## Sunday 17 September 2023

### On This Day in Math - September 17

God is a child; and when he began to play, he cultivated mathematics.
It is the most godly of man's games.

~V Erath

The 260th day of the year; 260 is the constant for each row, column and diagonal of the first known(1891) 8x8 bimagic square.
The 8x8 is the smallest order possible for a bimagic square (the squares of the numbers also form a magic square) that uses consecutive digits. The constant for the magic square formed by the squares is 11,180.

More on the first of these in 1891 at the Feb 1 On This Day in Math.

260 is also the sum of the 8x8 pandiagonal square created by Emory McClintock in 1897.  A pandiagonal magic square, in addition to satisfying the requirement of a magic square, has the additional property that all diagonals, including broken diagonals, i.e. those that wrap around from one edge of the square to the opposite edge, add to the same sum.

260 =66^2-64^2 , and also 16^2 + 2^2 = 4^4 + 4^1, and 14^2 + 8^2

260 is a Palindrome in base 8 (404)

The Mayan Sacred Calendar had a 260 year cycle.

A 5x5 magic square with a constant of 260 can be formed by taking the standard 1-25 magic square and multiplying each term by four.  Another is to use 39, 40, 41,... , 64

260 is also the sum of the squares of the divisors of 15. /( 260 = 1^2 + 3^2 + 5^2 + 15^2 /)
See More Math Facts for every Year Day here

EVENTS

In 1683, the Dutch scientist Antonie van Leeuwenhoek wrote to the Royal Society reporting his discovery of microscopic living animalcules (live bacteria). He had made observations on the plaque between his own teeth, "a little white matter, which is as thick as if 'twere batter." Looking at these samples with his microscope, Leeuwenhoek reported how in his own mouth: "I then most always saw, with great wonder, that in the said matter there were many very little living animalcules, very prettily a-moving. The biggest sort. . . had a very strong and swift motion, and shot through the water (or spittle) like a pike does through the water. The second sort. . .oft-times spun round like a top. . . and these were far more in number." *TIS

1787 U.S. Constitution signed. Its format was inﬂuenced by the axiomatic approach of Euclidean Geometry. *VFR (I would appreciate insight into what this means? comments? Suggestions? Wild guesses?)

1789 William Herschel discovers the small moon Mimas, Saturns smallest and innermost moon.  The name of this, and the other six known moons of Saturn was suggested by William's son John in 1847.  All were named for mythological giants of Greek literature.  The large crater, now named for Herschel was not observed until photographed by the Cassinni probe on November 7, 2004.

 *Tech Explorist

1871 Opening of the Mount Cenis (Fréjus) Tunnel (1857-70) through the Alps, the world's first important mountain tunnel. The two track railway tunnel unites Italian Savoy (north of the mountains) through Switzerland with the rest of Italy to the south. At 8 miles long and it was more than double the length of any previous tunnel. In 1861, after three years of tedious hand-boring a mere eight inches a day into the rock face, Sommeiller introduced the first industrial-scale pneumatics for tunnel digging. He built a special reservoir, high above the tunnel entrance, to produce a head of water that compressed air (to 6 atm.) for pneumatic drills, able to dig up to 20 times faster. Authorized on 15 Aug 1857, the tunnel opened on 17 Sep 1871, as a major triumph of engineering.*TIS

During the 2000s, the Fréjus Rail Tunnel underwent a series of works to modernise and improve it, including the increase of its bore to accommodate wider rail vehicles, such as container trucks on piggy-back wagons, as part of the Autoroute Ferroviaire Alpine.

 *Wik

1901 Peter Cooper Hewitt patents the first mercury-vapor lamp.Hewitt was issued U.S. patent #682692 on September 17, 1901. *Wik

In 1902, Hewitt developed the mercury arc rectifier, the first rectifier that could convert alternating current power to direct current without mechanical means. It was widely used in electric railways, industry, electroplating, and high-voltage direct current (HVDC) power transmission.

In 1907, he developed and tested an early hydrofoil. In 1916, Hewitt joined Elmer Sperry to develop the Hewitt-Sperry Automatic Airplane, one of the first successful precursors of the cruise missile. *Wik

