Monday 6 January 2020

On This Day in Math - January 6

One would be hard put to find a set of whole numbers with a
more fascinating history and more elegant properties surrounded
by greater depths of mystery—and more totally useless—than the perfect numbers
.—Martin Gardner (a perfect quote for the first of the two year days that are perfect numbers)

The sixth day of the year; six is the smallest perfect number, and Lord Karl Voldevive@Karl4MarioMugan pointed out that, "All other known perfect numbers end in 44 in base 6 as do all powers of ten greater than ten."  (aptly supporting the quote above)

\( \pi^4 + \pi^5 = e^6 \) almost, (403.428775... vrs 403.428793...)

The Feynman point is a sequence of six 9s that begins at the 762nd decimal place of the decimal representation of π. It is named after physicist Richard Feynman, who once stated during a lecture he would like to memorize the digits of π until that point, so he could recite them and quip "nine nine nine nine nine nine and so on", suggesting, in a tongue-in-cheek manner, that π is rational.

There are five equable (area and perimeter "equal" and integer side  lengths) triangles . All of them have area/perimeter divisible by six. (I'm willing to learn why if you know) [W. A. Whitworth and D. Biddle proved this in 1904]

Every prime greater than three is either one more, or one less than a multiple of six.

Six is an unincorporated community in McDowell County, West Virginia, United States. Six is located on West Virginia Route 16 5 miles (8.0 km) southwest of Welch.


1680 Hooke writes to Newton to give the results of his experiments on Newtons suggestion that a falling body would consistently deviate to the east due to the earth’s rotation. Newton had submitted these suggestion the  previous November to the Royal Society.  Hooke found a small south-easterly deviation in all three trials, but the results were seen as inconclusive.

1699 Newton wrote Flamsteed, probably alluding to Bernoulli’s challenge of the brachistochrone problem, “I do not love ... to be dunned and teezed by forreigners about Mathematical things ... ” *VFR

1757 d'Alembert writes to Formey, Secretary of the Berlin Academy, complaining of the language used by Euler to reject a paper, and insisting that the paper be published.  He agreed to change some language in the paper if Euler would publicly state that d'Alembert had been the first to show that all imaginaries could be reduced to the form a+bi (he wrote sqrt of -1 in place of i) and other conditions.  *Thomas L. Hankins,Jean d'Alembert: science and the Englightenment
pg 58

1819  Gauss, in a letter to his former student, Christian Ludwig Gerling, describes how he came to his construction of the 17-gon while still in bed.

In 1838, Samuel Morse, with his partner, Alfred Vail, gave the first public demonstration of their new invention electric telegraphic system at the Speedwell Iron Works in Morristown, NJ. *TIS

1851 At 2am in the morning, Leon Foucault first saw the earth turn.  In the basement of his Paris home at the corner of rue de Vaugirard and rud d’Assas he watched his 5 Kg bob swing on a two meter wire, he observed a slight, but clearly perceptible change in the motion of the pendulum.  *Amir Aczel, Pendulum, pg 5-7
After weeks of work, he recorded in his journal that he made this discovery at 2:00 am working with a pendulum in the cellar of the house he shared with his mother. Using a steel wire 2-m long with a 5-kg brass bob, he had made a pendulum suspended in a way that freely permitted it, he found that its plane of oscillation slowly rotated relative to the ground. This led to using much longer versions of his pendulum. He found that the angular velocity of the rotation equalled w*sin(q) where w is the angular velocity of the Earth rotating on its axis, and q is the latitude of the site of the pendulum. He demonstrated his discovery on 31 Mar 1851 for Napoleon.*TIS

1887 Sherlock Holmes “born”—at age 33—in a short story, “A Study in Scarlet,” published in London in the now defunct Strand Magazine. Mr. Holmes no longer lives at 221 B. Baker Street. “At the moment he is in retirement in Sussex keeping bees.” All mathematicians should admire and emulate his deductive powers. *VFR

