## Wednesday 22 November 2023

### On This Day in Math - November 22

Ulam Spiral
PrimeSpiral_1000.gif
mathworld.wolfram.com

I believe there are
15,747,724,136,275,002,577,605,653,961,181,555,468,044,717,
914,527,116,709,366,231,025,076,185,631,031,296
protons in the universe,
and the same number of electrons.
— Sir Arthur Stanley Eddington

The 326th day of the year; 326 is the maximum number of pieces that may be produced in a pizza with 25 straight cuts. These are sometimes called "lazy caterer numbers" and more generally they are centered polygonal numbers.

326 is also the sum of the first 14 consecutive odd primes: 326 = 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47. *MAA

326 prefixed or followed by any digit still remains composite.  *Derek's Daily Math

EVENTS

1670  Rene Francois de Sluse had discovered a method of tangents for polynomials f(x)=0 that was well-known throughout the continent by 1650.  On 22 Nov, 1670 (NS) he wrote to Oldenburg about a method by Isaac Barrow published in 1669, that Sluse had just read, commenting that is method was similar to his own earlier method.  He wrote that, "...monachos, tangents, maxima, and minima are the same thing." Sluse's method was essentially identical to the method of Jan Hudde also well known throughout the continent  by mid-century.  *Correspondence of John Wallis, volume IV.
"When they state that Collins had been four years in circulating the letter in which the method of fluxions was sufficiently described to any intelligent person, they suppress two facts: first, that the letter itself was in consequence of Newton's learning that Sluse had a method of tangents; secondly, that it revealed no more than Sluse had done. ...this method of Sluse is never allowed to appear ...Sluse wrote an account of the method which he had previously signified to Collins, for the Royal Society, for whom it was printed. The rule is precisely that of Newton... To have given this would have shown the world that the grand communication which was asserted to have been sent to Leibniz in June 1676 might have been seen in print, and learned from Sluse, at any time in the previous years: accordingly it was buried under reference. ...Leibniz had seen Hudde at Amsterdam, and had found that Hudde was in possession of even more than Sluse." *Augustus De Morgan

 *Wik

1850 J J Sylvester called to the Bar. Rather than practicing law he gave private instruction in mathematics, and counted among his pupils Florence Nightingale. [Osiris, 1(1936), 102] *VFR (This idea of Sylvester tutoring Nightingale, to the best of my knowledge, originates from the Herbert Baker obituary. Karen Hunger Parshall, among others, has questioned the accuracy of this statement.)

1906 An International Radiotelegraphic Convention adopted the S.O.S radio distress signal, ... The Convention met in Berlin in 1906. This body signed an international agreement on November 3, 1906, with an effective date of July 1, 1908. An extensive collection of Service Regulations was included to supplement the Convention, and in particular Article XVI adopted Germany's Notzeichen distress signal as the international standard, stating: "Ships in distress shall use the following signal: · · · — — — · · · repeated at brief intervals".
The first well documented use of the SOS distress call is by the Arapahoe on August 11, 1909, when it suffered a broken shaft in the Atlantic Ocean, near Cape Hatteras, North Carolina. However, an article titled "Notable Achievements of Wireless" in the September, 1910 Modern Electrics suggests that an earlier SOS distress call was transmitted by the Cunard liner Slavonia, on June 10, 1909.
[The wireless operator aboard S.S. Arapahoe, T. D. Haubner, radioed for help. A few months later, Haubner on the S.S. Arapahoe received an SOS from the SS Iroquois, the second use of SOS in America.(*TIS)]
The first radio distress call to be adopted appears to have been "CQD", by the Marconi International Marine Communication Company​, for Marconi-operated shipboard stations. It was announced on January 7, 1904 by the company's "Circular 57" that "...on and after the 1st February, 1904, the call to be given by ships in distress or in any way requiring assistance shall be 'C.Q.D.'." ("CQ" was a general call to all stations; amateur or "ham" radio operators still use it today when soliciting a contact with any station that hears the call.) *Citizens Compendium

Microsoft’s Xbox 360, the second in the Xbox line, is released in the US and Canada after a viral marketing campaign and intense hype. Initially, eighteen titles were available at launch, and of those, Call of Duty 2 was the best seller for the new console. An updated version of Xbox Live, which allowed online multi-player gaming and media streaming, was a major selling point for the 360, one of the top-selling consoles of all time. The 360’s main competitors were Nintendo’s Wii and Sony’s PlayStation 3, all of which were 7th generation video game consoles. Its successor, the Xbox One, was released 8 years later.

