Friday 9 June 2023

On This Day in Math - June 9

The Boat House, Paducah, Ky

I've been giving this lecture to first-year classes
for over twenty-five years. 
You'd think they would begin to understand it by now.
~ J E Littlewood

The 160th day of the year; 160 is the smallest number which is sum of cubes of 3 distinct primes, the first three. (23+33+53) *Prime Curios (It is also the sum of the first power of the first 11 primes )

160! - 159! + 158! - ... -3! + 2! - 1! is prime.

160 is also the sum of two non-zero squares (122 + 42) and like all such numbers, you can show that 1602n+1 will also be the sum of two non-zero squares.

160 is the longest edge of the integer Heronian tetrahedron with smallest possible surface area and volume.  Its edges are 25, 39, 56, 120, 153, and 160; for a total surface area of 6384, and volume 8064.

160 is the largest year day (and second largest known) for which the alternating factorial sequence is prime: 160!- 159! + 158! - 157! .... + 2! - 1!. The alternating factorial 5! - 4! + 3! - 2! + 1! = 121. The alternating factorial sequence is prime for n= 3 through 8 (5, 19, 101, 619, 4421, 35899). In spite of this run of consecutive primes, John D Cook checked and found only 15 n values for which the alternating factorial starting with n is prime (There are now at least 17 known primes). 14 are year days, the largest being 160. 

More info on these here 
Find more math facts for each year day here


1750 Euler finally was able to prove the pentagonal theorem on June 9, 1750, in a letter to Goldbach. His proof is algebraic. The proof was first published in 1760, and Euler gives more details about points which were vague in his letter to Goldbach.
Euler had mentioned the theorem many times in the years following his first correspondence with Daniel Bernoulli (January 28,1741), in letters to Niklaus Bernoulli, Christian Goldbach, d’Alembert, and others, and in the first publication of 1751. (This paper was written on April 6, 1741 and had no proof. Euler wrote so many papers that the publishers fell dramatically behind; they were publishing new papers many years after his death.) A typical entry, from a letter to Goldbach, reads “If these factors \((1 − n)(1 − n^2)(1 − n^3) etc. are multiplied out onto infinity, the following series \(1 − n − n^2 + n^5 + n^7− etc is produced. I have however not yet found a method by which I could prove the identity of these two expressions. The Hr. Prof. Niklaus Bernoulli has also been able to prove nothing beyond induction.” Here the word “induction” means “by experiment” rather than “a proof by induction”. *Dick Koch, The Pentagonal Theorem and All That

1795 a provisional meter bar was constructed in brass by Lenoir. On 1 Aug 1793, the metre had been defined to be 1/10 000 000 of the northern quadrant of the Paris meridian (5 132 430 toises of Paris, from the north pole to the equator). On 7 Apr 1795, the first legal definition of the metre was made by the French National Assembly. A second measure was made along the Dunkirk-Barcelona axis (5 130 740 toises of Paris).
Closeup of National Prototype Metre Bar No. 27, made in 1889 by the International Bureau of Weights and Measures (BIPM) and given to the United States, which served as the standard for defining all units of length in the US from 1893 to 1960.  (the distance between two lines on a standard bar of an alloy of platinum with 10% iridium, measured at the melting point of ice) *Wik

1798 Napoleon’s fleet of 500 ships arrived in Malta, and three days later they captured the place. Monge started fifteen elementary schools and one high school there.*VFR

1905  Albert Einstein published his analysis of Planck's quantum theory and its application to light. His article appeared in Annalen der Physik. Though no experimental work was involved, it was for these insights that Einstein earned his Nobel Prize. *TIS
 Einstein quickly realized that Planck’s hypothesis about the quantization of radiant energy could also explain the photoelectric effect.

1934 First Donald Duck Cartoon. Amazingly, the "Donald in Mathland" videos that were popular in the eighties in middle schools are still for sell.