1896, The first English-language account  of X-ray discovery. German scientist, Wilhelm Röntgen announced his discovery of x-rays on Jan 1st of this year. He sent copies of his manuscript and some of his x-ray photographs to several renowned physicists and friends, including Lord Kelvin in Glasgow and Henre Poincare in Paris. Four days later, on 5 Jan 1896, Die Presse published the news in a front-page article which described the discovery and suggested new methods of medical diagnoses might be made with this new kind of radiation. One day later, the London Standard cabled the news to other countries around the world about "a light which for the purpose of photography will penetrate wood, flesh, cloth, and most other organic substances." It printed the first English-language account the next day. *TIS

1900 Frege wrote to Hilbert: “Suppose we know that the propositions (1) A is an intelligent being, (2) A is omnipresent, (3) A is omnipotent, together with all their consequences did not contradict one another; could we infer from this that there was an omnipotent, omnipresent, intelligent being?” *Frege’s Philosophical and Mathematical Correspondence

In 1904, Marconi Co established "CQD" as first international radio distress signal. It didn't last long. Two years later, "SOS" became the radio distress signal because it was more convenient - meaning quicker - to send by wireless radio.*TIS


1561 Thomas Fincke (6 Jan 1561 in Flensburg, Denmark (now Germany) - 24 April 1656 in Copenhagen, Denmark) His most famous book Geometriae rotundi (1583), was intended as a textbook. Based on works of Ramus from whom he took the word 'radius', the book introduces the terms 'tangents' and 'secants' and Fincke devised new formulae such as the law of tangents.
Fincke's book was recommended by Clavius, Napier and Pitiscus all of whom adopted much from it. His other books on astronomy and astrology are of much less interest despite the fact that he was in touch with Brahe and Kepler. *SAU

1654 Jakob Bernoulli (27 December 1654 – 16 August 1705) He was so fascinated with the way the logarithmic spiral reproduces itself in its involute, its evolute, and its caustics of reflection and refraction, that he requested it be engraved on his tombstone, together with the inscription Eadem mutata resurgo (Though changed, I will arise the same). *VFR He was one of the first to fully utilize differential calculus and introduced the term "integral" in integral calculus. Jacob Bernoulli's first important contributions were a pamphlet on the parallels of logic and algebra (1685), work on probability in 1685 and geometry in 1687. His geometry result gave a construction to divide any triangle into four equal parts with two perpendicular lines.(a nice exercise to try) By 1689 he had published important work on infinite series and published his law of large numbers in probability theory. He published five treatises on infinite series (1682 - 1704). He was the first of the Bernoulli family of mathematicians. *TIS

1807 Joseph Petzval (German: Josef Maximilian Petzval; Hungarian: Petzvál József Miksa; (January 6, 1807, Zipser Bela – September 19, 1891) was a Hungarian mathematician, inventor, and physicist of Germanorigin, born in Upper Hungary (today Slovakia). He is best known for his work in optics.
Petzval is considered to be one of the main founders of geometrical optics, modern photography and cinematography. Among his inventions are the Petzval portrait lens and opera glasses, both still in common use today. He is also credited with the discovery of the Laplace transform and is also known for his extensive work on aberration in optical systems.*Wik

1841 Friedrich Otto Rudolf Sturm (6 Jan 1841 in Breslau, Germany (now Wrocław, Poland) - 12 April 1919 in Breslau, Germany) Sturm wrote extensively on geometry and, other than the teaching textbook on descriptive geometry and graphical statics and one other teaching text Maxima und Minima in der elementaren Geometrie which he published in 1910. All his work was on synthetic geometry.
He wrote a three volume work on line geometry published between 1892 and 1896, and a four volume work on projective geometry, algebraic geometry and Schubert's enumerative geometry the first two volumes of which he published in 1908 and the second two volumes in 1909. These two multi-volume works collect together most of his life's research. *SAU

1942 Peter Denning is born. He received a BEE from Manhattan College in 1965 and a PhD from MIT in 1968. He was head of the computer science department at Purdue University (1979-83), co-founder of CSNET and first chair of the CSNET executive committee (1981-1986), and the founding director of the Research Institute for Advanced Computer Science at the NASA Ames Research Center (1983-1990). Since 1991 he has become Professor of Computer Science at George Mason University. He was president of the Association for Computing Machinery (1980-1982), and chair of the ACM publications board (1992-1998) where he led the development of the ACM digital library. Denning has published six books and 260 articles on computers, networks, and their operating systems. Denning published two well-received papers that established a scientific and rational basis for virtual memory computer operating systems in 1966 and 1970.*CHM


