Tuesday 19 September 2023

On This Day in Math - September 19


Mankind will not remain on the earth forever, but, in search of light and space, will at first timidly penetrate beyond the limits of the atmosphere and then finally conquer the spaces of the solar system.
— Konstantin Eduardovich Tsiolkovsky
tombstone inscription
(But first, can we learn to be indigenous to our own planet?) PB

The 262nd day of the year; 262 is the 5th meandric number. A meander is a self-avoiding closed curve which intersects a line a number of times. Intuitively, a meander can be viewed as a straight road crossing a river over a number of bridges.[ The term meander is drawn from the Greek name of an actual winding river, the Maiandros.]

262 should be day of the year for 2022, 262 in  base five is 2022.

262 is the number of equilateral triangles formed out of matches in a hexagonal chunk with four matchsticks on a side..(Can you find the 38 equilaterals in the hexagon with two matchsticks on a side)


1648 The theory of atmospheric pressure and the existence of a vacuum were confirmed by experiments designed by Blaise Pascal.*VFR.  Pascal himself did not make the trudge up the mountain with barometer in hand, but asked his brother -in-law, Florian Perier. Accompanied by "worthy gentleman" , to make the measure.  It is clear from Torricelli's correspondence with Ricci that he knew the weight of air decreased with Altitude, but it was Pascal who first instructed the measure, and calculated the weight of all the air pressing on the Earth.   

The weather was good on Saturday, Sep. 19, 1648, so Périer rose early, and he began by visiting the Minim convent in Clermont, where he set up two identical Torricellian tubes, and checked that they read the same.  He left one of the tubes there in the monastery, instructing a monk to check the level regularly and see if it changed over the course of the day.  Then, with an accompanying party, Périer headed with the other tube for the top of the Puy de Dôme, some 4800 feet above sea level and about 3000 higher than the Minim convent in Clermont.  Sure enough, the mercury level at the summit dropped three inches, while the level in the stationary tube (Périer would later discover) did not change at all.

The Puy de Dôme experiment attracted some attention in subsequent decades, but it was not acclaimed at the time as a new kind of experiment.  But over the centuries it has achieved canonical status from scientists and philosophers of science, and many historians.  It appeals to writers on scientific method because it was designed to test a specific hypothesis – that the mercury in the tube is held up by atmospheric pressure – and to rule out competing hypotheses, such as that the mercury is held up by nature’s abhorrence of a vacuum.  Even better, Périer used a control, a duplicate tube that was not subjected to the crucial variable, a change in altitude.  And he brought along witnesses, and kept detailed notes.  This was a perfect example of an experimentum crucis, a crucial experiment, years before Robert Hooke coined the term, and Isaac Newton demonstrated it with his prism experiments on light and color.

In 1923, there was a celebration of the tercentenary of Pascal’s birth.  It was held at Clermont (now Clermont-Ferrand), and the banquet was at the summit of the Puy de Dôme, with the evening address delivered by the President of France, Alexandre Millerand. We like the art deco poster printed for the event, showing Clermont, the Puy de Dôme, and the statue of Pascal that was installed in a city park in 1880. *Linda Hall Org

1680 Francis and Mary Huntrodds die within five hours on their mutual birthday, and marriage anniversary. Statisticians sometimes hold "probability" parties in honor of Huntrodd's Day. *David Spiegelhalter, understandinguncertainty.org

1783 The brothers Montgolfier repeated their experiment of 4 June 1783, in the presence of Louis XVI at Versailles. At one o’clock the crowd went wild as the balloon soared gracefully free carrying a rooster, a sheep, and a duck.*VFR

In 1783 Étienne carried out an initial tethered attempt, which was successful and which he repeated a second time seven days before the demonstration in front of the king at Versailles. Unfortunately, the balloon tore open and he had to stitch it back together quickly. The balloon was made of cotton canvas with paper glued onto both sides, measured 18.47m tall by 13.28m wide, and weighed 400 kg. It was named Le Réveillon after Étienne's friend Jean-Baptiste Réveillon, the Director of the Royal Manufacture of printed paper, who had designed a motif on a sky-blue background decorated with the king’s cypher – two interweaving L’s – linked with decorative elements all in gold. *chateauversailles.