2022, Jan Łukasiewicz's remains were reburied in Warsaw's Old Powązki Cemetery. He had died and been buried in Dublin in 1956. Łukasiewicz is best known as the inventor of "Polish notation",  which allowed expressions to be written unambiguously without the use of brackets. It  is a mathematical notation in which operators precede their operands, such as +3 4 for 3+4.  In postfix notation 3  4  + .
Polish notation, usually in postfix form, is the chosen notation of certain calculators, notably from Hewlett-Packard. 2(3+4)  could be written as  3   4  +  2  x without brackets.

Warsaw's Old Powązki Cemetery

BIRTHS

1796 Charles Bonnycastle (22 Nov 1796 - 31 Oct, 1840). The University of Virginia's second Professor of Mathematics, Charles Bonnycastle, was born in Woolwich, England. His father, John, was Professor of Mathematics at the Royal Military Academy there, and so Charles grew up and received his education in an environment that very much influenced his own subsequent career. The contributions that the son made to the thirteenth edition of his father's textbook, Introduction to Algebra (1824), in fact, augmented the credentials he presented to Francis Walker Gilmer, agent for the newly forming University of Virginia.
Bonnycastle actually came to the University at its opening in 1825 as the first professor, not of mathematics, but of natural philosophy (as physics was then called). When Thomas Key, the first Professor of Mathematics, resigned to return to his native England, Bonnycastle shifted over to the mathematical chair and remained in that post until his untimely death on 31 October 1840 at the age of only forty-three. "Old Bonny," as he was fondly called by the students, moved away from what was increasingly becoming the antiquated synthetic approach to mathematical pedagogy that had been so typical of Oxbridge mathematical teaching in the eighteenth and early nineteenth centuries and introduced the more avant-garde analytic approach of late eighteenth-century French authors such as Silvestre Lacroix. In 1834, he published his own textbook, Inductive Geometry, in which he aimed to unite the best of the synthetic and the analytic approaches to geometry for the college- and university-level audience. Bonnycastle also contributed works on mathematical and physical topics to the Transactions of the American Philosophical Society, one of the few venues available in early nineteenth-century America for the publication of original work in the sciences.
Bonnycastle apparently also entrusted a number of mathematical papers to his friend, Princeton physics professor and (after 1846) first Secretary of the Smithsonian Institution, Joseph Henry. Shortly before his death in 1878, Henry deposited these in the library at the University of Virginia. They did not survive the infamous Rotunda fire of 1895. *History of the U V Math Dept. He was buried in University of Virginia Cemetery, Charlottesville, Virginia. His gravestone reads:
Sacred to the memory of
Charles Bonnycastle
late Professor of Mathematics
in the University of Virginia
who was born in London
on the 22nd day of November 1796
was made professor in the University in 1825
and continued in this station until his death
on the 31st of October 1840.
For Michigan residents around Kalamazoo, Charles Bonnycastle's brief stay in the area with his brother Humphrey is still marked by Bonniecastle Lake west of the city.

1803 Giusto Bellavitis (22 Nov 1803 in Bassano, Vicenza, Italy - 6 Nov 1880 in Tezze (near Bassano) Italy ) Bellavitis solved various mechanical problems by original methods, among them Hamilton's quaternions. He developed very personal critical observations about the calculus of probabilities and the theory of errors. He also explored physics, especially optics and electrology, and chemistry. As a young man, Bellavitis weighted the problem of a universal scientific language and published a paper on this subject in 1863. He also devoted time to the history of mathematics and, among other things, he vindicated Cataldi by attributing the invention of continued fractions to him. *SAU
According to Charles Laisant,
"His principle achievement, which marks his place, in the future and the present, among the names of geometers that will endure, is the invention of the method of equipollences, a new method of analytic geometry that is both philosophical and fruitful."
Bellavitis anticipated the idea of a Euclidean vector with his notion of equipollence. Two line segments AB and CD are equipollent if they are parallel and have the same length and direction. The relation is denoted AB + BC ≏  AC. In modern terminology, this relation between line segments is an example of an equivalence relation.