1607 Guidobaldo Marchese del Monte (11 Jan 1545; Pesaro, Italy - 6 Jan 1607; Montebaroccio, Italy) Italian mathematician, philosopher and astronomer of the 16th century.
His father, Ranieri, was from a leading wealthy family in Urbino. Ranieri was noted for his role as a soldier and also as the author of two books on military architecture. The Duke of Urbino, Duke Guidobaldo II, honoured him with the title Marchese del Monte so the family had only become a noble one in the generation before Guidobaldo. On the death of his father Guidobaldo inherited the title of Marchese.
Guidobaldo studied mathematics at the University of Padua in 1564 and then pursued research into mathematics, mechanics, astronomy and optics. He studied mathematics under Federico Commandino during this period and became one of his most staunch disciples. He also became a friend of Bernardino Baldi, who was also a student of Commandino around the same time.
He corresponded with several mathematicians including Giacomo Contarini, Francesco Barozzi and Galileo Galilei. His invention of a drafting instrument for constructing regular polygons and dividing a line into any number of segments was incorporated as a feature of Galileo's geometric and military compass.
Guidobaldo was also important in helping Galileo Galilei in his academic career. Galileo, then a promising, but unemployed 26-years old, had written an essay on hydrostatic balance, which struck Guidobaldo as being nothing short of genius. He then commended Galileo to his brother, the Cardinal Del Monte, who referred him to the powerful Duke of Tuscany, Ferdinando I de' Medici. Under his patronage, Galileo got an indication to a professorship of mathematics at the University of Pisa, in 1589. Guidobaldo became a staunch friend of Galileo and helped him again in 1592, when he had to apply to the chair of mathematics at the University of Padua, due to the hatred and machinations of Giovanni de' Medici, a son of Cosimo I de' Medici, against Galileo. Notwithstanding their friendship, Guidobaldo was a critic of Galileo's principle of the isochronicity of the pendulum, a major discovery which Guidobaldo thought it was impossible.
Guidobaldo wrote an influential book about perspective, titled Perspectivae Libri VI, published at Pisa in 1600. Several painters, architects and the theater stage designer Nicola Sabbatini used this geometrical knowledge in their works. *Wik

1689 Seth Ward (1617 – 6 January 1689) was an English mathematician, astronomer, and bishop. In the 1640s, he took instruction in mathematics from William Oughtred, and stayed with relations of Samuel Ward.
In 1649 he became Savilian professor of astronomy at Oxford University, and gained a high reputation by his theory of planetary motion. It was propounded in the works entitled In Ismaelis Bullialdi astro-nomiae philolaicae fundamenta inquisitio brevis (Oxford, 1653), against the cosmology of Ismael Boulliau, and Astronomia geometrica (London, 1656) on the system of Kepler. About this time he was engaged in a philosophical controversy with Thomas Hobbes, in fact a small part of the debate with John Webster launched by the Vindiciae academiarum he wrote with John Wilkins which also incorporated an attack on William Dell.
He was one of the original members of the Royal Society of London. In 1659 he was appointed President of Trinity College, Oxford, but not having the statutory qualifications he resigned in 1660.*Wik

1702 Thomas Franklin (1636? - Jan 6, 1702) Uncle of Benjamin Franklin. Designed the mechanical clockworks in Ecton, Northamptonshire.
Like his famous nephew, he was an inventor of some repute. He was also an enthusiastic musician; the village’s schoolteacher; a clerk of the county courts, and to the archdeacon; a lawyer; and a successful bell-founder. He and his business partner Henry Bagley cast many bells, most notably those for Lichfield Cathedral.
In July 1758, the celebrated American polymath Benjamin Franklin and his son William came to poke around in the churchyard at Ecton. Benjamin was in Britain on a diplomatic mission, and took the opportunity to investigate his roots. The Franklins had lived on a thirty-acre freehold in Ecton since at least 1555, and when Benjamin’s servant had cleared the moss away from one of the gravestones, the following inscription was revealed:

Here Lyeth the Body of Thomas Franklin
who Departed this Life January the 6 Anno Dni 1702
In the Sixty Fifth year of his age.