1669 Leonty Filippovich Magnitsky (9 June 1669 in Ostashkov, Russia - 30 October 1739 in Moscow, Russia) Peter the Great, Tsar of Russia, founded the School of Mathematics and Navigation in Moscow in 1701. Russia was a major power at this time but had no access to the sea. Peter decided that he would push north to try to dislodge the Swedes who controlled the Baltic coast and war had begun on this front in 1700. The many reforms, including the start of secular education, which Peter introduced to modernize Russia aimed to ensure victory in his wars for access to the seas. The declaration setting up the Moscow School was dated 14 January 1701, but formal classes did not begin immediately. There was a delay since facilities were not properly in place to allow teaching to begin. Peter the Great then appointed Magnitskii to the School on 2 February
In February, Magnitskii was appointed to the school and simultaneously ordered to compile a book "in the Slavonic dialect, selected from arithmetic, geometry and navigation." The 'Arithmetic' was therefore specifically commissioned to be the textbook of the Moscow School. Little is known about the classes in the school while the book was being prepared. It was sent to the publisher on 2 November 1702, and appeared bearing the date 11 January 1703. With its appearance the success of the school was assured.
The 'Arithmetic' was the first mathematics textbook published in Russia by a Russian which was not a translation or adaptation of a foreign textbook. It was a textbook for the courses which Magnitskii himself taught at the school, essentially a published version of his lecture notes. It was in effect an encyclopaedia of the mathematical sciences of its day, based strongly on applications in navigational astronomy, geodesy and navigation. It used the methods of algebra, geometry, and trigonometry. The 'Arithmetic',remained the basic Russian mathematics textbook for 50 years. *SAU

1812 Johann Gottfried Galle (9 June 1812 – 10 July 1910) German astronomer who on 23 Sep 1846, was the first to observe the planet Neptune, whose existence had been predicted in the calculations of Leverrier. Leverrier had written to Galle asking him to search for the 'new planet' at a predicted location. Galle was then a member of the staff of the Berlin Observatory and had discovered three comets. In 1838, while assistant to Johann Franz Encke, Galle discovered the dark, inner C ring of Saturn at the time of the maxium ring opening. In 1851, he became professor of astronomy at Breslau and director of the observatory there. In 1872, he proposed the use of asteroids rather than regular planets for determinations of the solar parallax, a suggestion which was successful in an international campaign (1888-89).

1885 John Edensor Littlewood born. (9 June 1885 – 6 September 1977) Littlewood’s Miscellany (1986) is a delightful little book, for it shows a mathematician having fun.*VFR
He collaborated for many years with G. H. Hardy. Together they devised the first Hardy–Littlewood conjecture, a strong form of the twin prime conjecture, and the second Hardy–Littlewood conjecture.
In a 1947 lecture, the Danish mathematician Harald Bohr said, "To illustrate to what extent Hardy and Littlewood in the course of the years came to be considered as the leaders of recent English mathematical research, I may report what an excellent colleague once jokingly said: 'Nowadays, there are only three really great English mathematicians: Hardy, Littlewood, and Hardy–Littlewood.'"
There is a story (related in the Miscellany) that at a conference Littlewood met a German mathematician who said he was most interested to discover that Littlewood really existed, as he had always assumed that Littlewood was a name used by Hardy for lesser work which he did not want to put out under his own name; Littlewood apparently roared with laughter. There are versions of this story involving both Norbert Wiener and Edmund Landau, who, it is claimed, "so doubted the existence of Littlewood that he made a special trip to Great Britain to see the man with his own eyes"*Wik

1906 Albert Cyril Offord FRS FRSE (9 June 1906 – 4 June 2000) was a British mathematician. He was the first professor of mathematics at the London School of Economics.
 He was educated at Hackney Downs Grammar School. He then studied Mathematics at University College, London. He then went to St John's College, Cambridge as a postgraduate, working with Prof John Edensor Littlewood.

He received two Ph.D.s in mathematics: the first from the University of London (under Bosanquet) in 1932, the second from Cambridge (under Hardy) in 1936.

In 1940 he left Cambridge to lecture at University College, Bangor. In 1942 he moved to King's College, Newcastle-upon-Tyne (later being named the University of Newcastle). He was created Professor of Mathematics in 1945.

In 1946 he was elected a Fellow of the Royal Society of Edinburgh. His proposers were Sir Edmund Whittaker, John William Heslop-Harrison, Alexander Aitken and Alfred Dennis Hobson. He was elected a Fellow of the Royal Society of London in 1952.

