## Sunday, 15 November 2020

### On This Day in Math - November 15

We see it [the as-yet unseen, probable new planet, Neptune] as Columbus saw America from the coast of Spain. Its movements have been felt, trembling along the far-reaching line of our analysis with a certainty hardly inferior to that of ocular demonstration.
~Sir William Herschel

The 320th day of the year; 320 is the maximum value of the determinant of a 10x10 binary matrix (all entries are either one or zero). (Students might explore all possible determinants of smaller matrices looking for a pattern)

320!+1 is prime.

320 = 8^2 + 16^2 = 2^8 + 2^6=4^4 + 4^3

EVENTS

1593 Giovanni Antonio Magini responds to a claim by Thomas Fincke that he had made an error in his tables because they were not in agreement with the list by Ptolemy. The letter contains Magini's step by step work and challenges Fincke to find an error. Magini was one of the first to use decimals, using a comma in 1592, almost a full year before Clavius used of the decimal point was published. He may actually have gotten his method from an even lesser known mathematician, the Italian Knight, Hercules Butrigarius (I would love to have any information you know on this man) *J. Ginsburg, Scripta Mathematica 1932

1638 It appears that the ﬁrst mathematician of note to suggest that an odd perfect number exists was R. Descartes. In a letter to Mersenne dated November 15, 1638, he announced that he could demonstrate that every odd perfect number must be of the form ps2, where p is a prime. Furthermore, he stated that he saw no reason to prevent the existence of an odd perfect number and cited the example of p = 22021 and s = 3 • 7 • 11 • 13 as evidence. For, ps2 would be an odd perfect number provided one pretends that 22021 is prime. *John Jaroma, Irish Math. Soc. Bulletin 63 (2009), 33–43  In the same letter, Descartes gives a method for producing multiply perfect numbers of a higher ${P}_{4}$  order (the sum of the divisors including the number itself sum to four times the number)  from those of a lower order ${P}_{3}$ (120 is an early known example).
He states
I) if n is a  ${P}_{3}$ not divisible by 3, then 3n is a  ${P}_{4}$.
II) if n is a  ${P}_{3}$  divisible by 3, but not by 5 or 9,  then 45n is a a  ${P}_{4}$
and three more such rules. *L E Dickson, The History of the Theory of Numbers

1747 "Clairaut, at a public session of the [French] Academy, announced in rather pompous phrases that the Newtonian Theory of gravity was false!” *VFR Euler and d’Alembert simultaneously came to the same conclusion as all had been working on the motion of the moon as a special case of the three body problem. One of the boldest attempts to reconcile the observed and theoretical descriptions of the moon's motion was made not by Euler, but Clairaut, who announced in November 15, 1747 at a public session in the French Academy of Sciences that Newton's theory of gravity was wrong.
Clairaut suggested that the strength of gravity was proportional not to 1/r2, but the more complicated 1/r2 +c/r4 for some constant c. Over large distances, the c/r4 term would effectively disappear, accounting for the utility of the inverse square law over large distances. He then began trying to find a value of c which could account for the moon's motion. He would continue to pursue this idea until May 17, 1749, when he made an equally dramatic announcement in which he claimed that Newton was right after all.

1763 Charles Mason and Jeremiah Dixon arrive in Philadelphia for their work on establishing the boundaries of Pennsylvania, Maryland, Delaware, and Virginia (now West Va.) *@CMason1763

1783 At the Paris Academie des Sciences, Etienne de Montgolﬁer discusses in mathematical terms the problem of navigating balloons.*VFR

1819 The Cambridge Philosophical Society was founded in 1819 'for the purpose of promoting scientific inquiry'. It became a Body Corporate by virtue of a Charter granted by King William IV in 1832. Instrumental in the foundation were William Whewell, John Henslow, and Adam Sedgwick, and George Peacock.

