## Saturday, 6 March 2021

### On This Day in Math - March 6

 Santa Sindone in Turin.

Nobody since Newton has been able to use geometrical methods to the same extent for the like purposes; and as we read the Principia we feel as when we are in an ancient armoury where the weapons are of gigantic size; and as we look at them we marvel what manner of man he was who could use as a weapon what we can scarcely lift as a burden.
~William Whewell

The 65th day of the year; 65 is the smallest hypotenuse of two different primitive Pythagorean triangles (and of two other triangles that are not primitive) with all integral sides. (Don't just sit there, find them!)
John Golden@mathhombre not only found them, he made the image below.
And $65 = 1^5 + 2^4 + 3^3 + 4^2 + 5^1$ *jim wilder ‏@wilderlab

OR, $65= 0^2 + 1^4 + 2^5 + 3^3 + 4^1 + 5^0$ *@Expert_says

65 is the constant of a 5x5 normal magic square.
A magic square with the integers 1 through 25 has a sum of 65 in each row, column, and major diagonal.

Euler found 65 integers, which he called "numeri idonei," that could be used to prove the primality of certain numbers.[idoneal numbers (also called suitable numbers or convenient numbers) are the positive integers D such that any integer expressible in only one way as $x^2 ± Dy^2$ (where x2 is relatively prime to Dy2) is a prime, prime power, twice one of these, or a power of 2. In particular, a number that has two distinct representations as a sum of two squares (such as 65) is composite. Every idoneal number generates a set containing infinitely many primes and missing infinitely many other primes.]

65 is the difference of fourth powers of two consecutive  primes. And a note about fourth powers of primes.  For any prime greater than five, the last digits of a p^4 either ends in an odd digit followed by six, or an even digit followed by one.

EVENTS
1620 Edmund Gunter appointed Gresham Professor of Astronomy. In 1619 the wealthy but earnest Sir Henry Savile put up money to fund Oxford University's first two science faculties, the chairs of astronomy and geometry. Gunter applied to become professor of geometry but Savile was famous for distrusting clever people, and Gunter's behavior annoyed him intensely. As was his habit, Gunter arrived with his sector and quadrant, and began demonstrating how they could be used to calculate the position of stars or the distance of churches, until Savile could stand it no longer. "Doe you call this reading of Geometric?" he burst out. "This is mere showing of tricks, man!" and, according to a contemporary account, "dismissed him with scorne." He was shortly thereafter championed by the far wealthier Earl of Bridgewater, who saw to it that on 6 March 1619 Gunter was appointed professor of astronomy in Gresham College, London. This post he held till his death. Gunter created the first logarithmic scale. Gunter's scale or Gunter's rule, generally called the "Gunter" by seamen, is a large plane scale, usually 2 feet (0.61 m) long by about 1½ inches broad (600 mm by 40 mm), and engraved with various scales, or lines. On one side are placed the natural lines (as the line of chords, the line of sines, tangents, rhumbs, etc.), and on the other side the corresponding artificial or logarithmic ones. By means of this instrument questions in navigation, trigonometry, etc., are solved with the aid of a pair of compasses. It is a predecessor of the slide rule, a calculating aid used from the 17th century until the 1970s.
He is also known for Gunter's chain , a geodetic measuring device used for land survey. When the Northwest territory (Ohio, Indiana, Michigan, Illinois etc) was created, the decreed official measure was the Gunther Chain.*Wik On a visit to Stratford on Avon while at Hall's croft, the home of Shakespeare's daughter Susanna and her husband, Dr John Hall, I came across an early map of the town and the only legend shown was in Gunter's Chains. Watching an English Cricket match one day in Dec of 2006, I realized that the length of the bowling area (between the two wickets) is one chain also.

In 1661, the Royal Society, London, England, elected Sir Robert Moray as their first president. *TIS

 @royalsociety
1665 first appearance of the Philosophical Transactions of the Royal Society. The Journal des sçavans (later renamed Journal des savants), founded by Denis de Sallo, was the earliest academic journal published in Europe, that from the beginning also carried a proportion of material that would not now be considered scientific. The first edition appeared as a twelve page quarto pamphlet on Monday, 5 January 1665. This was shortly before the first appearance of the Philosophical Transactions of the Royal Society, on 6 March 1665. *Wik

1689 Edmond Halley first wrote about diving equipment in a paper of 6 March 1689, perhaps prompted by his work on the Thames survey undertaken around that time. Halley proposed a mobile diving bell built on four wheels, and while he didn’t build that particular bell, he did build another as part of his salvage work on the wreck of the Guynie frigate. *halleyslog

 *http://laurenroyal.com/
1703 Robert Hooke is buried at the church of St Helen, Bishopsgate, London. He had died on March 3. The only known portrait of Robert Hooke, which hung in Gresham College, mysteriously disappeared shortly after his death. A memorial window to him was destroyed by a bomb in 1992.
Hooke was elected to the Royal Society in 1663 and became its curator for the rest of his life. He was Professor of Geometry at Gresham College, London, and lived there as a bachelor until his death in 1703.
For those who do not know his story, Lisa Jardines, biography is wonderful.