 *Wik

1840 Émile Michel Hyacinthe Lemoine (22 Nov 1840 in Quimper, France - 21 Feb 1912 in Paris, France) Lemoine work in mathematics was mainly on geometry. He founded a
new study of properties of a triangle in a paper of 1873 where he studied the point of intersection of the symmedians of a triangle. He had been a founder member of the Association Française pour l'Avancement des Sciences and it was at a meeting of the Association in 1873 in Lyon that he presented his work on the symmedians.
A symmedian of a triangle from vertex A is obtained by reflecting the median from A in the bisector of the angle A. He proved that the symmedians are concurrent, the point where they meet now being called the Lemoine point. Among other results on symmedians in Lemoine's 1873 paper is the result that the symmedian from the vertex A cuts the side BC of the triangle in the ratio of the squares of the sides AC and AB. He also proved that if parallels are drawn through the Lemoine point parallel to the three sides of the triangle then the six points lie on a circle, now called the Lemoine circle. Its centre is at the mid-point of the line joining the Lemoine point to the circumcentre of the triangle. Lemoine gave up active mathematical research in 1895 but continued to support the subject. He had helped to found a mathematical journal, L'intermédiaire des mathématiciens., in 1894 and he became its first editor, a role he held for many years. *SAU
Image:  A triangle with medians (black), angle bisectors (dotted) and symmedians (red). The symmedians intersect in the symmedian point L, the angle bisectors in the incenter I and the medians in the centroid G.

 *Wik

1904 Louis-Eugène-Félix Néel (22 Nov 1904; 17 Nov 2000) French physicist, corecipient (with the Swedish astrophysicist Hannes Alfvén) of the Nobel Prize for Physics in 1970 for his pioneering studies of the magnetic properties of solids. His contributions to solid-state physics have found numerous useful applications, particularly in the development of improved computer memory units. About 1930 he suggested that a new form of magnetic behavior might exist - called antiferromagnetism. Above a certain temperature (the Néel temperature) this behaviour stops. Néel pointed out (1947) that materials could also exist showing ferrimagnetism. Néel has also given an explanation of the weak magnetism of certain rocks, making possible the study of the past history of the Earth's magnetic field.*TIS

DEATHS

1606  Henry Billingsley a merchant, amateur linguist, and Lord Mayor of London, died Nov. 22, 1606; we do not know the date or even the year of his birth.  In 1570, long before he became mayor of London, Billingsley published the first English translation of Euclid, which he called Elements of Geometrie.  The book contained a mathematical preface by the renowned John Dee, was published by the eminent London printer John Day, and is famous mostly because of the pop-up geometrical figures that are spread throughout Book 11, on solid geometry. Dee has received quite a bit of attention for his preface (which is not about Euclid but about the proper education of a natural philosopher), and Day has received credit as well for the printing (and the pop-ups) – indeed, both Dee and Day have been featured here as Scientists of the Say.  But Billingsley has generally not received his proper share of the credit.  Since mayors of London have seldom been scholars, it has usually been assumed either that Dee did the translation, or that Billingsley had considerable help from a real scholar.
However, we now know – and should have known since 1879 – that not only did Billingsley make the translation himself, he did it from the original Greek, rather than from one of the Latin translations from Arabic that were available.  We know this because the actual copy of the Greek edition that Billingsley used, printed in Basel in 1533, survives in the Princeton University Library.  Bound with it is a 1558 Latin translation of Euclid’s Elements that has Billingsley’s beautiful signature right on the title page.  And the Greek edition of 1533 has copious annotations and corrections in Greek in the same neat hand that is clearly Billingsley’s.  There seems to  be no doubt that Billingsley read Greek well, made his own translation, and then compared it with the translation of 1558, in order to produce the best text possible.  *Linda Hall Org