1957 Brazil issued a stamp commemorating the centenary of the death of Auguste Compte, French mathematician and philosopher. [Scott #854]. *VFR

1971 The first advertisement for a microprocessor, the Intel 4004, appears in the journal Electronic News. The chip was designed by a four-person team at Intel, a start-up company founded by Gordon Moore​ and Robert Noyce​ a few years earlier. Intel engineers Federico Faggin​, Ted Hoff​, Stan Mazor, and Matushoshi Shima designed the 4004 while undertaking a custom circuit design for Busicom, a Japanese calculator maker. The Intel 4004​ had 2,250 transistors, handling data in four-bit chunks, and could perform 60,000 operations per second. *CHM

BIRTHS

1688 Louis Castel was a French mathematician who was a strong opponent of Newton's philosophy.Castel's physics was based on reason, not observation. He also opposed Newton on religious grounds, believing Newtonian theory to be materialistic. He made this clear in an early article written in the Journal de Trévoux in 1721 in which he stated that Newton had been influenced by Democritus in substituting the void for divine intelligence.Castel's system to replace the theories of Newton did not bring him fame. However he did achieve this from a rather unusual source. In the November 1725 issue of Mercure de France he set out his ideas for an instrument, the clavecin oculair, which made colours and musical tones correspond. Two articles in the Journal de Trévoux in 1735, namely Nouvelles expériences d'optique et d'acoustique and L'optique des couleurs fondée sur les simples observations, took the idea further describing an instrument to accomplish the colour-tone correspondence, namely the ocular harpsichord. *SAU

1738 Sir William (Frederick) Herschel (15 Nov 1738; 25 Aug 1822) German-born British astronomer, the founder of sidereal astronomy for the systematic observation of the heavens. In 1773, Herschel made and began using his first telescope. With it he began a project that would continue for the rest of his life: that of systematically studying the sky. Through this study he discovered the planet Uranus, many new nebulae, clusters of stars and binary stars. Herschel hypothesized that nebulae are composed of stars, developed a theory of stellar evolution and was the first person to correctly describe the form of our Galaxy, the Milky Way. He discovered the Saturnian satellites Mimas and Enceladus (1789) and the Uranian satellites Titania and Oberon (1787). He was probably the most famous astronomer of the 18th century. *TIS Herschel is also known for the twenty-four symphonies, and many other musical pieces, that he composed. Hear his eighth symphony here.

1793 Michel Chasles (15 Nov 1793; 18 Dec 1880)French mathematician who, independently of the Swiss-German mathematician Jakob Steiner, elaborated the theory of modern projective geometry, the study of the properties of a geometric line or plane figure that remain unchanged when the figure is projected onto a plane from a point not on either the plane or the figure. In his text Traité de géométrie in 1852 Chasles discusses cross ratio, pencils and involutions, all notions which he introduced. Chasles was the victim of a celebrated fraud paying the equivalent of 20,000 pounds for various letters from famous men of science and others which turned out to be forged.*TIS Chasles was a historian of mathematics. From 1861 to 1869 he was the victim of the clever and prolific literary forger, Denis Vrain-Lucas, who sold him thousands of fake manuscripts including some of Newton and Pascal.