In 1948 he left Newcastle to become Professor of Mathematics at Birkbeck College in London replacing Prof Dienes. He left in 1966 to take up a new chair at London School of Economics. He retired in 1973 then becoming a senior research fellow at Imperial College, London.

He died in Oxford on 4 June 2000.

1960  Carlo W. J. Beenakker (born June 9, 1960) is a professor at Leiden University and leader of the university's mesoscopic physics group, established in 1992. In 1997, he was awarded the Spinoza Prize, the "Dutch Nobel prize". *Wik

1751 John Machin (bapt. 1686?—June 9, 1751) was an English mathematician and astronomer best known for the formulas he invented for calculating π.*VFR
He was a professor of astronomy at Gresham College, London, and is best known for developing a quickly converging series for Pi in 1706 and using it to compute Pi to 100 decimal places.
Machin's formula is:
\frac{\pi}{4} = 4 \cot^{-1}5 - \cot^{-1}239
The benefit of the new formula, a variation on the Gregory/Leibniz series (Pi/4 = arctan 1), was that it had a significantly increased rate of convergence, which made it a much more practical method of calculation.
To compute Pi to 100 decimal places, he combined his formula with the Taylor series expansion for the inverse tangent. (Brook Taylor was Machin's contemporary in Cambridge University.) Machin's formula remained the primary tool of Pi-hunters for centuries (well into the computer era).*Wik "This formula of John Machin (1680–1751) was publicized by William Jones in his 1706 Synopsis palmariorum matheseos. Variations of it remained the standard method for calculating τ/2 (pi) until the 1970s, when better methods due to Ramanujan came to light." *Theorem of the Day

1818 Joel E. Hendricks, (March 10, 1818 - June 9, 1893) a noted mathematician, was born in Bucks County, Pennsylvania, March 10, 1818. He early developed a love of mathematics and began to teach school at nineteen years of age. He chanced to procure Moore's Navigation and Ostrander's Astronomy and, without instruction, soon became able to work in trigonometry and calculate solar and lunar eclipses. He took up algebra while teaching and soon became master of that science without instruction. He taught mathematics two years in Neville Academy, Ohio, and then occupied a position on a Government survey in Colorado in 1861. In 1864 he located in Des Moines, Iowa and pursued his mathematical studies. In 1874 he began the publication of the Analyst, a journal of pure and applied mathematics and soon won a reputation in Europe among eminent scholars as one of the most advanced mathematicians of the day. His Analyst was taken by the colleges and universities of Europe and found a place in the best foreign libraries. His name became famous among all mathematical experts of the world. Among his correspondents were Benjamin Silliman, John W. Draper and James D. Dana; while his journal was authority at Yale and Johns Hopkins Universities. For ten years, up to 1884, this world-famous Analyst was published at Des Moines by Dr. Joel E. Hendricks. Up to the time it was discontinued, no journal of mathematics had been published so long in America. It is one of the remarkable events of the Nineteenth Century that a self-educated man should, by his own genius and industry, without instruction, reach such an exalted place among the world's great scholars. Dr. Hendricks died in Des Moines on the 9th of June, 1893. *History of Iowa From the Earliest Times to the Beginning of the Twentieth Century/Volume 4 by Benjamin F. Gue
A more complete mathematical biography of Mr. Hendricks can be found in The American Mathematical Monthly, Vol 1, #3, 1894.

1847 John Hailstone (13 Dec, 1759– 9 June, 1847), English geologist, born near London, was placed at an early age under the care of a maternal uncle at York, and was sent to Beverley school in the East Riding. Samuel Hailstone was a younger brother. John went to Cambridge, entering first at Catharine Hall, and afterwards at Trinity College, and was second wrangler and second in the Smith Prize of his year (1782). He was second in both competitions to James Wood who became master of Saint Johns, and Dean of Ely. Hailstone was elected fellow of Trinity in 1784, and four years later became Woodwardian Professor of Geology, an office which he held for thirty years.
He went to Germany, and studied geology under Werner at Freiburg for about twelve months. On his return to Cambridge he devoted himself to the study and collection of geological specimens, but did not deliver any lectures. He published, however, in 1792, ‘A Plan of a course of lectures.’
He married, and retired to the vicarage of Trumpington, near Cambridge, in 1818, and worked zealously for the education of the poor of his parish. He devoted much attention to chemistry and mineralogy, as well as to his favourite science, and kept for many years a meteorological diary. He made additions to the Woodwardian Museum, and left manuscript journals of his travels at home and abroad, and much correspondence on geological subjects. He was elected to the Linnean Society in 1800, and to the Royal Society in 1801, and was one of the original members of the Geological Society. Hailstone contributed papers to the ‘Transactions of the Geological Society’ (1816, iii. 243–50), the ‘Transactions of the Cambridge Philosophical Society’ (1822, i. 453–8), and the British Association (Report, 1834, p. 569). He died at Trumpington in his eighty-eighth year. *Wik

