Thursday, 1 October 2026

Parallelepiped , Epicycle ... History and Etymology of Math Terms

    Parallelepiped This word for a solid made by intersecting pairs of parallel planes forming six faces that are each parallelograms is rapidly becoming obsolete, although no good word has emerged to replace it.

A rectangular or orthogonal parallelepiped is the shape of a room or a shoe box. The word is condensed from the Greek word parallelepipedon for the same shape. The roots are para (beside) + allel (other) + epi (on) and pedon (ground). Parallelepipedon was the word used by Billingsley in his 1570 translation of Euclid, the first known use of the word in English. According to John Conway, this was the common term in use until around 1870 to 1900 when it gave way to parallelepiped; although the OED lists its use by John Playfair as early as 1812. A posting from John Albree of Auburn University cited an earlier use. [In Charles Hutton's *Dictionary* (volume 2, 1795, p.199), the terms "parallelopiped" and "parallelopipedon" are presented equally, and he remarks that such a polyhedron "is only a particular species" of a prism.]



This newer term now seems headed for demise due to changes in school curriculum and the reduced coverage of solid geometry, although one correspondent suggests that "parallelepipedo" would be known by most Spanish students. I was somewhat surprised to find that parallelepiped is present in my computer spell check, which I find often omits technical terms.


The word is pronounced with the accent on the epi syllable. The para root is common in math words and is related to other words like parlor, paragraph, and parable. Allel became our alter, for other, and gives us alternate and alternative. The epi root shows up in epidermis (on the skin), epitaph (over the grave), epicycle (on the circle), and epidemic (on the people). Pedon is from ped for foot, and was also generalized for plane.


The term EPICYCLE was used in the astronomical system of Claudius Ptolemy to signify a small circle, having its center on the circumference of a bigger circle. The English word came via Latin from the Greek upon + circle. The earliest quotation in the OED is from Chaucer's Treatise on the Astrolabe (about 1391): "The Moone Moeuyth the contrarie from othere planetes as in hire Episicle." The term EPICYCLOID was used by Philippe de La Hire in Traité des épicycloïdes et leur usage en mécanique, which he read to the Academy of Sciences in 1694. A footnote in the Collected Works of Jacob Bernoulli says the term is apparently due to La Hire. [Information provided by François Ziegler.] Epicycloid is found in English in 1695 in "The Quadrature of a Portion of the Epicycloid" by a Mr. Caswel or Caswell (both spellings appear) in Philosophical Transactions For the Month of October, 1695. [Google print search by James A. Landau]


On This Day in Math - October 2

    


Euler calculated without effort, just as men breathe, as eagles sustain themselves in the air.
~François Arago


The 275th day of the year; 275 is the number of partitions of 28 in which no part occurs only once. (Students might try finding the similar number of partitions for 10, or some smaller number to get a sense for how they grow)

275 can be written in 5 ways as a sum of consecutive naturals, for example, 20 + ... + 30

275 is an arithmetic number, because the mean of its divisors, 62, is an integer

275 is the maximum number. of pieces that can be formed from an annulus with 22 straight lines. 



EVENTS

479 B.C.: an Annular Solar Eclipse known as "Xerxes' eclipse" as noted by Herodotus occurred. David Dickinson ‏@Astroguyz  The questions about this eclipse basically boil down to two questions, Why did his advisors think the predicted solar eclipse was a GOOD omen, and why was there no eclipse in the area that day,  One of these we have some idea about. The Babylonians had a mathematical relationship for the period between solar eclipses, but didn't seem to understand the actual mechanics of the occurrence.  Sometimes when they predicted a solar eclipse it happened, but not where they were.  There predictions were accurate often enough that these "hidden" eclipses were significant in there way also.  

This cuneiform text mentions the murder of Xerxes I (r. 485-465 BCE) by his son and a lunar eclipse (609-447 BCE). From Babylon, Iraq. British Museum





1608, the Dutch Estates General examined an application for a patent for "a device to observe things at a distance" presented by a certain Hans Lipperhey (?-1619) an obscure spectacles-maker from Middelburg, in southwestern Holland The patent application was rejected on the grounds that, although the usefulness of the device was recognised, especially for military purposes it was deemed impossible to keep the secret of its construction for very long. And especially considering that, in those same days, another instrument-maker - a certain Sacharias Janssen (1588-1630), he too a spectacles-maker in Middelburg, indicated by Pierre Borel (c. 1620-1671) a few decades later as the true inventor of the telescope - declared that he knew how to build the instrument.*Institute and Museum of the History of Science
I doubt that many modern science/math historians believe that Lipperhey invented the telesccope, and neither did any of the myriad other names suggested over the years.
The first historical construct concerns the ‘invention’ itself, because what happened in
1608 was in fact not an invention at all, but merely a recognition of the great potential of a device, which must have been around for some decades, as a kind of toy or as a device whose purpose was to correct or improve vision. Indications of the awareness of the magnifying power of a combination of two lenses, long before the year 1608, are indeed abundant in the contemporary literature. For instance, in 1538 the Italian scholar Girolamo Fracastoro wrote: ‘If someone looks through two eye-glasses, of which one is placed above the other, he shall see everything larger and more closely.’
After seeing or hearing of Lipperhey’s telescope, many scholars had a kind of déjà vu -feeling. Girolamo Sirtori, who in 1612, only four years after the emergence of the instrument, composed his well-known Telescopium, captured this feeling in the following phrase: "It appeared that this conception was in the minds of many men, so that once they
heard about it, any ingenious person began trying to make one, without [the help of ]
a model."
*Huib J. Zuidervaart, The ‘true inventor’ of the telescope. A survey of 400 years of debate origins of the telescope


1667 On this day in 1667, Isaac Newton became a fellow at Trinity College, Cambridge. He had earned his bachelor's degree in 1665 and then spent two years at home in Lincolnshire inventing much of differential and integral calculus while Cambridge was closed due to the plague.


Woolsthorpe by Colsterworth, Newton's childhood hom



1759 “Your solution of the isoperimetric problems leaves nothing to be desired and I rejoice that this subject, with which I have been so completely occupied since my first efforts, has been carried by you to such a high degree of perfection. The importance of the subject has stimulated me to develop, aided by your lights, an analytical solution that I will keep secret as long as your own meditations are not published, lest I take away from you a part of the glory you deserve.” So wrote Euler to the young Lagrange. See Allen Shields, “Lagrange and the M´ecanique Analytique,” The Mathematical Intelligencer, 10:4, Fall 1988, pp. 7– 10. *VFR





1836 Charles Darwin returned from his voyage on the HMS Beagle to the Pacific. It would be 23 years before he published Origin of Species. *TIS

The second survey expedition of HMS Beagle took place from 27 December 1831 to 2 October 1836. Robert FitzRoy, the newest commander of Beagle, had thought of the advantages of having someone onboard who could investigate geology, and sought a naturalist to accompany them as a supernumerary. At the age of 22, the graduate Charles Darwin hoped to see the tropics before becoming a parson, and accepted the opportunity. He was greatly influenced by reading Charles Lyell's Principles of Geology during the voyage. By the end of the expedition, Darwin had made his name as a geologist, and fossil collector, and the publication of his journal (later known as The Voyage of the Beagle) gave him wide renown as a writer.