1794 Franz Taurinus was a German mathematician best known for his work on non-Euclidean geometry. In 1697 Girolamo Saccheri assumed the fifth postulate is false and attempted to derive a contradiction. Of course, although he did not intend it to be so, he was then studying non-euclidean geometry. In 1766 Lambert followed a similar line to Saccheri. Lambert noticed that, in this new geometry where the sum of the angles of a triangle was less than 180 degrees, the angle sum of a triangle increased as the area of the triangle decreased. Schweikart himself is famed for investigating this new geometry which he called astral geometry.
Taurinus not only corresponded on mathematical topics with his uncle but he also corresponded with Gauss about his ideas on geometry. At first Taurinus tried to prove that Euclidean geometry was the only geometry but, in 1826, he accepted the lack of contradiction in other geometries. He published Theorie der Parallellinien in Cologne in 1825 and in the following year he published Geometriae prima elementa also in Cologne.
In this last mentioned publication Taurinus accepts that a third system of geometry exists in which the sum of the angles of a triangle is less than 180 degrees. He called this geometry "logarithmic-spherical geometry" and he recognized the lack of a contradiction in this geometry as meaning that it was internally consistent. He had developed a non-euclidean trigonometry which he applied to a number of elementary problems.
Taurinus came up with the important idea that elliptic geometry could be realized on the surface of a sphere, an idea taken up by Riemann. He also realized that there were an infinite number of non-euclidean geometries and this, Taurinus claimed, was highly significant. It showed that euclidean geometry held a unique dominating role. This is an interesting sideways move since his original aim had been to prove that euclidean geometry was the unique geometry. Finding that this was not so, he still wanted to demonstrate that euclidean geometry was "the" geometry. *SAU

1900 László Rédei (Rákoskeresztúr, 15 November, 1900—Budapest, 21 November, 1980) was a Hungarian mathematician.
His mathematical work was in algebraic number theory and abstract algebra, especially group theory. He proved that every finite tournament contains an odd number of Hamiltonian paths. He gave several proofs of the theorem on quadratic reciprocity. He proved important results concerning the invariants of the class groups of quadratic number fields. In several cases, he determined if the ring of integers of the real quadratic field Q(√d) is Euclidean or not. He successfully generalized Hajós's theorem. This led him to the investigations of lacunary polynomials over finite fields, which he eventually published in a book. He introduced a very general notion of skew product of groups, both the Schreier-extension and the Zappa-Szép product are special case of. He explicitly determined those finite noncommutative groups whose all proper subgroups were commutative (1947). This is one of the very early results which eventually led to the classification of all finite simple groups.*Wik

1907 Edward Marczewski (15 November 1907 – 17 October 1976) was a Polish mathematician. His surname until 1940 was Szpilrajn. Marczewski was a member of the Warsaw School of Mathematics. His life and work after the Second World War were connected with Wrocław, where he was among the creators of the Polish scientific centre.
Marczewski's main fields of interest were measure theory, descriptive set theory, general topology, probability theory and universal algebra. He also published papers on real and complex analysis, applied mathematics and mathematical logic.
Marczewski proved that the topological dimension, for arbitrary metrisable separable space X, coincides with the Hausdorff dimension under one of the metrics in X which induce the given topology of X (while otherwise the Hausdorff dimension is always greater or equal to the topological dimension). This is a fundamental theorem of fractal theory. *Wik

2007 Albert Vinicio Báez ( 15 Nov, 1912 – 20 March, 2007) was a Mexican-American physicist, and the father of singers Joan Baez and Mimi Fariña, and of Pauline Bryan. He was born in Puebla, Mexico; his family moved to the United States when he was two years old because his father was a Methodist minister, having left Catholicism when his son was two. The son grew up in Brooklyn, and considered becoming a minister, before turning to mathematics and physics. He made important contributions to the early development of X-ray microscopes and later X-ray telescopes. He also influenced John Baez's, his nephew, interest in science. *Wik