Amidst stupefaction and applause, the balloon left the ground and soared 600 metres into the air. Damaged by a rip in the fabric, it descended slowly eight minutes later after travelling 3.5 km and came back to earth in the Wood of Vaucresson, at the Maréchal crossroads.

The first human would go aloft on 21 November of 1783.

In 1848, Hyperion, moon of Saturn, discovered by William Cranch Bond(US), George Phillips Bond(US) and William Lassell(UK)*TIS  It was the first non-round moon to be discovered. Hyperion's discovery came shortly after John Herschel had suggested names for the seven previously-known satellites of Saturn in his 1847 publication Results of Astronomical Observations made at the Cape of Good Hope. Lassell, who saw Hyperion two days after William Bond, had already endorsed Herschel's naming scheme and suggested the name Hyperion in accordance with it. He also beat Bond to publication. *Wik


1861 Russian chemist Alexander Butlerov first presented a definition for "chemical structure".
Chemical structure refers to the way atoms are arranged within molecules. Butlerov realized that chemical compounds are not a random cluster of atoms and functional groups, but structures with definite order. *.rsc.org  

 He was the first to incorporate double bonds into structural formulas, the discoverer of hexamine (1859), the discoverer of formaldehyde (1859) and the discoverer of the formose reaction (1861). He first proposed the idea of possible tetrahedral arrangement of valence bonds in carbon compounds in 1862. *Wik


1894 In a letter to Felix Klein (19 September 1894) Peano wrote: “The purpose of mathematical logic is to analyze the ideas and reasoning that especially figure in the mathematical sciences.” Peano was neither a logicist nor a formalist. He believed rather that mathematical ideas are ultimately derived from our experience of the material world. *Hubert Kennedy, "Eight Mathematical Biographies" Pg 27

1994   Andrew Wiles has an "AHA" moment,    Over the course of three lectures delivered at Isaac Newton Institute for Mathematical Sciences on June 21, 22, and 23 of 1993, Wiles had announced his proof of the Taniyama–Shimura conjecture, and hence of Fermat's Last Theorem. There was a relatively large amount of press coverage afterwards.
After announcing his results, (Nick) Katz was a referee on his manuscript and he asked Wiles a series of questions that led Wiles to recognize that the proof contained a gap. There was an error in a critical portion of the proof which gave a bound for the order of a particular group: the Euler system used to extend Flach's method was incomplete. Wiles and his former student Richard Taylor spent almost a year resolving it. Wiles indicates that on the morning of September 19, 1994 he realized that the specific reason why the Flach approach would not work directly suggested a new approach with the Iwasawa theory which resolved all of the previous issues with the latter and resulted in a CNF that was valid for all of the required cases. On 6 October Wiles sent the new proof to three colleagues including Faltings. The new proof was published and, despite its size, widely accepted as likely correct in its major components. *Wik

1995 Ahoy Matey,  International "Talk Like a Pirate Day is born"  is a parodic holiday created in 1995 by John Baur (Ol' Chumbucket) and Mark Summers (Cap'n Slappy), of Albany, Oregon, who proclaimed September 19th each year as the day when everyone in the world should talk like a pirate.For example, an observer of this holiday  would greet friends not with "Hello," but with "Ahoy, matey!" The  holiday, and its observance, springs from a romanticized view of the Golden Age of Piracy. *Wik

2009  at the autumn meeting of the British Society for the History of Mathematics (BSHM), The Archimedes Codex by Reviel Netz and William Noel was awarded the Neumann Prize for the best book in the history of mathematics aimed a broad audience. Reviel Netz is Professor of Classics at Stanford University, California, and Dr William Noel is the curator of manuscripts and rare books at The Walters Art Museum in Baltimore, Maryland.
The prize was awarded for the first time this year and will henceforth be bestowed every two years. The prize is named after Dr Peter Neumann, Emeritus Fellow of The Queen’s College, Oxford, and a former president of the BSHM. He was awarded the OBE in 2008 for his services to education.
The Archimedes Codex is a biography of one of the ancient world’s greatest mathematicians Archimedes of Syracuse (c.287 BC – c.212 BC) and tells the story of the rediscovery of a 10th-century copy of some of his writings and drawings, which were found hidden beneath a 13th-century prayer book. *History Today, September 23, 2009

Winners to date (2023) are :

2021: Tony Royle. The Flying Mathematicians of World War I. 