Beagle sailed across the Atlantic Ocean, and then carried out detailed hydrographic surveys around the coasts of southern South America, returning via Tahiti and Australia, after having circumnavigated the Earth. The initial offer to Darwin told him the voyage would last two years; it lasted almost five.

Darwin spent most of this time exploring on land: three years and three months on land, 18 months at sea. Early in the voyage, Darwin decided that he could write a geology book, and he showed a gift for theorising. At Punta Alta in Argentina, he made a major find of gigantic fossils of extinct mammals, then known from very few specimens. He collected and made detailed observations of plants and animals. His findings undermined his belief in the doctrine that species are fixed, and provided the basis for ideas which came to him when back in England, leading to his theory of evolution by natural selection.



1856 Sylvester was to dine with Charles Wheatstone, the noted physicist and inventor, and had invited Arthur Cayley to attend and meet Wheatstone. Wheatstone had supported Sylvester's successful candidacy for the Royal Society in 1836. James Joseph Sylvester: Life and Work in Letters, *James Joseph Sylvester: Life and Work in Letters
edited by Karen Hunger Parshall





1912 Ernest Rutherford presents his theory of the structure of the Atom to a session of the Manchester Literary and Philosophical Society. He rejected Thompson's "Plum Pudding" model for an atom with most of its mass concentrated into a tiny charged core in its center. *Brody&Brody, The Science Class You Wish You Had

Rutherford's model proposed that the negatively charged electrons surround the nucleus of an atom. He also claimed that the electrons surrounding the nucleus revolve around it with very high speed in circular paths. He named these circular paths as orbits.



1937 The London Illustrated News had a picture of a wolf bone discovered in Czechoslovakia by Karl Absolom which has 55 notches in groups of 5, the first 25 being separated from the rest by one of double length. Dating from 30,000 BC, this is the earliest record of counting. [Bunt, Jones, Bedient, The Historical Root of Elementary Mathematics, p 2]. *VFR (The head of an ivory Venus figurine was excavated close to the bone.)





1950 On October 2, 1950, Charles M. Schulz introduced the world to what would become one of the most influential comic strips in history with the debut of Peanuts. Syndicated in only seven newspapers, the first four-panel strip featured a character named Shermy praising a passing Charlie Brown to another kid named Patty, only to bluntly conclude in the final frame, "How I hate him!". This simple interaction established the strip's signature blend of childhood innocence and sharp, melancholy humor. However, the famous title wasn't Schulz's choice. He had originally named the strip Li'l Folks, but United Features Syndicate forced a change to avoid legal conflicts with an older, retired cartoon. A production manager at the syndicate arbitrarily chose "Peanuts"—likely inspired by the "Peanut Gallery" audience on the popular Howdy Doody Show—and slapped it on the comic without Schulz's input. Schulz deeply hated the name his entire life, believing it lacked dignity and made no sense. Despite his ongoing resentment toward the title, this momentous publication laid the groundwork for a counterculture phenomenon that would eventually expand to feature legendary characters like Snoopy, who would appear on Ocrober 4, have touch millions of readers worldwide, and permanently redefined the landscape of American newspaper comics.*AI edited



1955 The Electronic Numerical Integrator and Computer (ENIAC) retired. After disassembly, parts of this computer were shipped to the Smithsonian for display. *Goldstein, The Computer from Pascal to von Neumann, p. 234–5.
After eleven years of calculating and processing programs, the ENIAC was retired. Designers John Mauchly and J. Presper Eckert had unveiled the machine in February 1946, showing off its 1,000-time improvement in speed over its contemporaries. The ENIAC ran at 5,000 operations a second with a system of plug boards, switches, and punch cards. It occupied 1,000 square feet of floor space. *CHM




1956, the Atomicron, the first atomic clock in the U.S., was unveiled at the Overseas Press Club in New York City. The basis of the timing was the constant frequency of the oscillations of the caesium atom - 9,192,631,830 MHz. It was priced at $50,000. The Atomicron measured 84" high, 22" wide and 18" deep. *TIS

The Atomichron was the world's first commercial atomic clock, built by the National Company, Inc. of Malden, Massachusetts. It was also the first self-contained portable atomic clock and was a caesium standard clock. More than 50 clocks with the trademarked Atomichron name were produced.

 *Wlk

A radio-controlled atomic clock from American Time offers a simple way to get synchronized time from a real atomic clock synced by radio broadcast from the National Institute of Standards and Technology (NIST) in Fort Collins, Colorado.


Looks incredibly like battery operated clock on my kitchen wall,
without atomic correction, (thrift store purchase for $2.00



1959 At the New England eclipse of October 2, 1959, Dr. E. H. Land, inventor of the Polaroid Land camera, had accompanied Harvard astronomers on a DC-6 plane that flew above the heavy overcast. On this flight, Dr. Land and his colleagues secured several excellent photographs of the corona, using Polaroid cameras with telephoto lenses. *NSEC





2002 Why no one trusts medical research: On this date Ig Nobel prizes were awarded to two groups of medical researchers, one from the US who proved that Coca-Cola is an effective spermicide (New England Journal of Medicine, 1985), and one from Taiwan who proved that it is not(Human Toxicology, 1987). *Improbable.com

Come on science, figure this out, teenagers around the world need to know.






BIRTHS


1568 Marino Ghetaldi (2 Oct 1568, 11 April 1626) was a Croatian mathematician who published work with early applications of algebra to geometry. *SAU His best results are mainly in physics, especially optics, and mathematics. He was one of the few students of François Viète. He took over Viète's work to restore Apollonius' lost works. He followed Pappus's description of the contents of certain lost books and to do this he had to solve the problems which the books were supposed to contain. He published Apollonius redivivus seu restituta Apollonii Pergaei inclinationum geometria and Supplementum Apollonii Galli seu exsuscitata Apollonii Pergaei tactionum geometriae pars reliqua both in Venice in 1607.

* National Maritime Museum

Renowned for the application of algebra in geometry and his research in the field of geometrical optics on which, he wrote 7 works, including the Promotus Archimedus (1603) and the De resolutione et compositione mathematica (1630). He also produced a pamphlet with the solutions of 42 geometrical problems, Variorum problematum colletio, in 1607 and set grounds of algebraization of geometry. His contributions to geometry had been
cited by Dutch physicist Christiaan Huygens and Edmond Halley in England.
Ghetaldić was the constructor of the parabolic mirror (66 cm in diameter), kept today at the National Maritime Museum in London. During his sejourn in Padua he met Galileo Galilei, with whom he corresponded regularly. He was a good friend to the French mathematician François Viète. He was offered the post of professor of mathematics in Leuven in Belgium, at the time one of the most prestigious university centers in Europe.