1784 Paolo Frisi (13 Apr 1728, 22 Nov 1784) Italian mathematician, astronomer, and physicist who is best known for his work in hydraulics (he designed a canal between Milan and Pavia). He was, however, the first to introduce the lightning conductor into Italy. His most significant contributions to science, however, were in the compilation, interpretation, and dissemination of the work of other scientists, such as Galileo Galilei and Sir Isaac Newton. His work on astronomy was based on Newton's theory of gravitation, studying the motion of the earth (De moto diurno terrae). He also studied the physical causes for the shape and the size of the earth using the theory of gravity (Disquisitio mathematica, 1751) and tackled the difficult problem of the motion of the moon. *TIS

1880 James Craig Watson (January 28, 1838 – November 22, 1880) was a Canadian-American astronomer born in the village of Fingal, Ontario Canada. His family relocated to Ann Arbor, Michigan in 1850.
At age 15 he was matriculated at the University of Michigan, where he studied the classical languages. He later was lectured in astronomy by professor Franz Brünnow.
He was the second director of Detroit Observatory (from 1863 to 1879), succeeding Brünnow. He wrote the textbook Theoretical Astronomy in 1868.
He discovered 22 asteroids, beginning with 79 Eurynome in 1863. One of his asteroid discoveries, 139 Juewa was made in Beijing when Watson was there to observe the 1874 transit of Venus. The name Juewa was chosen by Chinese officials (瑞華, or in modern pinyin, ruìhuá). Another was 121 Hermione in 1872, from Ann Arbor, Michigan, and this asteroid was found to have a small asteroid moon in 2002.
He was a strong believer in the existence of the planet Vulcan, a hypothetical planet closer to the Sun than Mercury, which is now known not to exist (however the existence of small Vulcanoid planetoids remains a possibility). He believed he had seen such two such planets during a July 1878 solar eclipse in Wyoming.
He died of peritonitis at the age of only 42. He had amassed a considerable amount of money through non-astronomical business activities. By bequest he established the James Craig Watson Medal, awarded every three years by the National Academy of Sciences for contributions to astronomy.
The asteroid 729 Watsonia is named in his honour, as is the lunar crater Watson. *Wik

1896 George Washington Gale Ferris Jr. (February 14, 1859,  Galesburg, Illinois - November 22, 1896) was an American civil engineer. He is mostly known for creating the original Ferris Wheel for the 1893 Chicago World's Columbian Exposition.
After a childhood in Nevada, he attended school in California, and then studied engineering at Rensselaer Polytechnic Institute (RPI) in New York, an institution that turned out many of American's top engineers at the time.  Ferris was interested in the engineering potential of structural steel, and he established a company in Pittsburgh to test structural steel and to build bridges, starting with one over the Monongahela River at 6th St. in Pittsburgh (since demolished, like all of the Pittsburgh river bridges of the 1880s and 1890s).  He was apparently very good at his job and a genius with steel.
In 1891, the World’s Columbian Exposition was getting ready to open on the Midway in Chicago in the spring of 1893, and the Director felt that they lacked a “wow factor”, like the Eiffel tower that made its debut at the Paris Exposition in 1889.  So he issued a challenge to the nation's engineers: what can we build at our Exposition to trump the French?  There were not interested in a tower, even if taller.  Ferris had apparently already had an idea for a vertical wheel to carry sightseers up into the air, but now he began to think more grandly, and he proposed a gigantic version of his wheel to the fair organizers.  There were initial questions about safety, and whether it would work, but Ferris was persuasive, and apparently his idea was better that the proposals of anyone else, and his idea was finally approved.  However, he would have to bear construction costs himself, and even worse, it was now mid-December 1892, and the exposition was set to open four months later.
The Ferris wheel drew immense crowds for the six months of the fair, carrying 1.5 million passengers and pulling in $750,000 at fifty cents a pop. Ferris became America’s most famous engineer almost overnight, and he was only 34 years old. But it was one of the few bright spots in the rest of his life. There was considerable contentiousness between the Exposition committee and Ferris's company as to how profits were to be distributed, once receipts paid off the cost of construction (which was about$364,000), and Ferris came out of the lawsuits much poorer than he expected.  He was certainly not happy when Chicago dismantled the Wheel after the fair closed, although it was re-erected in Lincoln Park as a sight-seeing attraction.  Apparently, Chicagoans had a more short-sighted view of their monuments than Parisians, who allowed the Eiffel Tower to stand right where it was built.  Ferris’s health had suffered during the ordeal of construction and went further downhill during the subsequent litigation.  Then his wife left him.  And in 1896, he came down with typhoid fever; he was hospitalized, and breathed his last on Nov. 22, 1896.  He was 37 years old. *Linda Hall Org