2019: Martin Beech. Going Underground

2017: Jimmy Soni & Rob Goodman.  A Mind at Play 

2015: Sydney Padua, The Thrilling Adventures of Lovelace and Babbage

2013:  Jacqueline Stedall. The history of mathematics: A very short introduction

2011: Clifford A. Pickover, The Math Book

2009: Reviel Netz and William Noel, The Archimedes Codex


1749 Jean-Baptiste Joseph Delambre (19 Sep 1749; 18 Aug 1822)  He conducted a geodetic survey be-tween Dunkerque and Rodez which was instrumental in establishing the length of the meter. *VFR

1840 John Emory McClintock (19 Sept 1840 , 10 July 1916) for many years the leading actuary in America. He published 30 papers between 1868 and 1877 on actuarial questions. His publications were not confined to questions relating to life insurance policies however. He published about 22 papers on mathematical topics. One paper treats difference equations as differential equations of infinite order and others look at quintic equations which are soluble algebraically. He published A simplified solution of the cubic in 1900 in the Annals of Mathematics. Another work, On the nature and use of the functions employed in the recognition of quadratic residues (1902), published in the Transactions of the American Mathematical Society, is on quadratic residues.*SAU

1888 James Waddell Alexander (19 Sep 1888; 23 Sept 1971) American mathematician and a founder of the branch of mathematics originally known as analysis situs, now called topology. In 1912, he joined the faculty of the mathematics department at Princeton. Soon after, Alexander generalised the Jordan curve theorem and, in 1928, he discovered the Alexander polynomial which is much used in knot theory.*TIS

1908 Victor Frederick Weisskopf (September 19, 1908 – April 22, 2002) was an Austrian-born American theoretical physicist. He did postdoctoral work with Werner Heisenberg, Erwin Schrödinger, Wolfgang Pauli and Niels Bohr.[1] During World War II he worked at Los Alamos on the Manhattan Project to develop the atomic bomb, and later campaigned against the proliferation of nuclear weapons.
His brilliance in physics led to work with the great physicists exploring the atom, especially Niels Bohr, who mentored Weisskopf at his institute in Copenhagen. By the late 1930s, he realized that, as a Jew, he needed to get out of Europe. Bohr helped him find a position in the U.S.
In the 1930s and 1940s, 'Viki', as everyone called him, made major contributions to the development of quantum theory, especially in the area of Quantum Electrodynamics.[3] One of his few regrets was that his insecurity about his mathematical abilities may have cost him a Nobel prize when he did not publish results (which turned out to be correct) about what is now known as the Lamb shift. *Wik

1964  Simon Singh (19 September, 1964 - )In 1950 my parents emigrated to Taunton. A few years later they moved to Wellington, and that is where I was born. Somerset is a fertile ground for budding scientists. Just 5 miles from where I was born is the town of Milverton, the birthplace of Thomas Young, the polymath who made breakthroughs in a wide range of subjects. Most important of all, he advocated the wave theory of light. He studied at Emmanuel College Cambridge, and in due I course I attended the same college, but I failed to make any significant contributions to the foundations of physics.
Before starting my physics degree at Imperial College, London, I spent a year at GEC Hirst Research Centre, Wembley, working on gallium arsenide monolithic microwave integrated circuits. GEC were sponsoring me during my studies. It was an interesting year and I grew up a bit, but the main lesson I learned was that my future did not rest in industrial research and development.
My PhD in experimental particle physics was based at Cambridge University, but I spent most of my three years working at the European Centre for Particle Physics (CERN) in Geneva. I worked as part of the UA2 collaboration, which had previously won the Nobel Prize for discovering the W and Z bosons. It was a wonderful three years.
Particle physics was great fun. My three years at Cambridge and CERN were challenging and stimulating. However, I could see that there were people around me who were on a different planet when it came to understanding and researching physics, and it would be they who would go on to make their names as pioneers. As for me, it was time to change career. I had always enjoyed talking about and explaining science, so I took the decision to move towards a career in journalism and science communication. In particular, I have always loved television and felt that this was the most influential medium, so I started applying for a job at the BBC.  *From his personal biography on his web page. 
Simon Singh is the author of numerous popular science books, including the one below:


1710 Olaus Roemer, (25 Sep 1644 - 19 Sep 1710) Danish astronomer,  He was the first to measure the speed of light. *VFR  Astronomer who demonstrated conclusively that light travels at a finite speed. He measured the speed by precisely measuring the length of time between eclipses of Jupiter by one of its moons. This observation produces different results depending on the position of the earth in its orbit around the sun. He reasoned that meant light took longer to travel the greater distance when earth was traveling in its orbit away from Jupiter.*TIS

1761 Pieter van Musschenbroek (14 Mar 1692; 19 Sep 1761 at age 69) Dutch mathematician and physicist who invented the Leyden jar, the first effective device for storing static electricity. He grew up in a family that manufactured scientific instruments such as telescopes, microscopes and air pumps. Before Musschenbroek's invention, static electricity had been produced by Guericke using a sulphur ball, with minor effects. In Jan 1746, Musschenbroek placed water in a metal container suspended on silk cords, and led a brass wire through a cork into the water. He built up a charge in the water. When an unwary assistant touched the metal container and the brass wire, the discharge from this apparatus delivered a substantial shock of static electricity. The Leyden name is linked to the discovery having being made at the University of Leiden. *TIS

1843 Gaspard Gustave de Coriolis (21 May 1792, 19 Sept 1843) Coriolis is best remembered for the Coriolis force. He showed that the laws of motion could be used in a rotating frame of reference if an extra force called the Coriolis acceleration is added to the equations of motion. *SAU  

He was the first to apply the term travail (translated as "work") for the transfer of energy by a force acting through a distance.

Coriolis's name began to appear in the meteorological literature at the end of the 19th century, although the term "Coriolis force" was not used until the beginning of the 20th century. 

1935 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  (He is buried at the Park of the Cosmonauts' Museum, Kaluga Province, Russian Federation)

1968 Chester Floyd Carlson (8 Feb 1906, 19 Sep 1968) American physicist who invented xerography (22 Oct 1938), an electrostatic dry-copying process that found applications ranging from office copying to reproducing out-of-print books. The process involved sensitizing a photoconductive surface to light by giving it an electrostatic charge Carlson developed it between 1934 and 1938, and initially described it as electrophotography It was immediately protected by Carlson with an impenetrable web of patents, though it was not until 1944 that he was able to obtain funding for further development. In 1947 he sold the commercial rights for his invention to the Haloid Company, a small manufacturer of photographic paper (which later became the Xerox Corporation).*TIS

2010 Joseph Bernard Kruskal, Jr. (January 29, 1928 – September 19, 2010) was an American mathematician, statistician, computer scientist and psychometrician. He was a student at the University of Chicago and at Princeton University, where he completed his Ph.D. in 1954, nominally under Albert W. Tucker and Roger Lyndon, but de facto under Paul Erdős with whom he had two very short conversations.Kruskal has worked on well-quasi-orderings and multidimensional scaling.
He was a Fellow of the American Statistical Association, former president of the Psychometric Society, and former president of the Classification Society of North America.
In statistics, Kruskal's most influential work is his seminal contribution to the formulation of multidimensional scaling. In computer science, his best known work is Kruskal's algorithm for computing the minimal spanning tree (MST) of a weighted graph. In combinatorics, he is known for Kruskal's tree theorem (1960), which is also interesting from a mathematical logic perspective since it can only be proved nonconstructively. Kruskal also applied his work in linguistics, in an experimental lexicostatistical study of Indo-European languages, together with the linguists Isidore Dyen and Paul Black.
Kruskal was born in New York City to a successful fur wholesaler, Joseph B. Kruskal, Sr. His mother, Lillian Rose Vorhaus Kruskal Oppenheimer, became a noted promoter of Origami during the early era of television.  He died in Princeton. *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

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