1791 Aléxis Thérèse Petit (2 Oct 1791, 21 June 1820) was a French mathematician who worked on the theory of heat.*SAU

Alexis-Thérèse Petit was a precocious child. A student at the central school in Besançon , it is said that "at ten and a half years old he had already acquired the necessary knowledge to be admitted to the École Polytechnique .  " Thanks to the mathematician Jean Nicolas Pierre Hachette , he continued his studies in Paris at the École des Sciences et Belles-Lettres . In 1807, at the age of sixteen, the minimum age, he sat the entrance exams for the École Polytechnique, where he was admitted first in his class. He studied there for two years, after which his exceptional academic results led the school's graduating jury to place him at the very top of his class. He was then appointed tutor of analysis (1809), then tutor of physics (1810) under Jean Henri Hassenfratz , and simultaneously professor of physics at the Lycée Bonaparte, where he was replaced by Claude Pouillet from 1817. In 1811, he became one of the very first Doctors of Science from the Faculty of Sciences of Paris . After Hassenfratz's resignation in 1814, he was put in charge of the course as assistant professor (Charles Lehot replaced him as tutor), he was then 23 years old, then as full professor (1815), a position he held until his death from tuberculosis , which occurred shortly after that of his wife. He became a member of the Philomathic Society of Paris inFebruary 1818.

He is known for having proposed in 1819 , with Pierre Louis Dulong , a theory to explain the value of the specific heat of metals known as the Dulong and Petit law .

He was François Arago 's brother-in-law (their wives were sisters).

A street and a school in Vesoul ( Haute-Saône ), his hometown, bear the name of Rue Petit.*Wik





1825 John James Walker (2 Oct 1825, 15 Feb 1900) The range of Walker's mathematical research was quite impressive. He wrote some articles on theoretical mechanics but his more elaborate papers were on advanced algebra and geometry. Walker was a strong advocate of Hamilton's quaternions and strongly believed that they had not been given as wide a use as they merited. He applied quaternions to a variety of problems, mostly of an elementary nature.
The three most important papers that Walker wrote were on the analysis of plane curves and curved lines. The papers were closely connected and all appeared in the Proceedings of the London Mathematical Society. He wrote further articles on cubic curves and in this area he wrote the memoir On the diameters of cubic curves which was published in the Transactions of the Royal Society in 1889. *SAU




1852 Sir William Ramsay (2 Oct 1852; 23 Jul 1916) Scottish chemist who discovered the "inert gases", neon, krypton and xenon, and co-discovered argon, radon, calcium and barium. Nobel laureate (1904) "in recognition of his services in the discovery of the inert gaseous elements in air, and his determination of their place in the periodic system." Died in High Wycombe, Buckinghamshire.*TIS

#Linda Hall Org



1886 Robert Julius Trumpler (2 Oct 1886; 10 Sep 1956) Swiss-born U.S. astronomer who moved to the US in 1915 and worked at the Lick Observatory. In 1922, by observing a solar eclipse, he was able to confirm Einstein's theory of relativity. He made extensive studies of galactic star clusters, and demonstrated (1930) the presence throughout the galactic plane of a tenuous haze of interstellar material that absorbs light generally that dims and reddens the light from of distant clusters. The presence of this obscuring haze revealed how the size of spiral galaxies had been over-estimated. Whereas Harlow Shapley, in 1918, determined the distance to the centre of the Milky Way to be 50,000 light-years away, Trumpler's work reduced this to 30,000 light-years.*TIS




1901 Charles Stark Draper (2 Oct 1901; 25 Jul 1987) American aeronautical engineer, educator, and science administrator who earned degrees from Stanford, Harvard, and MIT then, in 1939, became head of MIT's Instrumentation Laboratory, which was a centre for the design of navigational and guidance systems for ships, airplanes, and missiles from World War II through the Cold War. He developed gyroscope systems that stabilized and balanced gunsights and bombsights and which were later expanded to an inertial guidance system for launching long-range missiles at supersonic jet targets. He was "the father of inertial navigation." The Project Apollo contract for guiding man and spacecraft to the moon was also placed with the Instrumentation Lab. *TIS




1908 Arthur Erdélyi studied in Brno and Prague and came to Scotland before the Second World War to avoid the Nazi invasion of Czechoslovakia. He became a lecturer at Edinburgh and after a period in the USA he returned to Edinburgh as a Professor. He was an expert on Special Functions. He became President of the EMS in 1971. *SAU



1926 Michio Suzuki (October 2, 1926 – May 31, 1998) was a Japanese mathematician who studied group theory.
He was a Professor at the University of Illinois at Urbana-Champaign from 1953 to his death. He also had visiting positions at the University of Chicago (1960–61), the Institute for Advanced Study (1962–63, 1968–69, spring 1981), the University of Tokyo (spring 1971), and the University of Padua (1994). Suzuki received his Ph.D in 1952 from the University of Tokyo, despite having moved to the United States the previous year. He was the first to attack the Burnside conjecture, that every finite non-abelian simple group has even order.
A notable achievement was his discovery in 1960 of the Suzuki groups, an infinite family of the only non-abelian simple groups whose order is not divisible by 3. The smallest, of order 29120, was the first simple group of order less than 1 million to be discovered since Dickson's list of 1900.
He classified several classes of simple groups of small rank, including the CIT-groups and C-groups and CA-groups.
There is also a sporadic simple group called the Suzuki group, which he announced in 1968. The Tits ovoid is also referred to as the Suzuki ovoid. *Wik




1929 Branko Grünbaum ( October 2, 1929  in Osijek , Croatia ; September 14, 2018 in Seattle , Washington) was an Israeli mathematician of Yugoslavian descent who worked on discrete geometry.

A scholarship allowed Grünbaum to spend from September 1958 to June 1960 at the Institute for Advanced Study at Princeton, USA. Branko and Zdenka, with their son Ram, sailed on the T.S.S. Olympia arriving in New York on 5 September 1958 having left Lisbon exactly one month earlier. From New York they travelled by train to Princeton. After two years at Princeton, they spent one year in Seattle at the University of Washington where their second son Daniel Grünbaum was born on 2 November 1960. The family had spent the summer of 1960 at the University of California, Los Angeles, living during this time in Santa Monica. While in Seattle, Grünbaum accepted a position at the Hebrew University in Jerusalem.

There now arose a complication with his marriage. Branko and Zdenka's Orthodox Jewish marriage had been annulled because Branko's mother was not Jewish. In the City of Seattle, on 5 September 1961, Branko Grünbaum and Zdenka Bienenstock were married by a Justice of the Peace at 9:30 a.m. just before they left the United States for Jerusalem. Back at the Hebrew University his career went extremely well and he was promoted to Associate Professor in 1964. By this time he had over fifty publications and, let us note at this point, that he carried on with a remarkably high publication rate throughout his life; MathSciNet list 271 publications in total.

