Sunday, 22 September 2024

On This Day in Math - September 22

  




Nothing is too wonderful to be true if it be consistent with the laws of nature.


~Michael Faraday in his Laboratory Notebook

The 265th day of the year; 265 is !6 (sub-factorial 6), the number of ways that six ordered objects can be mis-ordered so that each is in the wrong spot. See Subfactorial 

The term "subfactorial "was introduced by Whitworth (1867 or 1878; Cajori 1993, p. 77). Euler (1809) calculated the first ten terms. For example, the only derangements of {1,2,3} are {2,3,1} and {3,1,2}, so !3=2  (Pssst, students... You can find !n by dividing n! by e, and rounding to nearest integer)

265 is the sum of two squares in two different ways, including one that is the sum of consecutive squares. \(265 = 3^2 + 16^2 = 11^2 + 12^2 \)

2652 is also the sum of two squares in two different ways, making 265 the hypotenuse of two Pythagorean Triangles. One of them is 23, 264, 265.

265 = 16^2 + 3^2 and 29^2 - 24^2,

265 is a semi-prime, 5 x 53. The sum of the digits of 265 is the same as the sum of the digits of its factors, sometimes called Joke numbers.

To form a 5x5 magic square with a constant of 265, take the standard 5x5 using 1-25, and add forty to each term. You can also multiply all the digits from 1-25 by four, then add one, using the numbers 5, 9, 13,....., 101 




EVENTS


1602 In a public address at T¨ubingen University, Michael Mastlin, Kepler’s teacher, on the basis of chronological research put Jesus’ birth more than four years before the conventional date of A.D. 1. This date is now generally accepted. *VFR


1636 From a letter by Fermat to Roberval, it is clear that Fermat conceived the idea of analytic geometry as early as 1629, yet he published nothing on the subject. [Struik, Source Book, p. 397] *VFR  In the same letter he found the first new pair of amicable numbers since the early Greeks found 220 & 284. Fermat's pair was 17296 & 18416. Two numbers are called amicable, if the sum of the aliquot divisors of each, sums to the other. *L E Dickson, History of Theory of Numbers




1792 This date is considered the beginning of the Republican Calendar of France, for on this date the Republic was proclaimed and this was also the date of the autumnal equinox in that year. The new calendar was not officially approved until 5 October 1793. *Cecil B. Read, “A book printed in the year VII,” The Mathematics Teacher, 59(1966), 138–140.


1822 “Jean-Francoise Champollion the younger wrote his famous Lettre `a Monsieur Dacier, secr´etaire perp´etuel de l’Acad´`ero¬emie royale des inscriptions et belles-lettres, relative a l’alphabet des hi´glyphes phon´etiques. On that day he opened the great book of Ancient Egypt, sealed for some two thousand years and now at last decipherable.” Quoted from p. 15 of Tutankhamen (1963) by Christiane Desroches-Noblecourt. *VFR


1986 In a decisive victory for the makers of a computer's insides, a federal judge ruled that code used to run computers and other electronic devices could be copyrighted like printed material.*CHM


2006 Britney Crystal Gallivan of Pomona, California was a keynote speaker at the September 22, 2006 National Council of Teachers of Mathematics convention. As a Junior in high school in 2002 she had disproved a commonly held mathematical myth that a piece of paper could not be folded more than eight times. Gallivan demonstrated that a single piece of toilet paper 4000 ft in length can be folded in half twelve times. Not only did she provide the empirical proof, but she also derived an equation that yielded the width of paper or length of paper necessary to fold a piece of paper of thickness t any n number of times. Wik







BIRTHS


1711 Thomas Wright (
22 September 1711 – 25 February 1786) was an English astronomer, mathematician, instrument maker, architect and garden designer. He was the first to describe the shape of the Milky Way and speculate that faint nebulae were distant galaxies.
Wright is best known for his publication An original theory or new hypothesis of the Universe (1750), in which he explains the appearance of the Milky Way as "an optical effect due to our immersion in what locally approximates to a flat layer of stars."
Another of Thomas Wright's ideas, which is often attributed to Kant, was that many faint nebulae are actually incredibly distant galaxies.*Wik




1759  William Playfair (22 September 1759 – 11 February 1823), a Scottish engineer and political economist, served as a secret agent on behalf of Great Britain during its war with France. The founder of graphical methods of statistics, Playfair invented several types of diagrams: in 1786 the line, area and bar chart of economic data, and in 1801 the pie chart and circle graph, used to show part-whole relations. As a secret agent, Playfair reported on the French Revolution and organized a clandestine counterfeiting operation in 1793 to collapse the French currency.