1908  The Wright Flyer flown by Orville Wright, with Lieutenant Thomas Selfridge as passenger, crashes, killing Selfridge, who becomes the first airplane fatality. *the painter flynn

 the painter flynn

1914  In 1898, with the aid of his friend, Charles Walcott, Director of the U.S. Geological Survey, Samuel Pierpont Langley became the third Secretary of the Smithsonian Institution , secured funding, including $50,000 from the U.S. War Department, to build a full-scale, piloted flying machine that he named, Aerodrome A. Langley had his first genuine success on May 6, 1896, with his Aerodrome Number 5. It made the world's first successful flight of an unpiloted, engine-driven, heavier-than-air craft of substantial size. It was launched from a spring-actuated catapult mounted on top of a houseboat on the Potomac River near Quantico, Virginia. On October 3, 1903, the first flight attempt of Aerodrome A splashed into the Potomac River with Langley’s assistant, Charles Manly, at the controls. A second attempt on December 9 proved equally disastrous with the aircraft breaking apart soon after launch and crashing into the water. Though the pilot was unharmed, public ridicule in the press forever damaged Langley’s aviation dreams. He died three years later without making another flight. In 1917, Walcott tried Langley's Aerodrome 5 using pontoons made by Glenn Curtiss. . On September 17, 1914, the Great Aerodrome made a successful flight over Lake Keuka in New York. Secretary Walcott now felt that he had evidence to resurrect Langley’s rightful place in aviation history.  *Washington Post 1971 RCA withdraws from computer market, losing$490M *CHM

1985 The Los Angeles Times reported that scientists at Chevron tested their new \$10 million Cray X­MP supercomputer and discovered the 30th Mersenne Prime and largest known prime (to that date), 2216091− 1
*[Part I, pp. 3, 19; Mathematics Magazine

2008, On September 17, a team of researchers at the University of Texas at Dallas led by Founders Professor Hal Sudborough announced the acceptance by the journal Theoretical Computer Science of a more efficient algorithm for pancake sorting than the one proposed by Gates and Papadimitriou in 1979. This establishes a new upper bound of (18/11)n, improving upon the existing bound of (5/3)n from 1979 by William H Gates, soon to be known as Bill Gates of Microsoft, then a Sophomore student at Harvard. *wik

BIRTHS

1794 Marie Jean Antoine Nicolas de Caritat, Marquis of Condorcet (French: [; 17 September 1743 – 29 March 1794), known as Nicolas de Condorcet, was a French philosopher and mathematician. His ideas, including support for a liberal economy, free and equal public instruction, constitutional government, and equal rights for women and people of all races, have been said to embody the ideals of the Age of Enlightenment, of which he has been called the "last witness", and Enlightenment rationalism. A critic of the constitution proposed by Marie-Jean Hérault de Séchelles in 1793, the Convention Nationale — and the Jacobin faction in particular — voted to have Condorcet arrested. He died in prison after a period of hiding from the French Revolutionary authorities.

From 1765 to 1774, he focused on science. In 1765, he published his first work on mathematics, entitled Essai sur le calcul intégral, which was well received, launching his career as a mathematician. He went on to publish more papers, and on 25 February 1769, he was elected to the Académie royale des Sciences.

Condorcet worked with Leonhard Euler and Benjamin Franklin. He soon became an honorary member of many foreign academies and philosophic societies, including the American Philosophical Society (1775), the Royal Swedish Academy of Sciences (1785), the American Academy of Arts and Sciences (1792) and also in Prussia and Russia.

In 1785, Condorcet published his Essay on the Application of Analysis to the Probability of Majority Decisions, one of his most important works. This work described several now famous results, including Condorcet's jury theorem, which states that if each member of a voting group is more likely than not to make a correct decision, the probability that the highest vote of the group is the correct decision increases as the number of members of the group increases, and Condorcet's paradox, which shows that majority preferences can become intransitive with three or more options – it is possible for a certain electorate to express a preference for A over B, a preference for B over C, and a preference for C over A, all from the same set of ballots.

The paper also outlines a generic Condorcet method, designed to simulate pair-wise elections between all candidates in an election. He disagreed strongly with the alternative method of aggregating preferences put forth by Jean-Charles de Borda (based on summed rankings of alternatives). Condorcet was one of the first to systematically apply mathematics in the social sciences.[citation needed]

He also considered the instant-runoff voting elimination method, as early as 1788, though only to condemn it, for its ability to eliminate a candidate preferred by a majority of voters.

Condorcet's statue by Jacques Perrin, on Quai de Conti in Paris, France

1764 John Goodricke (17 Sep 1764; 20 Apr 1786) English astronomer who was the first to notice that some variable stars were periodic. Born a deaf-mute, after a proper education he was able to read lips and to speak. He was the first to calculate the period of Algol to 68 hours and 50 minutes, where the star was changing its brightness by more than a magnitude as seen from Earth. Even better, he suggested that the variability was caused by a dark object, possibly a planet, that regularly passed in front of the star. The modern explanation is that Algol is a binary star, with the eclipse caused by the smaller orbiting star.