Grünbaum now felt slightly uneasy in Israel since, despite having a Jewish father, he had been declared a non-Jew since his mother was not Jewish. This eventually contributed to his decision to leave Israel and emigrate to North America. In 1965 he went to Michigan State University to spend a sabbatical year. While there he learnt of another marriage being annulled in similar circumstances to his own and the Israeli immigrant from the mixed marriage had her passport and citizenship revoked; this tipped the balance. It was not an easy decision, however, since Zdenka had been half way through her Ph.D. studies in Chemistry when they left Israel and she would have liked to have returned to complete the degree. Grünbaum had two possible places in North America which were particularly attractive because of his interest in geometry, the University of Toronto where Donald Coxeter was a professor, and the University of Washington in Seattle where he could work with Victor Klee. He chose the University of Washington where he was appointed to a full professorship in 1966 and remained there for the rest of his career until he retired in 2001. *SAU








DEATHS

1853 Dominique François Jean Arago (26 Feb 1786, 2 Oct 1853) was a French physicist and astronomer who discovered the chromosphere of the sun (the lower atmosphere, primarily composed of hydrogen gas), and for his accurate estimates of the diameters of the planets. Arago found that a rotating copper disk deflects a magnetic needle held above it showing the production of magnetism by rotation of a nonmagnetic conductor. He devised an experiment that proved the wave theory of light, showed that light waves move more slowly through a dense medium than through air and contributed to the discovery of the laws of light polarization. Arago entered politics in 1848 as Minister of War and Marine and was responsible for abolishing slavery in the French colonies. *TIS A really great blog about Arago, With the catchy title, "François Arago: the most interesting physicist in the world!" is posted here. Read this introduction, and you will not be able to resist:

When he was seven years old, he tried to stab a Spanish solider with a lance
When he was eighteen, he talked a friend out of assassinating Napoleon
He once angered an archbishop so much that the holy man punched him in the face
He has negotiated with bandits, been chased by a mob, broken out of prison
He is:
François Arago, the most interesting physicist in the world

 Admit it, this guy is so cute, you want to hit him for existing.   



1929 Andrei Mikhailovich Razmadze (11 Aug 1889, 2 Oct 1929) His work was on the calculus of variations, continuing work by Weierstrass and Hilbert. The fundamental lemma of the calculus of variations is named after him. He also did important work on discontinuous solutions.*SAU



1933 Philipp Forchheimer (7 Aug 1852, 2 Oct 1933) Austrian hydraulic engineer who made significant studies of groundwater hydrology. Early in his academic career, he worked on problems of soil mechanics. Later, he turned to hydraulic problems, establishing the scientific basis of the discipline by applying standard techniques of mathematical physics - in particular Laplace's equation - to problems of groundwater movement. Laplace's equation had already been well developed for heat flow and fluid flow. Forchheimer extended the preexisting mathematical theory to calculations of groundwater flow. He was also the first to both mathematically and experimentally examine the features of dambreak waves in a rectangular channel (with his PhD student Armin Schoklitsch).*TIS



1962 Boris Yakovych Bukreyev (6 September 1859 – 2 October 1962) was a Russian and Soviet mathematician who worked in the areas of complex functions and differential equations.
In 1889, Bukreyev became a professor of mathematics at the University of Kiev, in Ukraine, Russian Empire. He studied Fuchsian functions of rank zero. He was interested in projective and non-Euclidean geometry. He worked on differential invariants and parameters in the theory of surfaces, being interested in the history of mathematics.*Wik



1977 Arthur Erdélyi ( December 12, 1977; October 2, 1908) studied in Brno and Prague and came to Scotland before the Second World War to avoid the Nazi invasion of Czechoslovakia. He became a lecturer at Edinburgh and after a period in the USA he returned to Edinburgh as a Professor. He was an expert on Special Functions. He became President of the EMS in 1971. *SAU



2006 Paul Richard Halmos​ (March 3, 1916 – October 2, 2006) was a Hungarian-born American mathematician who made fundamental advances in the areas of probability theory, statistics, operator theory, ergodic theory, and functional analysis (in particular, Hilbert spaces). He was also recognized as a great mathematical expositor. In a series of papers reprinted in his 1962 Algebraic Logic, Halmos devised polyadic algebras, an algebraic version of first-order logic differing from the better known cylindric algebras of Alfred Tarski and his students. An elementary version of polyadic algebra is described in monadic Boolean algebra.
In addition to his original contributions to mathematics, Halmos was an unusually clear and engaging expositor of university mathematics. This was so even though Halmos arrived in the USA at 13 years of age and never lost his Hungarian accent. He chaired the American Mathematical Society committee that wrote the AMS style guide for academic mathematics, published in 1973. In 1983, he received the AMS's Steele Prize for exposition. Some of his classics were:
How to read mathematics
How to write mathematics
How to speak mathematics.
In the American Scientist 56(4): 375–389, Halmos argued that mathematics is a creative art, and that mathematicians should be seen as artists, not number crunchers. He discussed the division of the field into mathology and mathophysics, further arguing that mathematicians and painters think and work in related ways.
Halmos's 1985 "automathography" I Want to Be a Mathematician is an account of what it was like to be an academic mathematician in 20th century America. He called the book “automathography” rather than “autobiography”, because its focus is almost entirely on his life as a mathematician, not his personal life. The book contains the following quote on Halmos' view of what doing mathematics means:
“ "Don't just read it; fight it! Ask your own questions, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? What happens in the classical special case? What about the degenerate cases? Where does the proof use the hypothesis?”
In these memoirs, Halmos claims to have invented the "iff" notation for the words "if and only if" and to have been the first to use the “tombstone” notation to signify the end of a proof, and this is generally agreed to be the case. The tombstone symbol ∎ (Unicode U+220E) is sometimes called a halmos. *Wik




2009 Shaun Wylie (17 January 1913 – 2 October 2009) was a British mathematician and World War II codebreaker.  Wylie was born in Oxford, England. The fourth son of Sir Francis Wylie (later the first Warden of Rhodes House, Oxford) and his wife Kathleen (formerly Kelly), he was educated at the Dragon School (in Oxford) and then Winchester College. He won a scholarship to New College, Oxford where he studied mathematics and classics. In 1934, he went to study topology at Princeton University, obtaining a PhD in 1937 with Solomon Lefschetz as his supervisor. At Princeton he met fellow English mathematician Alan Turing. He became a fellow of Trinity Hall, Cambridge in 1938/1939.

During World War II, Turing had been recruited to work at Bletchley Park, Britain's codebreaking centre. Turing wrote to Wylie around December 1940, who was by then teaching at Wellington College, inviting him to work at Bletchley Park. He accepted, and arrived in February 1941. He joined Turing's section, Hut 8, which was working on solving the Enigma machine as used by the Kriegsmarine. He became head of the crib subsection,[8] and allocated time on the bombe codebreaking machines.  Hugh Alexander, successor to Turing as head of Hut 8, commented that "except for Turing, no-one made a bigger contribution to the success of Hut 8 than Shaun Wylie; he was astonishingly quick and resourceful and contributed to theory and practice in a number of different directions".

Wylie transferred in Autumn 1943 to work on "Tunny", a German teleprinter cipher. He married Odette Murray, a WREN in the section. In 1945, soon after the victory in Europe, Wylie demonstrated how Colossus – electronic machines used to help solve Tunny – could have been used unmodified to break the Tunny "motor wheels", a task which had been previously done by hand. While at Bletchley Park, he became president of the dramatic club. He had also played international hockey for Scotland, but according to fellow codebreaker I. J. Good, he "never mentioned any of his successes".

Wylie supervised five PhD students at Cambridge, through whom he had over 1600 "descendants" in 2021 according to the American Mathematical Society Mathematical Genealogy Project.[5] In addition he influenced the intellectual development of generations of pupils at the Cambridgeshire High School for Boys/Hills Road Sixth Form College where he taught maths (particularly statistics, with his beloved chi-squared distribution) and classical Greek and where he also produced plays (such as Chekhov's The Cherry Orchard) and supervised the school chess team. He also came out of retirement temporarily to teach Mathematics at Long Road Sixth Form College.