1938 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

DEATHS

Saint Albertus Magnus (about 1200 in Lauingen an der Donau, Swabia (now Germany)
- 15 Nov 1280 in Cologne, Prussia (now Germany)) Albert (or Albertus Magnus) was a German Dominican who wrote a commentary on Euclid's Elements. He taught at Saint-Jacques, giving courses on the Bible and on the theological textbook The Book of the Sentences which had been written by Peter Lombard. In 1245 he received the degree of Master of Theology from the University of Paris and, after receiving this degree, one of the first students he taught was Thomas Aquinas. While in Paris Albertus began the task of presenting the entire body of knowledge, natural science, logic, rhetoric, mathematics, astronomy, ethics, economics, politics and metaphysics. He wrote commentaries on the Bible, Peter Lombard's Book of the Sentences, and all of Aristotle's works. These commentaries contained his own observations and experiments. By 'experiment' Albertus meant 'observing, describing and classifying'. For example, in De Mineralibus Albertus wrote, "The aim of natural science is not simply to accept the statements of others, but to investigate the causes that are at work in nature."
We should not underestimate the importance of such ideas, for most scholars at that time believed that knowledge could only be obtained from a study of the scriptures. In the 13th century few were prepared to even consider the possibility of scientific research, and most considered that knowledge all came from God through ancient divinely inspired writings. Not only did Albertus advocate what we would call today the scientific approach to studying the real world, but he did so in such a way that his ideas were accepted by the Church.
Although he did an immense amount of valuable work in collecting and propagating the ideas of earlier scientists in his numerous and wide ranging writings, he also saw the value of new research by experiment.
Albertus was made a Saint and declared a Holy Doctor of the Church on 16 December 1931 and his feast day is 15 November in each year. In 1941 Albertus was made patron of natural scientists by Pope Pius XII. *SAU

1630 Johannes Kepler (27 Dec 1571, 15 Nov 1630) German astronomer who formulated three major laws of planetary motion which enabled Isaac Newton to devise the law of gravitation. Working from the carefully measured positions of the planets recorded by Tycho Brahe, Kepler mathematically deduced three relationships from the data: the planets move in elliptical orbits with the Sun at one focus; (2) the radius vector sweeps out equal areas in equal times; and (3) for two planets the squares of their periods are proportional to the cubes of their mean distances from the sun. Kepler suggested that the tides were caused by the attraction of the moon. He believed that the universe was governed by mathematical rules, but recognized the importance of experimental verification. *TIS

1675 Francis Line (1595 – 15 November 1675), also known as Linus of Liège, was a Jesuit priest and scientist. He is known for inventing a magnetic clock. He is also remembered as a contemporary critic of the theories and work of Isaac Newton and for challenged Robert Boyle and his law of gases. * Wik

1761 Giovanni Poleni (23 Aug 1683 in Venice, Italy - 15 Nov 1761 in Padua, Italy) was an Italian mathematician who worked on hydraulics, physics, astronomy and archaeology. *SAU

1938 Andre-Eugene Blondel (28 Aug 1863, 15 Nov 1938) was a French physicist who invented (1893) the electromagnetic oscillograph, a device that allowed electrical researchers to observe the intensity of alternating currents. In 1894, he proposed the lumen and other new photometric units for use in photometry, based on the metre and the Violle candle. Endorsed in 1896 by the International Electrical Congress, his system is still in use with only minor modifications. Blondel was a pioneer in the high voltage long distance transport of electric power, and also contributed to developments in wireless telegraphy, acoustics, and mechanics. He proposed theories for induction motors and coupling of a.c. generators. *TIS He invented both the the bifilar and soft iron oscillographs. These instruments won the grand prize at the St. Louis Exposition in 1904. They were more powerful than the classical stroboscope, invented in 1891 then in use. They remained the best way to record high-speed electrical phenomena for more than 40 years when they were replaced by the cathode ray oscilloscope. They paved the way for a greater understanding of the behavior of alternating current. *Wik

1959 C.T.R. Wilson (14 Feb 1869, 15 Nov 1959)Scottish physicist who, with Arthur H. Compton, received the Nobel Prize for Physics in 1927 for his invention of the Wilson cloud chamber, which became widely used in the study of radioactivity, X rays, cosmic rays, and other nuclear phenomena. His discovery was a method of rendering visible the tracks of such electrically charged particles. It is based upon the formation of clouds, which develop when sufficiently moist air is suddenly expanded, thus dropping the temperature below the dew-point. Thereafter, vapour condenses into small drops, formed round dust particles, or even, an electrically charged atomic particle. The formation of droplets is so dense that photographs show continuous tracks of particles traveling through the chamber as white lines. *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