*Linda Hall org



1765 Paolo Ruffini (22 September 1765 – 10 May 1822) He anticipated Abel by providing an almost correct proof of the insolubility of the quintic. *VFR Italian mathematician and physician who made studies of equations that anticipated the algebraic theory of groups. 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 (He also published the method now often called Horner's method ,,, see Horner below)



1769 Louis Puissant (22 Sept 1769, 10 Jan 1843) He is best remembered for his invention of a new map projection for a new map of France, and he was involved in the production of the map. The map was produced with considerable detail, the projection used spherical trigonometry, truncated power series and differential geometry. Puissant wrote on geodesy, the shape of the earth and spherical trigonometry. *SAU




1791 Michael Faraday born. (22 Sep 1791; 25 Aug 1867) English physicist and chemist whose many experiments contributed greatly to the understanding of electromagnetism. Although one of the greatest experimentalists, he was largely self-educated. Appointed by Sir Humphry Davy as his assistant at the Royal Institution, Faraday initially concentrated on analytical chemistry, and discovered benzene in 1825. His most important work was in electromagnetism, in which field he demonstrated electromagnetic rotation and discovered electromagnetic induction (the key to the development of the electric dynamo and motor). He also discovered diamagnetism and the laws of electrolysis. He published pioneering papers that led to the practical use of electricity, and he advocated the use of electric light in lighthouses. *TIS



1824 Robert Patterson (May 30, 1743 – July 22, 1824) was an Irish-American mathematician and director of the United States Mint from 1806 to 1824. He was a professor of mathematics at the University of Pennsylvania from 1779 to 1810, professor of natural history and mathematics and vice provost from 1810 to 1813. At the request of Thomas Jefferson, he advised Meriwether Lewis on the purchase and usage of navigational equipment for the Lewis and Clark Expedition.
He taught at schools in Hinkletown and Northampton, Pennsylvania. He moved to Philadelphia and opened a school to teach navigational mathematics to ship captains. One of his students was Andrew Ellicott who became a notable surveyor. He operated a country store in Bridgeton, New Jersey for two years.

In 1774, he became principal of Wilmington Academy[3] in Wilmington, Delaware. Classes were suspended at the outbreak of the American Revolutionary War[1] and he served in the war for about three years as a military instructor, an assistant surgeon, adjutant to the 1st Delaware Regiment under John Haslet,  and as a brigade major.

He worked as a professor of mathematics at the University of Pennsylvania from 1799 to 1810 as well as professor of natural history and mathematics and vice provost from 1810 to 1813. He was elected president of Philadelphia's Select Council in 1799.

He was elected a member of the American Philosophical Society in 1783, served as secretary in 1784, vice-president in 1799 and president from 1819 to 1823. He published The Newtonian System (1808) and edited various works on mathematics and physics.[9]

In 1803, Thomas Jefferson wrote a letter to Patterson requesting that he meet with Meriwether Lewis and provide further instruction and advice on calculating latitude and longitude during the Lewis and Clark Expedition. Patterson was one of five American Philosophical Society members who were consulted by Lewis prior to the expedition. In anticipation of the visit from Lewis, Patterson began to calculate astronomical formulas for usage on the expedition for the calculation of longitude from lunar observations and for altitude and time.

Patterson advised Lewis on the navigational equipment to purchase for the expedition and trained him on their usage. Jefferson recommended that Lewis use a theodolite for the calculation of latitude and longitude, however Patterson recommended usage of a sextant instead since it would handle better under the rigors of field work. Patterson advised Lewis on the purchase of a chronometer necessary for calculation of latitude and longitude as well as other techniques in case the chronometer malfunctioned. The chronometer was purchased in Philadelphia for $250, the most expensive single item purchased for the expedition.