1897 Alvan Graham Clark (July 10, 1832 – June 9, 1897) U.S. astronomer, one of an American family of telescope makers and astronomers who supplied unexcelled lenses to many observatories in the U.S. and Europe during the heyday of the refracting telescope. He began a deep interest in astronomy while still at school, then joined the family firm of Alvan Clark & Sons, makers of astronomical lenses. In 1861, testing a new lens, he looked through it at Sirius and observed faintly beside it, Sirius B, the twin star predicted by Friedrich Bessel in 1844. Carrying on the family business, after the deaths of his father and brother, Clark made the 40" lenses of the Yerkes telescope (still the largest refractor in operation in the world). Their safe delivery was a source of anxiety. He died shortly after their first use.

1969 Harold Davenport (30 October 1907 – 9 June 1969) worked on number theory, in particular the geometry of numbers, Diophantine approximation and the analytic theory of numbers. He wrote a number of important textbooks and monographs including The higher arithmetic (1952)*SAU

1977 Dr. Gustav Doetsch (November 29, 1892 – June 9, 1977) was a German mathematician, aviation researcher, decorated war veteran, and Nazi supporter. The modern formation and permanent structure of the Laplace transform is found in Doetsch's 1937 work Theorie und Anwendung der Laplace-Transformation,[5] which was well-received internationally. He dedicated most of his research and scientific activity to the Laplace transform, and his books on the subject became standard texts throughout the world, translated into several languages. His texts were the first to apply the Laplace transform to engineering. *Wik

1995  Vivienne Lucille Malone-Mayes (February 10, 1932 – June 9, 1995) was an American mathematician and professor. Malone-Mayes studied properties of functions, as well as methods of teaching mathematics. She was the fifth African-American woman to gain a PhD in mathematics in the United States, and the first African-American member of the faculty of Baylor University (which had rejected her application to study there five years earlier).
She decided to attend the University of Texas full-time as a graduate student when rejected entry at Baylor. In graduate school she was very much alone. In her first class, she was the only Black, the only woman. Her classmates ignored her completely, even terminating conversations if she came within earshot. She was denied a teaching assistantship, although she was an experienced and excellent teacher.
She wrote, "... it took a faith in scholarship almost beyond measure to endure the stress of earning a Ph.D. degree as a Black, female graduate student. I could not join my advisor and other classmates to discuss mathematics over coffee at Hilsberg's cafe .... Hilsberg's would not serve Blacks.
Some classes were closed to her despite the fact that the University of Texas was required to take Black students. For example R L Moore refused to have any Black students in his classes.
She was a member of the board of directors of the National Association of Mathematicians. She was elected Director-at-large for the Texas section of Mathematical Association of America and served as director of the High School Lecture Program for the Texas section.
She had a successful, lengthy career and served on several boards and committees of note, retiring in 1994 due to ill health.  She was the fifth African-American woman to be allowed in the White House.She was also active in her local community as a lifetime member of New Hope Baptist Church. She served on boards of directors for Cerebral Palsy, Goodwill Industries, and Family Counseling and Children. She was on the Texas State Advisory Council for Construction of Community Mental Health Centers and served on the board of the Heart of Texas Region Mental Health and Mental Retardation Center.
After Lillian K. Bradley in 1960, Malone-Mayes became one of the first African-American women to receive a PhD in Mathematics from University of Texas (and fifth African-American woman in the United States). She was the first African-American member of the faculty at Baylor University, and the first African-American person elected to Executive Committee of the Association of Women in Mathematics.
The student congress of Baylor voted her the "Outstanding Faculty Member of the Year" in 1971.  *Wik & *SAU


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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