He was also first to correctly propose that the distant sun is periodically occulted by a dark body. John Goodricke was admitted to the Royal Society on 16 April 1786, when 21 years old. He didn't recognize this honor, because he died four days later, in York, from pneumonia.*TIS

The constellation Perseus, engraving, in Johann Bayer, Uranometria, 1603. Algo (beta Persei) is the star in the right eye of the head of Medusa (Linda Hall Library)

1826 (Georg Friedrich) Bernhard Riemann (17 Sep 1826; 20 July 1866) was a German mathematician whose work widely influenced geometry and analysis. In addition, his ideas concerning geometry of space had a profound effect on the development of modern theoretical physics and provided the foundation for the concepts and methods used later in relativity theory. He clarified the notion of integral by defining what we now call the Riemann integral. He was an original thinker and a host of methods, theorems and concepts are named after him. Riemann suffered from tuberculosis and he spent his last years in Italy in an attempt to improve his health. *TIS (A nice cartoon about the Riemann Hypothesis)

1846 Seth Carlo Chandler (17 Sep 1846; 31 Dec 1913) an American astronomer best known for his discovery (1884-85) of the Chandler Wobble, a complex movement in the Earth's axis of rotation (now refered to as polar motion) that causes latitude to vary with a period of 14 months. His interests were much wider than this single subject, however, and he made substantial contributions to such diverse areas of astronomy as cataloging and monitoring variable stars, the independent discovery of the nova T Coronae, improving the estimate of the constant of aberration, and computing the orbital parameters of minor planets and comets. His publications totaled more than 200. *TIS

1857 Konstantin Eduardovich Tsiolkovsky (17 Sep 1857; 19 Sep 1935) Russian pioneer space theorist who, while a provincial Russian schoolteacher, worked out many of the principles of space travel. In 1883, he noted that vehicle in space would travel in the opposite direction to gas that it emitted, and was the first to seriously propose this method propulsion in space travel. He wrote various papers, including the 1903 article "Exploration of Space with Reactive Devices." The engineering equations he derived included parameters such as specific impulse, thrust coefficient and area ratio. He established that the most efficient chemical combination would be that of liquid hydrogen and liquid oxygen. He was later recognized by the Soviet Union as the "father of cosmonautics." He also built the first wind tunnel.*TIS

1905 Hans Freudenthal (September 17, 1905,– October 13, 1990) was a Dutch mathematician. He made substantial contributions to algebraic topology and also took an interest in literature, philosophy, history and mathematics education.
In 1937 he proved the Freudenthal suspension theorem.
Later in his life, Freudenthal focused on elementary mathematics education. In the 1970s, his single-handed intervention prevented the Netherlands from following the worldwide trend of "`new math"'. He was also a fervent critic of one of the first international school achievement studies.
In 1971 he founded the IOWO at Utrecht University, that after his death was renamed Freudenthal Institute, the current Freudenthal institute for science and mathematics education. He was awarded the Gouden Ganzenveer award in 1984, and died in Utrecht in 1990, sitting on a bench in a park where he always took a morning walk.*Wik

1916 Oswald Garrison "Mike" Villard Jr (17 Sep 1916; 7 Jan 2004) American electronics engineer who developed over-the-horizon radar (a way to detect objects out of direct sight by bouncing radar off the ionosphere, an electrically charged layer in the upper atmosphere) so radar could peer around the Earth's curvature to detect aircraft and missiles thousands of miles away. His interest in electricity began with a copy of Harper's Electricity Book for Boys. At age 12, he put together a radio from a kit. During WW II, he researched countermeasures to protect Allied forces against enemy radio and radar devices. He made pioneering studies of radar jamming. In 1947, he designed a simplified voice transmitter permitting two-way communication on a single radio channel, such as a telephone conversation. *TIS

