an abacus can perform simple addition, subtraction, multiplication, and division. *CHM

 From My Personal Collection

2013 An annular solar eclipse will take place on May 10, 2013, with a magnitude of 0.9544. A solar eclipse occurs when the Moon passes between Earth and the Sun, thereby totally or partially obscuring the image of the Sun for a viewer on Earth. An annular solar eclipse occurs when the Moon's apparent diameter is smaller than the Sun, causing the Sun to look like an annulus (ring), blocking most of the Sun's light. An annular eclipse appears as a partial eclipse over a region thousands of kilometres wide.
Annularity will be visible from northern Australia and the southern Pacific Ocean, with the maximum of 6 minutes 3 seconds visible from the Pacific Ocean east of French Polynesia. *Wik

BIRTHS

1788 Augustin Jean Fresnel (10 May 1788 - 14 July 1827, aged 39)did important work on optics where he was one of the founders of the wave theory of light.  In 1817, Young had proposed a small transverse component to light, while yet retaining a far larger longitudinal component. Fresnel, by the year 1821, was able to show via mathematical methods that polarization could be explained only if light was entirely transverse, with no longitudinal vibration whatsoever.  In the early 19th century, Poisson declared that since Fresnel’s ideas on the wave nature of light implied that the shadow cast by a disk would contain a bright spot at its center, Fresnel’s ideas were obviously flawed. The spot was later detected, proving Fresnel right!   He is perhaps best known to the general public as the inventor of the Fresnel lens, first adopted in lighthouses while he was a French commissioner of lighthouses, and found in many applications today.*Wikipedia

1821 Baldassarre Boncompagni, (10 May 1821 – 13 April 1894),  noted historian of mathematics. He set up his own publishing house and published his own journal dealing with the history of mathematics from 1868 to 1887. He was responsible for making known the importance of Leonardo Fibonacci to the history of mathematics. *VFR Boncompagni edited Bullettino di bibliografia e di storia delle scienze matematiche e fisiche ("The bulletin of bibliography and history of mathematical and physical sciences") (1868-1887), the first Italian periodical entirely dedicated to the history of mathematics. He edited every article that appeared in the journal. He also prepared and published the first modern edition of Fibonacci's Liber Abaci.*Wik

1847 Wilhelm Karl Joseph Killing (10 May 1847 in Burbach (near Siegen), Westphalia, Germany - 11 Feb 1923 in Münster, Germany)introduced Lie algebras independently of Lie in his study of non-euclidean geometry. The classification of the simple Lie algebras by Killing was one of the finest achievements in the whole of mathematical research.*SAU

1900 Cecilia Helena Payne-Gaposchkin (10 May 1900; 7 Dec 1979 at age 79) was an English-American astronomer who was the first to apply laws of atomic physics to the study of the temperature and density of stellar bodies, and the first to conclude that hydrogen and helium are the two most common elements in the universe. During the 1920s, the accepted explanation of the Sun's composition was a calculation of around 65% iron and 35% hydrogen. At Harvard University, in her doctoral thesis (1925), Payne claimed that the sun's spectrum was consistent with another solution: 99% hydrogen with helium, and just 1% iron. She had difficulty persuading her superiors to take her work seriously. It was another 20 years before Payne's original claim was confirmed, by Fred Hoyle. *TIS

 *MacTutor

1904 Edward James McShane is famous for his work in the calculus of variations, Moore-Smith theory of limits, the theory of the integral, stochastic differential equations, and ballistics. In the early 1950s United States senator Joseph R McCarthy whipped up strong feelings against communism. McShane had been asked to complete a questionnaire. One question asked:-
... whether he had ever been involved with organisations that had at any time advocated the violent overthrow of the U.S. government.
It was quite a brave move for McShane to reply "yes", because he was an employee of the State of Virginia! At the University of Virginia this sense of humour added to his popularity with both staff and graduate students.. *SAU

1926 Oliver Gordon Selfridge (May 10, 1926 – December 3, 2008), grandson of Harry Gordon Selfridge, the founder of Selfridges' department stores, was a pioneer of artificial intelligence. He has been called the "Father of Machine Perception."
Selfridge was born in England, educated at Malvern College and Middlesex School and then earned an S.B. from MIT in mathematics in 1945. He then became a graduate student of Norbert Wiener's at MIT, but did not write up his doctoral research and never earned a Ph.D. While at MIT, he acted as one of the earlier reviewers for Wiener's Cybernetics book in 1949. He was also technically a supervisor of Marvin Minsky, and helped organize the first ever public meeting on Artificial Intelligence (AI) with Minsky in 1955.
Selfridge wrote important early papers on neural networks and pattern recognition and machine learning, and his "Pandemonium" paper (1959) is generally recognized as a classic in artificial intelligence. In it, Selfridge introduced the notion of "demons" that record events as they occur, recognize patterns in those events, and may trigger subsequent events according to patterns they recognize. Over time, this idea gave rise to Aspect-oriented programming.
In 1968, in their formative paper "The Computer as a Communication Device", J. C. R. Licklider and Robert Taylor introduced a concept known as an OLIVER (Online Interactive Expediter and Responder) which was named in honor of Selfridge.
Selfridge spent his career at Lincoln Laboratory, MIT (where he was Associate Director of Project MAC), Bolt, Beranek and Newman, and GTE Laboratories where he became Chief Scientist. He served on the NSA Advisory Board for 20 years, chairing the Data Processing Panel. Selfridge retired in 1993.
Selfridge also authored four children's books, "Sticks", "Fingers Come In Fives", "All About Mud", and "Trouble With Dragons". *Wik