Patterson was interested in ciphers and regularly exchanged coded correspondence with Thomas Jefferson. One of Patterson's ciphers included in a December 19, 1801, dated letter to Jefferson was decoded in 2007 by Lawren Smithline. The cipher consists of 7 digit pairs and is decoded by decrypting 7 blocks at a time. The cipher was of the Declaration of Independence, of which Jefferson was the primary author. Patterson called it his "perfect cipher" and Jefferson considered adopting it for government use.

Jefferson appointed Patterson as director of the United States Mint in 1805 and he served in this role until his death. Patterson was one of the founders of the Franklin Institute in Philadelphia and served as the first chairman of their board of managers.

He died on July 22, 1824, and was initially interred in a churchyard in Philadelphia and reinterred in 1844 at Laurel Hill Cemetery along with his wife after her death.




1922 Chen Ning Yang (22 Sep 1922, )Chinese-American theoretical physicist who shared the 1957 Nobel Prize for Physics (with Tsung-Dao Lee) for a ground-breaking theory that the weak force between elementary particles did not conserve parity, thus violating a previously accepted law of physics. (Parity holds that the laws of physics are the same in a right-handed system of coordinates as in a left-handed system.) The theory was subsequently confirmed experimentally by Chien-Shiung Wu in observations of beta decay. Yang is also known for his collaboration with Robert L. Mills. They developed the Yang-Mills fields theory - a mathematical idea for describing interactions among elementary particles and fields*TIS



1959 Saul Perlmutter (born September 22, 1959) is a U.S. astrophysicist, a professor of physics at the University of California, Berkeley, where he holds the Franklin W. and Karen Weber Dabby Chair, and head of the International Supernova Cosmology Project at the Lawrence Berkeley National Laboratory.

He shared (with Brian P. Schmidt and Adam G. Riess) the 2011 Nobel Prize in Physics for “the discovery of the accelerating expansion of the Universe through observations of distant supernovae.” For this purpose, he had co-founded (1988) and led the international Supernova Cosmology Project based at the Lawrence Berkeley National Laboratory. *TiS





DEATHS



1703 Vincento Viviani died. His problem of cutting four congruent windows in a hemispherical cupolo so that the remainder was quadrable led to Euler’s development of the double integral. *VFR The leading geometer of his time, who founded the Accademia del Cimento. As one of the first important scientific societies, this organization came before England's Royal Society. In 1639, at age 17, he was a pupil of Torricelli and became the student, secretary and assistant of Galileo (now blind) in Arcetri, until Galileo died in 1642. During his long career, Viviani published a number of books on mathematical and scientific subjects. He edited the first edition of Galileo's collected works (1655-1656), and worked tirelessly to have his master's memory rehabilitated. In 1660, together with Borelli, he measured the velocity of sound by timing the difference between the flash and the sound of a cannon. They obtained the value of 350 metres per second. *TIS



1837 William George Horner (9 June 1786 – 22 September 1837) was a British mathematician and schoolmaster. The invention of the zoetrope, in 1834 and under a different name (Daedaleum), has been attributed to him. *Wik
Horner is largely remembered only for the method, Horner's method, of solving algebraic equations ascribed to him by Augustus De Morgan and others. He published on the subject in the Philosophical Transactions of the Royal Society of London in 1819, submitting his article on 1 July. But Fuller has pointed out that, contrary to De Morgan's assertion, this article does not contain the method, although one published by Horner in 1830 does. Fuller has found that Theophilus Holdred, a London watchmaker, did publish the method in 1820 and comments"At first sight, Horner's plagiarism seems like direct theft. However, he was apparently of an eccentric and obsessive nature ... Such a man could easily first persuade himself that a rival method was not greatly different from his own, and then, by degrees, come to believe that he himself had invented it. "
This discussion is somewhat moot because the method was anticipated in 19th century Europe by Paolo Ruffini (What a strange coincidence that he dies on Ruffini's birthdate) , but had, in any case, been considered by Zhu Shijie in China in the thirteenth century. In the 19th and early 20th centuries, Horner's method had a prominent place in English and American textbooks on algebra. It is not unreasonable to ask why that should be. The answer lies simply with De Morgan who gave Horner's name and method wide coverage in many articles which he wrote.
Horner made other mathematical contributions, however, publishing a series of papers on transforming and solving algebraic equations, and he also applied similar techniques to functional equations. It is also worth noting that he gave a solution to what has come to be known as the "butterfly problem" which appeared in The Gentleman's Diary for 1815. The problem is the following:-
Let M be the midpoint of a chord PQ of a circle, through which two other chords AB and CD are drawn. Suppose AD cuts PQ at X and BC cuts PQ at Y. Prove that M is also the midpoint of XY.