1934 Warren J. Mitofsky, (17 September 1934 - 1 September 2006)While working at the Census Bureau in the 1960s, he and a colleague, Joseph Waksberg, began to devise a random-digit dialing (RDD) system that now bears both their names.
Mr. Mitofsky went to work at CBS News in 1967. Not long afterwards, he organized the first "exit poll" in a Kentucky gubernatorial election, with his first national exit poll being in 1972. He directed the CBS News Election and Survey Unit until 1990, leading, in 1975, to the joint effort with the NYTimes, the CBS News/New York
Times Poll (which The Times calls the New York Times/CBS News Poll),
which he directed until 1990.
Since 2003, Mitofsky, considered the "Father of Exit Polling" by many, led election-night analysis for the News Election Pool, providing exit-poll results and projections. (Mitofsky disliked the term "exit poll"; he preferred "Election Day survey".)
In exit polls on Election Day in 2004, Mitofsky's early exit polls found Senator John Kerry leading over President Bush, which led some in the news media to prepare for Senator Kerry becoming President Kerry. But such was too premature, as Mitofsky readily acknowledged, later discovering that the pro-Kerry exit-poll lead was caused by Republicans refusing to participate at a greater rate than Democrats in the exit polls. [Guess this shows the importance of not ignoring nonresponse.]
However, despite all this, Mitofsky will probably be best remembered by many for his efficient method of sampling telephone numbers using random-digit dialing (RDD), which is now known as the Mitofsky-Waksberg Method. In 1970, Mitofsky wrote an unpublished CBS News memorandum titled "Sampling of Telephone Households" that helped make his name a household word in public-opinion polling. Eight years later, Joseph Waksberg published an analogous paper, "Sampling Methods for Random Digit Dialing", in the prestigious Journal of the American Statistical Association (JASA), thus resulting in the Mitofsky-Waksberg Method appellation.
The Mitofsky-Waksberg Method of RDD is a cluster-sampling method
for sampling residential telephone numbers that greatly increases
the percentage of calls that do reach residential households. *David Bee

DEATHS

1802 Baron Georg von Vega (b. 1754- September 17, 1754), a military officer and mathematician famous for his military campaigns and his table of logarithms, was murdered for “his money and his watch.” [Eves, Adieu, 257◦] *VFR

1823 Abraham-Louis Bréguet (10 Jan 1747, 17 Sep 1823) Swiss-French horologist and inventor who became the leading French watchmaker of his time because of his artistic as well as technical skill. His innovations included a self-winding or "perpétuelle" watch (1780), the gong spring which decreased the size of repeater watches, and the first anti-shock device or "pare-chute", which improved the reliability of his watches while making them less fragile. In 1775 he founded the Breguet watchmaking firm. After a two year interruption during the French Revolution, he continued business with more inventions. He sold the first modern carriage clock to Bonaparte, and created the tact watch by which time could be read by touch.*TIS

1877 William Fox Talbot (11 Feb 1800, 17 Sep 1877) English mathematician, physicist, chemist who invented the negative-positive photographic process. He improved Thomas Wedgewood's discovery (1802) that brushing silver nitrate solution onto paper produces a light-sensitive medium able to record negative images, but Wedgewood was unable to control the darkening. In February 1835, Fox Talbot found that a strong solution of salt fixed the image. Using a camera obscura to focus an image onto his paper to produce a negative, then - by exposing a second sheet of paper to sunlight transmitted through the negative - he was the first to produce a positive picture of which he was able to make further copies at will. His Pencil of Nature (1844) was the first photographically illustrated book. *TIS

1891 Józeph Miksa Petzval (6 Jan 1807, 17 Sept 1891) worked for much of his life on the Laplace transform. He was influenced by the work of Liouville and wrote both a long paper and a two volume treatise on the Laplace transform and its application to ordinary linear differential equations. His study is thorough but not entirely satisfactory since he was unable to use contour integration to invert the transform.
But for a student of Petzval we might today call the Laplace transform the Petzval transform. Petzval fell out with this student who then accused Petzval of plagiarising Laplace's work. Although this was untrue, Boole and Poincaré, influenced no doubt by the quarrel, called the transformation the Laplace transform.
Petzval is best remembered for his work on optical lenses and lens aberration done in the early 1840's (Petzval curvature is named after him) which allowed the construction of modern cameras. Petzval produced an achromatic portrait lens that was vastly superior to the simple meniscus lens then in use. *SAU

1908 Thomas E. Selfridge , a 1903 classmate of Douglas MacArthur at West Point, whose tombstone at West Point reads “Gave up his life in the service of his country at Fort Myers, Virginia, September 17, 1908, falling with the ﬁrst government aeroplane.” The pilot, an Ohio bicycle maker named Orville Wright, survived. [Rick Atkinson, The Long Grey Line (1989), pp. 1–2] (His father was a general, but Selfridge Field, now an Air Natl. Guard base near Detroit, is named for the Lt.,the first person to die in a crash of a powered airplane.)

For more information about Lt. Selfridge and his early relation to flying, the Fort Myers, and Alexander G. Bell, see this great article at the Smithsonian site sent to me by the author, Julia Blakely.

1999 Leonard Carlitz (26 Dec 1907, 17 Sept 1999) Carlitz published 771 papers, supervised 44 doctoral and 51 master's theses. His major mathematical contributions are to finite field theory, number theory, and combinatorics. But his publications extend beyond these areas to include algebraic geometry, commutative rings and algebras, finite differences, geometry, linear algebra, and special functions.*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