1826 John Farey, Sr. (1766 – January 6, 1826) was an English geologist and writer. However, he is better known for a mathematical construct, the Farey sequence named after him.
Farey's most famous work is General View of the Agriculture and Minerals of Derbyshire (3 volumes 1811-17) for the Board of Agriculture. In the first of these volumes (1811) he gave an able account of the upper part of the British series of strata, and a masterly exposition of the Carboniferous and other strata of Derbyshire. In this classic work, and in a paper published in the Philosophical Magazine, vol. 51, 1818, p. 173, on 'Mr Smith's Geological Claims stated', he zealously called attention to the importance of the discoveries of William Smith.
As well as being remembered by historians of geology, his name is more widely known by the Farey sequence which he noted as a result of his interest in the mathematics of sound (Philosophical Magazine, vol. 47, 1816, pp 385-6).
Farey died in London. Subsequently his widow offered his geological collection to the British Museum, which rejected it, and it was dispersed.*Wik

1852 Louis Braille (4 Jan 1809, 6 Jan 1852) French educator who developed a tactile form of printing and writing, known as braille, since widely adopted by the blind. He himself knew blindness from the age four, following an accident while playing with an awl. In 1821, while Braille was at a school for the blind, a soldier named Charles Barbier visited and showed a code system he had invented. The system, called "night writing" had been designed for soldiers in war trenches to silently pass instructions using combinations of  twelve raised dots. Young Braille realised how useful this system of raised dots could be. He developed a simpler scheme using six dots. In 1827 the first book in braille was published. Now the blind could also write it for themselves using a simple stylus to make the dots. *TIS

1884 Gregor Mendel (22 July 1822, 6 Jan 1884) Original name (until 1843) Johann Mendel. Austrian pioneer in the study of heredity. He spent his adult life with the Augustinian monastery in Brunn, where as a geneticist, botanist and plant experimenter, he was the first to lay the mathematical foundation of the science of genetics, in what came to be called Mendelism. Over the period 1856-63, Mendel grew and analyzed over 28,000 pea plants. He carefully studied for each their plant height, pod shape, pod color, flower position, seed color, seed shape and flower color. He made two very important generalizations from his pea experiments, known today as the Laws of Heredity. Mendel coined the present day terms in genetics: recessiveness and dominance.*TIS

1886 Adhémar Jean Claude Barré de Saint-Venant (August 23, 1797, Villiers-en-Bière, Seine-et-Marne – 6 January 1886, Saint-Ouen, Loir-et-Cher) was a mechanician and mathematician who contributed to early stress analysis and also developed the one-dimensional unsteady open channel flow shallow water equations or Saint-Venant equations that are a fundamental set of equations used in modern hydraulic engineering. Although his surname was Barré de Saint-Venant in non-French mathematical literature he is known simply as Saint-Venant. His name is also associated with Saint-Venant's principle of statically equivalent systems of load, Saint-Venant's theorem and for Saint-Venant's compatibility condition, the integrability conditions for a symmetric tensor field to be a strain.
In 1843 he published the correct derivation of the Navier-Stokes equations for a viscous flow and was the first to "properly identify the coefficient of viscosity and its role as a multiplying factor for the velocity gradients in the flow". Although he published before Stokes the equations do not bear his name.
Barré de Saint-Venant developed a version of vector calculus similar to that of Grassmann (now understood as exterior differential forms) which he published in 1845. A dispute arose between Saint-Venant and Grassmann over priority for this invention. Grassmann had published his results in 1844, but Barré de Saint-Venant claimed he had developed the method in 1832. *Wik