The butterfly problem, whose name becomes clear on looking at the figure, has led to a wide range of interesting solutions. Finally we mention that Horner published Natural magic, a familiar exposition of a forgotten fact in optics (1832). *SAU






1956 Frederick Soddy (2 Sep 1877, 22 Sep 1956). English chemist and physicist who received the Nobel Prize for Chemistry in 1921 for investigating radioactive substances. He suggested that different elements produced in different radioactive transformations were capable of occupying the same place on the Periodic Table, and on 18 Feb 1913 he named such species "isotopes" from Greek words meaning "same place." He is credited, along with others, with the discovery of the element protactinium in 1917 *TIS
Soddy is also the author of a mathematical poem about the solution to Descartes' four tangent circles theorem from the letter to Princess Elisabeth of Bohemia. The poem is called The Kiss Precise, and begins:

For pairs of lips to kiss maybe
Involves no trigonometry.
'Tis not so when four circles kiss
Each one the other three.
To bring this off the four must be
As three in one or one in three.
If one in three, beyond a doubt
Each gets three kisses from without.
If three in one, then is that one
Thrice kissed internally.


The complete poem and more about the history of the problem can be found here.








1970 Vojtěch Jarník (22 Dec 1897 , 22 Sept 1970) a Czech mathematician. 

In 1929, Vojtěch Jarník was appointed an extraordinary professor of mathematics at Charles University and six years later a full professor. He worked at the university until 1967 , when he retired. After the establishment of the Czechoslovak Academy of Sciences, he was appointed academician in 1952 and became the first chairman of its mathematical-physical section.

Vojtěch Jarník was interested in the history of mathematics, he paid special attention to the study of Bernard Bolzan's work . The main content of his work was in the areas of number theory and  mathematical analysis .

His main area of work was in number theory and mathematical analysis; he proved a number of results on lattice point problems. He also developed the graph theory algorithm known as Prim's algorithm. The Vojtěch Jarník International Mathematical Competition, held each year in Ostrava, is named in his honor. *Wik





1979 Charles Ehresmann (19 April 1905, 22 Sept 1979) He was one of the creators of differential topology. Beginning in 1941, Ehresmann made major contributions toward establishing the current view of fibre spaces, manifolds, foliations and jets. His work in the creation and development of fibre spaces followed on from the study of a special case made earlier by Seifert and Whitney.
After 1957 Ehresmann became a leader in category theory and he worked in this area for 20 years. His principal achievements in this area concern local categories and structures defined by atlases, and germs of categories. The article [3] contains a list of 139 articles written by Ehresmann during his productive career as well as listing several volumes which he edited. *SAU

Charles Ehresmann (right) at the topology conference 1949 in Oberwolfach, together with Paul Vincensini (middle) and Georges Reeb (left)



1979 Otto Robert Frisch OBE FRS (1 October 1904 – 22 September 1979) was an Austrian-born British physicist who worked on nuclear physics. With Otto Stern and Immanuel Estermann he first measured the magnetic moment of the proton. 

With his aunt Lise Meitner, they described the division of neutron-bombarded uranium into lighter elements. He named the process fission, borrowing a term from biology (1939). At the time, Meitner was working in Stockholm and Frisch (1934-39) at Copenhagen under Niels Bohr, who brought their observation to the attention of Albert Einstein and others in the United States. He did research with James Chadwick 1940-43, and was head of the Critical Assembly Group on the Los Alamos project 1943-46. After World War II, Frisch became a science writer on atomic physics for the layman.*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

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