1958 Ellen Ochoa (born May 10, 1958) is an American engineer, former astronaut and former director of the Johnson Space Center. In 1993, Ochoa became the first Hispanic woman to go to space when she served on a nine-day mission aboard the Space Shuttle Discovery. Ochoa became director of the center upon the retirement of the previous director, Michael Coats, on December 31, 2012. She was the first Hispanic director and the second female director of Johnson Space Center.

Ellen Ochoa aboard Space Shuttle Discovery during mission STS-56.

DEATHS

1822
Paolo Ruffini (September 22, 1765 – May 10, 1822) Italian mathematician and physician who made studies of equations that anticipated the algebraic theory of groups. He is regarded as the first to make a significant attempt to show that there is no algebraic solution of the general quintic equation (an equation with the variable in one term raised to the fifth power). In 1799 Ruffini published a book on the theory of equations with his claim that quintics could not be solved by radicals, General theory of equations in which it is shown that the algebraic solution of the general equation of degree greater than four is impossible. Ruffini used group theory in his work but he had to invent the subject for himself. He also wrote on probability and the application of probability to evidence in court cases. *TIS

1829 Thomas Young  (13 June 1773 – 10 May 1829) English physician and physicist who reinforced the wave theory of light with his study of interference of light. As a medical student, he had discovered the how the shape of the eye's lens changes to focus. In 1801, he recognized the cause of astigmatism. Young demonstrated the wave nature of light, polarization of light, interference fringes, and explained the colours seen in thin films such as soap bubbles. He associated wavelength with colour of light, and the eye's perception of any colour as a mixture of red, blue and green. Young's modulus is named after his work with elasticity. He also worked measuring the size of molecules, liquid surface tension. He was also an Egyptologist who helped decipher the Rosetta Stone. The museum in Cairo has another "roseta", the Decree of Canopus, in Hieroglyphic, Demotic and Greek, issued by Ptolemy III Euergetes in -238. It decrees leap years to be included in the calendar. It was not discovered until 1866, too late to assist Young and Champollion in deciphering, but which confirmed their work.

1924 August Gutzmer (2 Feb 1860 in Neu-Roddahn, near Neustadt an der Dosse, Germany -10 May 1924 in Halle, Germany) was a German mathematician who worked on differential equations. *SAU

1941 Diederik Korteweg (31 March 1848 – 10 May 1941) was a Dutch mathematician with wide interests, now best-known as the joint discoverer of the Korteweg-de Vries equation for solitary waves.

1989 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

2009 Carol Jo Crannell (November 15, 1938 – May 10, 2009) was a solar physicist known for her work on solar flares and on the astrophysical observation of x-rays and gamma rays. She worked for thirty years at the NASA Goddard Space Flight Center.
Crannell was born in Columbus, Ohio. She graduated from Miami University in 1960, and completed her Ph.D. in physics at Stanford University in 1967, with Robert Hofstadter as her doctoral advisor. She worked at the Goddard Space Flight Center from 1974 until 2004, when she retired.
Crannell also held an adjunct faculty position at Catholic University of America, where her husband, Hall L. Crannell, is an emeritus professor. Her daughter, Annalisa Crannell, is a mathematician at Franklin & Marshall College.
Crannell's doctoral research concerned particle showers. At Goddard, Crannell pushed for x-ray and gamma-ray observations of the sun, and led balloon-mounted experiments to make these observations.
Crannell played an active role in the struggle for equal opportunity for women in physics. She chaired the Committee on the Status of Women in Physics of the American Physical Society, and helped found the CSWP Gazette, the newsletter of the Committee. Through her position at the Catholic University she also helped bring underrepresented students to summer internships at Goddard.
Crannell became a Fellow of the American Physical Society in 1992, and a Fellow of the American Association for the Advancement of Science in 1998. In 1990, Women in Aerospace gave her their Outstanding Achievement Award "for her dedication to expanding women’s opportunities for career advancement and for increasing their visibility through her activities as an aerospace professional".
*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