1907 Asaph Hall (15 Oct 1829; 22 Nov 1907) American astronomer, discovered and named the two moons of Mars, Phobos and Deimos, and calculated their orbits.Born in Goshen, Conn. and apprenticed as a carpenter at age 16, he had a passion for geometry and algebra. Hall obtained a position at the Harvard Observatory in Cambridge, Mass. in 1857 and became an expert computer of orbits. In August 1862, he joined the staff of the Naval Observatory in Washington, D.C. where he made his discoveries, in mid- Aug 1877, using the Observatory's 26-inch "Great Equatorial" refracting telescope, then the largest of its kind in the world. He stayed there 30 years until 1891. His son, Asaph Hall, Jr., followed him and worked at the Observatory at various times between 1882-1929.*TIS

1944 Sir Arthur Stanley Eddington (28 Dec 1882, 22 Nov 1944) English astrophysicist, and mathematician known for his work on the motion, distribution, evolution and structure of stars. He also interpreted Einstein's general theory of relativity. He was one of the first to suggest (1917) conversion of matter into radiation powered the stars. In 1919, he led a solar eclipse expedition which confirmed the predicted bending of starlight by gravity. He developed an equation for radiation pressure. In 1924, he derived an important mass-luminosity relation. He also studied pulsations in Cepheid variables, and the very high densities of white dwarfs. He sought fundamental relationships between the principal physical constants. Eddington wrote many books for the general reader, including Stars And Atoms  . *TIS  One of my favorite stories about Eddington is this one: Ludwick Silberstein approached Eddington and told him that people believed he was one of only three people in the world who understood general relativity, and that included Einstein. When Eddington didn't respond for a moment he prodded, come on, don't be modest, and Eddington replied, "Oh, no.  It's not that.  I was just trying to figure out who the third was?"  *Mario Livio, Brilliant Blunders
Image:One of Eddington's photographs of the total solar eclipse of 29 May 1919, presented in his 1920 paper announcing its success, confirming Einstein's theory that light "bends"
 *Wik

1986 Nikolai Grigor'evich Chudakov (14 Dec 1904 in Lysovsk, Novo-Burassk, Saratov, Russia - 22 Nov 1986 in Saratov, Russia) Chudakov established a number of important results in number theory. He gave an estimate for the bounds of the zeta-function in the critical strip using techniques which had been introduced a few years earlier by Vinogradov. As a consequence of this work he was able to give a substantially improved remainder term in the asymptotic formula for the number of primes less than a fixed number N. Also, by these method, he improved the estimate for the difference between two consecutive primes. In his later work he extended these results to apply to arbitrary arithmetic progressions. In 1947 Chudakov published On Goldbach-Vinogradov's theorem in the Annals of Mathematics. In this paper he proves Vinogradov's theorem that every large odd integer is representable as a sum of three odd primes. *SAU

1996 Garrett Birkhoff (January 19, 1911, Princeton, New Jersey, USA – November 22, 1996, Water Mill, New York, USA) was an American mathematician. He is best known for his work in lattice theory.During the 1930s, Birkhoff, along with his Harvard colleagues Marshall Stone and Saunders Mac Lane, substantially advanced American teaching and research in abstract algebra. During and after World War II, Birkhoff's interests gravitated towards what he called "engineering" mathematics. Birkhoff's research and consulting work (notably for General Motors) developed computational methods besides numerical linear algebra, notably the representation of smooth curves via cubic splines.
The mathematician George Birkhoff (1884–1944) was his father.*Wik

2007 Andrew Ronald Mitchell (22 June 1921 – 22 November 2007), popularly known as Ron Mitchell, was a British applied mathematician and numerical analyst. He was a professor of mathematics at the University of St Andrews, Dundee, Scotland. He was known for his contribution to the field of numerical analysis of partial differential equations in general and finite difference method and finite element method in particular. Mitchell has authored several influential books on numerical solution of partial differential equations, including "The Finite Element Analysis in Partial Differential Equations" with Richard Wait and "The Finite Difference Method in Partial Differential Equations" with David F. Griffiths.*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