1741 Euler writes to Goldbach that he has proved “a theorem of Fermat’s” according to which primes p = 4n + 3 cannot divide a sum of two squares $a^2 + b^2$ except when both a and b are divisible by p. Correspondence of Euler and Goldbach.

1766 d’Alembert writes Lagrange to tell him Euler is leaving Berlin Academy:
Mr Euler is leaving, he says, for St.Petersburg because of some unhappiness he has had in Berlin. I wrote to him to dissuade him. If he leaves, and you want to replace him, you have only to write me and I will do my best to serve you.
Before 1766, Frederick II of Prussia had more than once invited both d’Alembert and Lagrange to move to Berlin. The d'Alembert had declined the offer and suggested the name of his Turinese friend. But Lagrange, even though he was on good terms with Euler, did not relish a "cohabitation" with him in the Berlin Academy. It seems he may have feared Euler would overshadow him. *Mauro Allengranza, Stack Exchange

1805 Legendre introduced least squares. Gauss had them ten years earlier but had not published, so some controversy ensued. *VFR It was on this day that he published the little 80 page appendix, Nouvelle me'thodes pur la determination des orbites des cometes. "Of all the principals that can be proposed fro this purpose, I think there is none more general, more exact, or easier to apply,... it consists of making the sum of the squares of the errors a minimum." *Stephen M. Stigler, The History of Statistics

1815 Wilhelm Olbers, an amateur German astronomer who was a doctor by profession, discovered the periodic comet now named for him.  This amateur astronomer would discover many comets, and his calculating method would change the science.  He became a lifelong friend of Gauss after their correspondence regarding the discovery of Ceres in January of 1802.  He would allow Guass to name the planet (now, asteroid, a term not in use then) that he discovered in 1807, Vesta. *Wik

1832 Gauss responds to his “old, unforgettable friend,” Farkas (Wolfgang) Bolyai, that he has been working on non-Euclidean geometry “in part already for 30–35 years.” In the same letter Gauss points out several ﬂaws in Euclid. *VFR Bolyai had included the work of Janos, his son, on non-Euclidean Geometry in a letter to Guass on the 20th of June 1831.. and again on the 16th of January 1832 Farkas sent the Appendix to Gauss again with another letter in which he wrote: My son appreciates Your critique more than that of whole Europe and it is the only thing he is waiting for''. In his response, One of Gauss' well-known sentences was: if I praised your son's work I would praise myself''. The letter deeply afflicted and upset János Bolyai, although it reflects appreciation, too: ... I am very glad that it is my old friend's son who so splendidly preceded me'' *Komal Journal

In 1869, Dmitry Mendeleev published his first version of the periodic table of the elements. He was a Russian chemist who developed the periodic classification of the elements. In his final version of the periodic table (1871) he left gaps, foretelling that they would be filled by elements not then known and predicting the properties of three of those elements. *TIS  Mendeleev had written the properties of elements on pieces of card and tradition has it that after organizing the cards while playing patience he suddenly realized that by arranging the element cards in order of increasing atomic weight that certain types of element regularly occurred.*Royal Society of Chemistry

1896 Dutch cryogenic physicist, Heike Kamerlingh Onnes, writes to James Dewar in England to explain the reason he had not made any recent experiments in cooling gases: "..you will be astonished to hear. The municipality of Leiden has made objections as to my working with condensed gases and has not been content with asking that additional means of precaution are taken, but is gone so far to claim in August last that my cryogenic laboratory be removed from the city! " *archive of the Kamerlingh Onnes Laboratory

In 1913, this date was written by Niels Bohr on his first paper describing his new ideas on atomic structure, and mailed to his mentor, Ernest Rutherford. It was one of three historic papers he wrote on this subject. *TIS

1953 James Watson and Francis Crick submitted to the journal Nature their first article on the structure of DNA. It was published in the 25 Apr 1953 issue. "We wish to put forward a radically different structure for the salt of deoxyribose nucleic acid. This structure has two helical chains each coiled around the same axis... Both chains follow right-handed helices... The novel feature of the structure is the manner in which the two chains are held together by purine and pyrimidine bases... They are joined together in pairs, a single base from one chain being hydrogen-bonded to a single base from the other chain, so that the two lie side by side with identical z-co-ordinates. One of the pair must be a purine and the other a pyrimidine in order for bonding to occur."*TIS

1967 A study of twelve industrial nations revealed that mathematics achievement is highest in Japan, lowest in the U.S. *VFR

1992 Michaelangelo Virus Strikes: Concerns over the Michelangelo virus sparked a scare among everyone from personal computer users to world governments. As many as 5 million computers reportedly were at danger of contracting the virus, set to erase data on the March 6 anniversary of the artist's birth. In fact, Michelangelo spread to only a few thousand machines. *CHM