After retirement from teaching, Wylie was instrumental in the founding of the Liberal Democrats and in the Cambridge-based University of the Third Age and at the time of his death was preparing to read in the next Cambridge Greek Play, Aeschylus' Agamemnon. sounds like a rich full life and he lived every minute of it.]

His eldest son, the late Keith Wylie (1945–1999), a barrister, was a croquet international and open champion of Great Britain.

Shaun Wylie died on 2 October 2009, aged 96




2011 Frank Levin (19 June 1927, Dayton, Ohio, USA, 2 October 2011, Swansea, Wales) was an American mathematician who worked mainly in infinite group theory.

Frank Levin was born 19 June 1927 in Dayton, Ohio, the eldest of two children. When the younger child, Julie, was born, their father deserted the family, leaving their mother the difficult task of bringing up two children, in some considerable poverty. This was in fact the time of the great depression in America. Because Julie lacked a father, Frank was forced to be the father substitute, which he did well, so that his sister was always grateful to him. Those difficult years obviously remained with him all his life, and he was always extremely careful in spending.

Early on he showed signs of academic brilliance and at Primary School did four years in one. His undergraduate degree from Wright State in Dayton, Ohio, was interrupted in his final year at the age of 18, when he was called up for military service.

To look at, he was an unlikely candidate for a soldier, being slight of build, and entirely non-aggressive, but a soldier is what he became. He was not involved in fighting but in the occupation of Japan after the Second World War. It is difficult to imagine a milder man, but he was nevertheless promoted, a consequence of his noticing a memo, and he realised it meant he could be promoted if he applied, and so of course he did.

He returned to the United States on a navy boat, which gave him a feel for travel. And travel he later on would. Having served in the U.S. army, he was entitled to a University education. He had to repeat his interrupted year at Wright State.

He took his Ph.D. in 1955 under the supervision of Arno Jäger with his thesis titled On the Algebraic Theory of Linear Multidifferential Polynomials.

His first job was at the Ford factory, where he was given the project of calculating the characteristics of the suspension of a car, a lengthy and laborious piece of calculation. When he had completed his results, his chief looked at them and said they were completely wrong. It turned out the chief had given Frank the wrong data to begin with. "Oh well," the boss said, "Here is the right data. Just do the calculation again."

Initially he taught at the University of Kentucky. His next appointment was at Rutgers University, but for much of his tenure he was elsewhere, in Europe, and finally the faculty insisted he make up his mind to return permanently. He then got a job in Germany in Ruhr-Universität Bochum with the aid of his former supervisor Arno Jäger. In Bochum he took the advanced qualification of docent, and became a professor.

Frank liked best of all to work with other mathematicians. In total there were thirteen co-authors, *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


Wednesday, 30 September 2026

# 1 from old math terms notes Obtuse, Amblygon (with explementary)

    Recovering some old notes I wrote for students over time and adding them as I go:


Obtuse is from the Latin formation ob (against) + tundere (to beat) and literally means to beat against. An object thus beaten becomes blunt, dull, or rounded, as in the application to an obtuse angle, one having more than 90 degrees but less than 180 degrees. A triangle with an obtuse angle is called an obtuse triangle.


You may (very rarely) encounter the name amblygon used for an obtuse triangle. It is also sometimes spelled ambligon. Amblygon is drawn from the Greek roots for blunt amblu preceding the root gon for angle (from knee). The use in English probably first occurred in Billingsley's translation of Euclid in 1570, although he wrote "amblygonum". Billingsley's translation was the first translation of Euclid's "Elements" in English. It was published at London in 1570 with the title The Elements of Geometric of the most auncient Philosopher Euclide of Megara. Faithfully (now first) translated into the Englishe toung, by H. Billingsley, Citizen of London


And a bonus

Explementary I first heard of the word explementary in July of 1999. It was "re-created" by Steve Wells of a company called Think3 while working on a new CAD program, thinkdesign. The word was needed to represent the angle required to complete a 360o angle. They wanted a word that would be a natural sounding extension of complement and supplement. The Latin explementum means "filling" or "stuffing" and it is in the OED as "that which fills up". This is actually very similar to the meanings of complement and supplement. After a couple of days, he found hte word was not as new to mathematics as we had thought. Several days later he wrote to tell me that the word already appeared on the "Dictionary of Technical Terms for Aerospace Use (Web Edition by Daniel R. Glover, Jr at the NASA Lewis Research Center, Cleveland, Ohio. Here is there definition, as sent to me by Mr. Wells: Explement -- An angle equal to 360 degrees minus a given angle. Thus, 150o is the explement of 210o and the two angles are called explementary angle--Two angles whose sum is 360o. My thanks to Mr. Wells for his advice and corrections as much of this content came directly from his emails. Later I found earlier citations of the mathematical term in the Oxford English Dictionary, which lists an 1830 book of Geometry by a Pierce Morton who published other editions in 1838. Morton also shared credits with Augustus De Morgan for a book title Mathematics II, from the Society for the Diffusion of Useful Knowledge. I have little information about has life and would seek input from anyone with additional information about his life. 

On This Day in Math - October 1

   



Scientists have one thing in common with children: curiosity. To be a good scientist you must have kept this trait of childhood, and perhaps it is not easy to retain just one trait. A scientist has to be curious like a child; perhaps one can understand that there are other childish features he hasn't grown out of.
~Otto Robert Frisch


The 274th day of the year; 274 is a tribonacci number..The tribonacci numbers are like the Fibonacci numbers, but instead of starting with two predetermined terms, the sequence starts with three predetermined terms and each term afterwards is the sum of the preceding three terms. The first few tribonacci numbers are 0, 0, 1, 1, 2, 4, 7,

274 is also the sum  of five cubes, 23 + 2 3 + 23 + 53 + 53, and of three triangular numbers 78 + 91 + 105. In 1796, Gauss proved that every positive integer could be expressed as the sum of (no more than) three triangular numbers.

274 is an example of Smith (or joke) numbers: composite numbers n such that sum of digits of n = sum of digits of prime factors of n (counted with multiplicity) 274= 2 * 137 and 2+ 7 +4 = 13 = 2 + 1 + 3 + 7. Find another. 

named by Albert Wilansky of Lehigh University after he noticed this property in his brother-in-law Harold Smith's telephone number (\(493-7775\)). [[[don't bother, I assume he changed the number years ago.





EVENTS


1386 University of Heidelberg founded 13 October. The Ruprecht-Karls-Universität Heidelberg (Heidelberg University, Ruperto Carola) is a public research university located in Heidelberg, Baden-Württemberg, Germany. It is the oldest university in Germany and was the fourth university established in the Holy Roman Empire. A coeducational institution since 1899, today Heidelberg consists of twelve faculties and offers degree programs at undergraduate, graduate and postdoctoral levels in some 100 disciplines.

As of 2021, 57 Nobel Prize winners have been affiliated with the city of Heidelberg and 33 with the university itself.