1918 Georg (Ferdinand Ludwig Philipp) Cantor (3 Mar 1845, 6 Jan 1918) was a Russian-German mathematician who created modern set theory and extended it to give the concept of transfinite numbers,with cardinal and ordinal number classes. Although Cantor's earliest work was concerned with Fourier series, his reputation rests upon his contribution to transfinite set theory. He began with the definition of infinite sets proposed by Dedekind in 1872: a set is infinite when it is similar to a proper part of itself. Sets with this property, such as the set of natural numbers are said to be 'denumerable' or 'countable'. His career was repeatedly interrupted after 1884 by mental illness. He died of heart failure in 1918 in a mental institution. *TIS

1920 Hieronymus Georg Zeuthen (15 February 1839 – 6 January 1920) was a Danish mathematician. He is known for work on the enumerative geometry of conic sections, algebraic surfaces, and history of mathematics. After 1875 Zeuthen began to make contributions in other areas such as mechanics and algebraic geometry, as well as being recognised as an expert on the history of medieval and Greek mathematics. He wrote 40 papers and books on the history of mathematics, which covered many topics and several periods.*Wik

1922 Jakob Rosanes (August 16, 1842 Brody, Austria-Hungary (now Ukraine) – January 6, 1922) was a German mathematician who worked on algebraic geometry and invariant theory. He was also a chess master.
Rosanes studied at University of Berlin and the University of Breslau. He obtained his doctorate from Breslau (Wrocław) in 1865 and taught there for the rest of his working life. He became professor in 1876 and rector of the university during the years 1903–1904.
Rosanes made significant contributions in Cremona transformations. *Wik

1930 Eduard Study (23 March 1862 in Coburg, Germany - 6 Jan 1930 in Bonn, Germany)Study became a leader in the geometry of complex numbers. He reformulated, independently of Severi, the fundamental principles of enumerative geometry due to Schubert. He also worked on invariant theory helping to develop a symbolic notation. In 1923 he published important work on real and complex algebras of low dimension publishing these results. Study's contribution is summarized by W Burau  as follows, "... Study demonstrated what he considered to be a thorough treatment of a problem. ... With Corrado Segre, Study was one of the leading pioneers in the geometry of complex numbers. ... Adept in the methods of invariant theory ... Study, employing the identities of the theory, sought to demonstrate that geometric theorems are independent of coordinates. ... Study was the first to investigate systematically all algebras possessing up to four generators over R and C. "
Other areas which Study worked on were straight lines in elliptic space, with his student at Bonn J L Coolidge, and he simplified the method of differential operators. In 1903 he published Geometrie der Dynamen which considered euclidean kinematics and the mechanics of rigid bodies. *SAU

1953 Giovanni Enrico Eugenio Vacca (18 November 1872 – 6 January 1953) was an Italian mathematician, Sinologist and historian of science. Vacca studied mathematics and graduated from the University of Genoa in 1897 under the guidance of G. B. Negri. He was a politically active student and was banished for that from Genoa in 1897. He moved to Turin and became an assistant to Giuseppe Peano. In 1899 he studied, at Hanover, unpublished manuscripts of Gottfried Wilhelm Leibniz, which he published in 1903. Around 1898 Vacca became interested in Chinese language and culture after attending a Chinese exhibition in Turin. He took private lessons of Chinese and continued to study it at the University of Florence. Vacca then traveled to China in 1907-8 and defended a PhD in Chinese studies in 1910. In 1911, he became a lecturer in Chinese literature at the University of Rome. In 1922, he moved to Florence and taught Chinese literature and language at university until 1947.
The interests of Vacca were almost equally split between mathematics, Sinology and history of science, with a corresponding number of papers being 38, 47 and 45. In 1910, Vacca developed a complex number iteration for pi. *Wik

1990 Pavel Alekseyevich Cherenkov (15 Jul 1904, 6 Jan 1990) Soviet physicist who discovered Cherenkov radiation (1934), a faint blue light emitted by electrons passing through a transparent medium when their speed exceeds the speed of light in that medium. Fellow Soviet scientists Igor Y. Tamm and Ilya M. Frank investigated the phenomenon from which the Cherenkov counter was developed. Extensive use of this Cherenkov detector was later made in applications of experimental nuclear and particle physics. For their work, the trio shared the 1958 Nobel Prize for Physics.*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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