BIRTHS
1847 Johann Georg Hagen (6 Mar 1847, 5 Sep 1930) Austrian Jesuit priest and astronomer who made a catalog of variable stars (1890-1908). Working at the Vatican Observatory he reexamined for accuracy the listing of all of the NGC (New General Catalogue of Nebulae and Star Clusters) objects north of about -30 degrees. He published lists of errata in the NGC. During his observations, he observed dark nebulae, tenuous dark clusters of interstellar matter sometimes known as Hagen's clouds. These strange clouds have not been recorded by others, and are now attributed to optical illusions associated with visual observations. Jesuits have been involved in astronomy since 1551 when Fr. Christoph Clavius, SJ, a mathematician and astronomer helped Pope Gregory XIII reform the calendar.*TIS

1866 Ettore Bortolotti (6 March 1866 in Bologna, Kingdom of Sardinia (now Italy)
- 17 Feb 1947 in Bologna, Italy) Italian mathematician who worked in various areas in analysis. He was interested in the history of mathematics. *SAU . He revealed the importance of Evange¬lista Torricelli’s inﬁnitesimal results and vindicated Cataldi’s claim to the discovery of continued fractions. *VFR

1901 Naum Ilyich Akhiezer (6 March 1901 – 3 June 1980) was a Soviet mathematician of Jewish origin, known for his works in approximation theory and the theory of differential and integral operators. He is also known as the author of classical books on various subjects in analysis, and for his work on the history of mathematics. He is the brother of the theoretical physicist Aleksander Akhiezer.*Wik

DEATHS
1683 Guarino Guarini (17 Jan 1624; 6 Mar 1683) Italian architect and theologian whose study of mathematics led him to a career in architecture in which he created the most fantastic geometric elaboration of all baroque churches. In his Santissima Sindone, Guarini created a diaphanous dome - a geometrical optical illusion in the dome made through the use of the actual structure which creates the illusion that the dome recedes farther up into space than it really does. He wrote two architectural treatises and other works that concentrate on his mathematical knowledge. Therein, Guarini discusses Desargue's projective geometry, which reveal a scientific basis for his daring structures. He worked primarily in Turin and Sicily, with his influence stretching into Germany, Austria and Bohemia.*TIS

1866 William Whewell (24 May 1794, 6 Mar 1866 at age 71) British scientist, best known for his survey of the scientific method and for creating scientific words. He founded mathematical crystallography and developed Mohr's classification of minerals. He created the words scientist and physicist by analogy with the word artist. They soon replaced the older term natural philosopher. (actually the use of scientist was a very slow process often not well received. see more of the interesting story here) Other useful words were coined to help his friends: biometry for Lubbock; Eocine, Miocene and Pliocene for Lyell; and for Faraday, anode, cathode, diamagnetic, paramagnetic, and ion (whence the sundry other particle names ending -ion). In metereology, Whewell devised a self-recording anemometer. He was second only to Newton for work on tidal theory. He died as a result of being thrown from his horse. *TIS
In a single letter to Faraday on 25 April, 1834; he invented the terms cathode, anode and ion. The letter is on display at the Wren Library at Trinity College, Cambridge, UK.

1939 Carl Louis Ferdinand von Lindemann (12 Apr 1852, 6 Mar 1939 at age 86) He showed π transcendental not the root of any algebraic equation with rational coefficients), consequently the circle cannot be squared. (constructing a square with the same area as a given circle using ruler and compasses alone.) In 1873, Lindemann visited Hermite in Paris and discussed the methods which Hermite had used in his proof that e, the base of natural logarithms, is transcendental. Following this visit, Lindemann was able to extend Hermite's results to show that pi was also transcendental. *TIS(the image is of his tombstone.... note the square and circle with Pi inside.

2005 Hans Bethe (2 Jul 1906, 6 Mar 2005 at age 98), German-born American theoretical physicist who helped to shape classical physics into quantum physics and increased the understanding of the atomic processes responsible for the properties of matter and of the forces governing the structures of atomic nuclei. Bethe did work relating to armor penetration and the theory of shock waves of a projectile moving through air. He studied nuclear reactions and reaction cross sections (1935-38). In 1943, Oppenheimer asked Bethe to be the head of the Theoretical Division at Los Alamos on the Manhattan Project. After returning to Cornell University in 1946, Bethe became a leader promoting the social responsibility of science. He received the Nobel Prize for Physics (1967) for his work on the production of energy in stars. *TIS

1944 Aleksandr Petrovich Kotelnikov (20 Oct 1865 in Kazan, Russia - 6 March 1944 in Moscow, USSR) In 1927 he published one of his most important works, The Principle of Relativity and Lobachevsky's Geometry. He also worked on quaternions and applied them to mechanics and geometry. Among his other major pieces of work was to edit the Complete Works of two mathematicians, Lobachevsky and Zhukovsky. He received many honours for his work, being named Honoured Scientist in 1934, then one year before he died he was awarded the State Prize of the USSR. *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