 *Wik



1610 Lodovico Cigoli writes to Galileo to inform him that Father Christoph Clavius SJ, the senior mathematician at the Collegio Romano, had said that if the telescope revealed four
new ‘planets’ around Jupiter to Galileo, then Galileo must have put them in the telescope to begin with. Two months later, Clavius had observed Jupiter’s moons himself. *Albert Van Helden, Galileo and the telescope, The origins of the telescope, Royal Netherlands Academy of Arts and Sciences, Amsterdam 2010
The original Galileo telescope, which is preserved today at the Museo Galileo in Florence, Italy. (They wouldn't let me look through it.)





1648 In a letter to Samuel Hartlib, Sir Balthazar Gerbier sends a description of Pascal's mechanical calculator. Wikipedia describes Gerbier as "an Anglo-Dutch courtier, diplomat, art advisor, miniaturist and architectural designer." Nathan Kesling ‏@nathan13109



1658 The closing date for Pascal’s prize problems on the cycloid. (T. Christie advised me that some give the date as Oct 2).  A toothache earlier that year caused him to return to mathematics and to study the cycloid. In 1654, late in the evening Pascal experienced a religious ecstasy that called him to give up his intermittent interest in mathematics and to devote his time to religious contemplation. For years he devoted no time to mathematics. Then one night, unable to sleep because of an abscessed tooth, Pascal began to think about some problems about the cycloid. His pain disappeared and he interpreted this as a sign that God was pleased by his mathematical studies. In a brief time he completed the investigation of the cycloid. Then he established a contest about the cycloid with himself and Roberval as the judges. The three problems he asked were:

1. Find the area and the center of gravity of the region BCD bounded by the cycloid, the horizontal line BC and the axis of symmetry AD.
2. Find the volume and center of gravity of the solids obtained by revolving the region BCD about AD and about BC.
3. For the solids in the previous question, find the center of gravity of the solids formed when each is cut by a plane parallel to its axis of revolution.
Only two contestants submitted solutions. No prize was awarded as the judges declared that the solutions were either incomplete or incorrect. Pascal then published his own results in a paper entitled "L'Histoire de la Roulette".  It is worth noting that all these investigations of the cycloid occurred before Newton and Leibnitz' work on the calculus!  *Historical Modules for the Mathematical Classroom There is a famous statue by Pajou in the Louvre of Pascal in which he is contemplating the Roulette (cycloid). (And in this photo, I am contemplating him contemplating the roulette) More on the cycloid, including a close up of the tablet in the statue is here.

1752  A letter of Benjamin Franklin written on October 1st, to Mr. Peter Collinson, FRS concerning an electrical kite, was read before the society on Dec 21.  Franklin describes the construction of the kite from two light strips of cedar and a large thin silk  handkerchief.
Benjamin Franklin Drawing Electricity from the Sky, an artistic rendition of Franklin's kite experiment painted by Benjamin West c. 1816




1812   Thomas Jefferson writes to William Duanne.  "The hand of age is upon me....last year it was the sight, this it is the hearing... but the mind is too weakened, When I was young, mathematics were the passion of my life. The same passion has returned upon me... 




1814 The terms "commutative" and "distributive" were used (in French) by François Joseph Servois in a memoir published in Annales de Gergonne (volume V, no. IV) *Jeff Miller, Earliest Known Uses of Some of the Words of Mathematics
Servois was the son of Jacques-Ignace Servois, a merchant, and Jeanne-Marie Jolliet. He was ordained a priest at Besançon at the beginning of the Revolution, but in 1793 he gave up his ecclesiastical duties in order to join the army. In 1794, after a brief stay at the artillery school of Châlons-sur-Marne, he was made a lieutenant. While serving in several campaigns as staff officer, he devoted his leisure time to the study of mathematics. With the support of Legendre, he was appointed professor of mathematics at the artillery school of Besançon in July 1801. A few months later he transferred to the school at Châlons-sur-Marne; in 1802, to the artillery school at Metz: and in 1808, to the school at La Fère. After a brief return to Metz as professor at the artillery and engineering school, he was appointed curator of the artillery museum at Paris in 1816. He held the post until 1827, when he retired to his native village.




1831 Michael Faraday discovers induced electric current using a helix made of two coils each of 203 feet of insulated copper wire. "A sudden jerk was perceived when the battery communication was made and broken... it was one way when made, and the other when broken." *A history of physics in its elementary branches By Florian Cajori





1831 (exact date unknown, October ?) Galois, while in prison, writes a preface to his "Memoires". As late as 1906, it had never been published, and Jules Tannery, reviewing the yet unpublished works of Galois, left it out, regarding it as too much like drunken raving. The ending is a fascinating hope for the future of mathematical publishing:
Evariste Galois 1811–1832
By Laura Toti Rigatelli





1842 Arthur Cayley's acceptance to Trinity was announced on this day. He was twenty-one years old and accepted on his first sitting, a rare event. He was the youngest man admitted to Trinity in the 19th Century. * A. J. Crilly, Arthur Cayley: Mathematician Laureate of the Victorian Age




1847 Maria Mitchell sees a comet... the first woman astronomer in the United States discovered a comet. On this night in the Autumn of 1847, Maria looked at the sky through the telescope in her homemade observatory at Nantucket, Mass. and saw a star five degrees above the North Star where there had been no star before. She had memorized the sky and was sure of her observation. It occurred to her that this might be a comet. Maria recorded the presumed comet's coordinates. The next night the star moved again. This time she was sure it was a comet. For this discovery, she was awarded *New England Historical Society's gold medal by the king of Denmark. She became the first woman elected to the American Academy of Arts and Sciences. *TIS
Maria Mitchell with student at Vassar Observatory  *New England Historical Society





1861 On Oct 1, a seemingly depressed Charles Darwin writes, "My Dear Lyell, ... I am very poorly today & very stupid & hate everybody & everything. One lives only to make blunders.–... I am
Ever yours
C. Darwin   [I've had days like that myself]





1891 On Oct 1 Stanford University​ opened its doors after six years of planning and building. The prediction of a New York newspaper that Stanford professors would "lecture in marble halls to empty benches" was quickly disproved. The first student body consisted of 555 men and women, and the original faculty of 15 was expanded to 49 for the second year. The university’s first president was David Starr Jordan​, a graduate of Cornell, who left his post as president of Indiana University​ to join the adventure out West.
The Stanfords engaged Frederick Law Olmsted​, the famed landscape architect who created New York’s Central Park​, to design the physical plan for the university. The collaboration was contentious, but finally resulted in an organization of quadrangles on an east-west axis. Today, as Stanford continues to expand, the university’s architects attempt to respect those original university plans. *Stanford Univ Web page



1895  On the first of October 1895, the first German institute of insurance science was founded at the University of Göttingen, as a result of joint efforts of Felix Klein (1849-1825) and his fellow student Ludwig Kiepert (1846-1934), who was then chairman of the Prussian Civil Service Association (today called Hannover Life Insurance).This was the first institute in Germany in which a curriculum in actuarial mathematics, insurance law, and insurance economics was offered. Successful studies led to the degree “Versicherungsverständiger” (insurance expert). The institute was divided into a mathematical section and an administrative section, and its first chairman was Wilhelm Lexis. *From Center for Statistics, History of Statistics in Gottingen.



1907 Delegates from 310 Esperanto societies throughout the world met to elect a committee to modify the language. Louis Couturat, influenced by Leibniz’s thought on the construction of a logical universal language, was elected one of the secretaries.  *VFR





1934 Paul Erdos stops in Cambridge to visit with mathematical friends, particularly Harrold Davenport and Richard Rado, on his way to a position in Manchester. *Bruce Schechter, My Brain is Open: The Mathematical Journeys of Paul Erdos




1954 IBM announced is 705 EDP, part of its 700 series of mainframe computers. A business-oriented machine, the 705 had magnetic core memory.*CHM

1957  Thalidomide was developed in West Germany and marketed in 1957 as a safe, over-the-counter sedative to treat insomnia, colds, and flu. It was also widely used off-label to combat morning sickness in pregnant women. It wasn’t until 1962 that the severe side effects were revealed, where it had caused the development of malformed limbs in babies. *rsc.org\: 
In the late 1950s and early 1960s, doctors in Germany and Australia began to notice an unusual spike in severe birth defects and miscarriages. In 1961, the link was definitively made between the drug and these birth defects, leading to its withdrawal from the market.
The most prominent and visible defects were severe limb malformations, such as shortened, underdeveloped, or missing arms and legs (a condition known as phocomelia). Other effects included malformations of the eyes, ears, heart, kidneys, and other internal organs.
 In Germany alone, 10,000 babies were born affected by Thalidomide. Many were too damaged to survive for long.  Today, fewer than 3,000 are still alive




1958  On July 29, 1958, Eisenhower signed the National Aeronautics and Space Act, establishing NASA. When it began operations on October 1, 1958, NASA absorbed the 43-year-old NACA intact; its 8,000 employees, an annual budget of US$100 million, three major research laboratories (Langley Aeronautical Laboratory, Ames Aeronautical Laboratory, and Lewis Flight Propulsion Laboratory) and two small test facilities  *Wik



-
1969 Concorde goes Mach 1 In 1969, the prototype French-built Concorde broke the sound barrier for the first time. The inaugural flight of the aircraft had taken place on 2 Mar 1969 in Toulouse, France, and its first commercial flight was on 21 Jan 1976. It was the first plane in the world to be entirely controlled by computer. As the only supersonic passenger aircraft, the Anglo-French Concorde remains a brilliant technological achievement, though its impact on international air travel has been limited by the high cost of buying and operating the aircraft. There was also widespread opposition from environmental groups on the grounds of the Concorde's noise on takeoff and its fuel consumption. Only British Airways and Air France have operated the aircraft. *TIS




1971 The first CT (Computed Tomography (CT) imaging is also known as "CAT scanning" (Computed Axial Tomography)Tomography is from the Greek word "tomos" meaning "slice" or "section" and "graphia" meaning "describing") scan of a patient was performed OTD in 1971 at the Atkinson Morley Hospital in Wimbledon and highlighted a brain cyst.  The tomograph was built by British engineer Godfrey Hounsefield that year. *StoriaMedicina





1988   The game Connect Four Solved first by James D. Allen (Oct 1, 1988), and independently by Victor Allis (Oct 16, 1988). First player can force a win. Strongly solved by John Tromp's 8-ply database (Feb 4, 1995). Weakly solved for all boardsizes where width+height is at most 15 (Feb 18, 2006). *Wik
Misère Connect Four (don’t make four) was solved (Oct 2024). Steele & Larremore give constructive results for misère Connect-4 (and generalized misère Connect-k on  w×h boards): perfect play is solved and outcomes depend on k,w,h.

A recent paper by Markus Böck (arXiv, 2025) revisits symbolic/Binary Decision Diagram (BDD) search and reports producing an explicit win/draw/loss lookup table for the classic 7×6 board (the paper says an ≈89.6 GB look-up table, computed on consumer-grade hardware). This goes beyond Tromp’s 8-ply database by producing a full table you can query for any legal position.  *PBnotes




2008  A Metrolink engineer at the helm of a commuter train in Los Angeles, California, was found to have been text messaging seconds before colliding with a freight train. 25 people were killed in the accident and numerous others were injured. Many states have passed laws enforcing hands-free only cellular use that restricts drivers from the distracted driving inherent in hands-on texting and cellular phone calls. *CHM




2012 With God's grace, Dame Kathleen Ollerenshaw will awake for her 100th birthday today . Happy Birthday to a Grand-Ol-Dame, and may a puzzle occupy her thoughts. (See 1912 Births below).
(she did indeed greet her 100th birthday, but Died: August 10, 2014, Didsbury, Manchester, United Kingdom ......  It's hard to keep a good woman down!)






BIRTHS

1535 Giambattista della Porta (? Oct 1535 - 4 Feb 1615) Italian natural philosopher, experimenter and mathematician, though he also sought the miraculous or magical. He studied optics, including refraction (De refractione, 1593). Porta did not invent the telescope, regardless of his published claim. He was the first to propose adding a convex lens to the camera obscura, and first to recognize the heating effect of light rays. He wrote on cryptography in De furtivis literarum (1563), and his other books included mechanics, squaring the circle, description of a steam engine in De spiritali (1606). He formed the society, Accademia dei Segreti, dedicated to discussing and studying nature, meeting at his home, until closed by the Inquisition (about 1578). *TIS




1671 Luigi Guido Grandi (1 October 1671 – 4 July 1742) was an Italian Jesuit who worked on geometry and hydraulics.Grandi was the author of a number of works on geometry in which he considered the analogies of the circle and equilateral hyperbola. He also considered curves of double curvature on the sphere and the quadrature of parts of a spherical surface.
In 1701 Grandi discussed the conical loxodrome, the curve that cuts the generators of a cone of revolution in a constant angle. He studied the curve the Witch of Agnesi in 1703. In fact his work of 1703 is important in introducing Leibniz's calculus into Italy.
In 1728 Grandi published Flores geometrici a work in which he defines the clelie curve. He named the curve after Countess Clelia Borromeo and dedicated his book to her. If the longitude and colatitude of a point P on a sphere is denoted by θ and φ and if P moves so that θ = m φ, where m is a constant, then the locus of P is a clelie. Grandi also applied the term "clelies" to the curves determined by certain trigonometric equations involving the sine function
a sin θ = b sin mφ
a sin θ = a - b sin mφ
Grandi also worked on hydraulics and was involved with a number of projects such as ones to drain the Chiana Valley and the Pontine Marshes. He also published a number of works on mechanics and astronomy. His practical work on mechanics included experimenting with a steam engine. *SAU 
He is noted for the roses that he introduced. His idea was to find a geometrical definition of curves which resemble flowers. These curves are still part of our calculus courses, except now we use polar coordinates to define them.*VFR





1873 Alfreds Arnolds Adolfs Meders (1 Oct 1873 , 1944) Meders worked on differential geometry and mathematical analysis. He often published papers written in German, in German journals. For example he published the following three papers in Crelle's Journal: Über einige Arten Singularer Punkte von Raumkurven (1896); Zur Theorie der singularen Punkte einer Raumkurve (1899); and Analytische Untersuchung singularer Punkte von Raumkurven (1910). In Monatshefte für Mathematik he published: Über die Determinante von Wronski (1906); and Zur Differentiation bestimmter Integrale nach einem Parameter (1911).
Meders was also interested in the history of mathematics and he wrote an important paper Direkte und indirekte Beziehungen zwischen Gauss und der Dorpater Universität (Direct and indirect connections between Gauss and the University of Dorpat) in 1928. His interests went outside mathematics and he sometimes lectured on astronomy, meteorology and biology where he had a special interest in birds. *SAU


1898 Béla Kerékjártó (October 1, 1898, –June 26, 1946) was a Hungarian mathematician who wrote numerous articles on Topology. He earned his Ph.D. degree from the University of Budapest. He taught at the Faculty of Sciences of the University of Szeged from 1922, and at the University of Budapest from 1938. In 1923, he published one of the first books on Topology; Hermann Weyl wrote that this book completely changed his views of the subject.*Wik




1904 Otto Robert Frisch (1 Oct 1904; 22 Sep 1979) Austrian-British nuclear physicist, born in Vienna, who, with his aunt Lise Meitner, described the division of neutron-bombarded uranium into lighter elements. He named the process fission, borrowing a term from biology (1939). At the time, Meitner was working in Stockholm and Frisch (1934-39) at Copenhagen under Niels Bohr, who brought their observation to the attention of Albert Einstein and others in the United States. He did research with James Chadwick 1940-43, and was head of the Critical Assembly Group on the Los Alamos project 1943-46. After World War II, Frisch became a science writer on atomic physics for the layman. *TIS

Feischwas working in Copenhagen, at the Bohr Institute, when Otto Hahn and Fritz Strassmann discovered fission at their lab in Berlin in December, 1938. Or rather, they discovered that when they bombarded uranium with neutrons, they produced barium as a byproduct. They had no idea what was going on. It was Frisch, working with his aunt Lise Meitner, who identified what had happened as the fission of uranium, and who in fact coined the very word "fission." Meitner had worked with Hahn for years (second image), and Frisch was visiting his aunt in Sweden at Christmas when she got a letter from Hahn, describing the experiment (third image) and his mystification at the results. Walking in the snow that fateful day, Meitner and Frisch figured out that the uranium atom must have split into two by-products, one of which was barium. Frisch, the next year, determined that a bomb using uranium 235, the scarce isotope of uranium, was a real possibility. His report, written with Rudolf Peierls, led to the formation of the Maud Committee in Great Britain, which in turn led to the establishment of the Manhattan Project in 1942 in the United States. Frisch worked at Los Alamos from 1943 to 1945, which was a pretty good trick, since he was in effect an enemy alien. He had to be granted British citizenship to do so. Frisch described all these happenings in a charming autobiography, full of colorful stories, with the equally charming title: What Little I Remember . Neither Frisch nor Meitner shared in the Nobel Prize awarded to Otto Hahn in 1944 for the discovery of nuclear fission.

Hahn and Meitner






1911 Zhou Weiliang (simplified Chinese: (October 1, 1911– August 10, 1995) was a Chinese mathematician born in Shanghai, known for his work in algebraic geometry.
He was a student in the USA, graduating from the University of Chicago in 1931. In 1932 he attended the University of Göttingen, then transferring to Leipzig where he worked with van der Waerden. They produced a series of joint papers on intersection theory, introducing in particular the use of what are now generally called Chow coordinates (which were in some form familiar to Arthur Cayley).
He married Margot Victor in 1936, and took a position at the National Central University in Nanjing. His mathematical work was seriously affected by the wartime situation in China. He taught at the National Tung-Chi University in Shanghai in the academic year 1946–47, and then went to the Institute for Advanced Study in Princeton, where he returned to his research. From 1948 to 1977 he was a professor at Johns Hopkins University. *Wik



1912 Dame Kathleen Mary Ollerenshaw, née Timpson, DBE (1 October 1912, August 10, 2014, Didsbury, Manchester, United Kingdom ) is a British mathematician and politician. Deaf since the age of eight, she loved doing arithmetic problems as a child. As a young woman, she attended St Leonards School and Sixth Form College in St Andrews, Scotland where today the house of young male boarders is named after her. At the age of 19, she gained admittance to Somerville College, Oxford to study mathematics. She completed her doctorate at Somerville in 1945 on "Critical Lattices" under the supervision of Theo Chaundy. She wrote five original research papers which were sufficient for her to earn her DPhil degree without the need of a formal written thesis.
Ollerenshaw served as a Conservative Councillor for Rusholme for twenty-six years (1956–1981), was Lord Mayor of Manchester (1975–1976), and the prime motivator in the creation of the Royal Northern College of Music. She was made a Freeman of the City of Manchester and was an advisor on educational matters to Margaret Thatcher's government in the 1980s.
She has published at least 26 mathematical papers, her best-known contribution being to most-perfect pandiagonal magic squares. An annual public lecture at the School of Mathematics, University of Manchester is named in her honour.
An amateur astronomer, Ollerenshaw donated her telescope to Lancaster University, and an observatory there bears her name. She is an honorary member of the Manchester Astronomical Society and held the post of Vice President for a number of years. *Wik A wonderful article about her approaching her 100th birthday is in Scientific American.







DEATHS


1768 Robert Simson (14 October 1687 – 1 October 1768) was a Scottish mathematician and professor of mathematics at the University of Glasgow. The pedal line of a triangle is sometimes called the "Simson line" after him. Edmond Halley suggested to him that he might devote his considerable talents to the restoration of the work of the early Greek geometers, such as Euclid and Apollonius of Perga. These are works that only survive in abbreviated accounts given by later mathematicians such as Pappus of Alexandria. He first studied Euclid's so-called porisms. Playfair's 1792 definition of porism is "a proposition affirming the possibility of finding such conditions as will render a certain problem indeterminate, or capable of innumerable solutions."
Simson's work on Euclid's porisms was published in 1723 in the Philosophical Transactions of the Royal Society, and his restoration of the Loci Plani of Apollonius appeared in 1749. Further work of his on porisms and other subjects including logarithms was published posthumously in 1776 by Lord Stanhope at his own expense. Simson also set himself the task of preparing an edition of Euclid's Elements in as perfect a form as possible, and his edition of Euclid's books 1-6, 11 and 12 was for many years the standard text and formed the basis of textbooks on geometry written by other authors. The work ran through more than 70 different editions, revisions or translations published first in Glasgow in 1756, with others appearing in Glasgow, Edinburgh, Dublin, London, Cambridge, Paris and a number of other European and American cities. Recent editions appeared in London and Toronto in 1933 under the editorship of Isaac Todhunter, and in São Paolo in 1944. Simson's lectures were delivered in Latin, at any rate at the beginning of his career. His most important writings were written in that language, however, his edition of Euclid, after its first publication in Latin, appeared in English, as did a treatise on conic sections that he wrote for the benefit of his students.
the Simson line does not appear in his work but Poncelet in Propriétés Projectives says that the theorem was attributed to Simson by Servois in the Gergonne's Journal. It appears that the theorem is due to William Wallace.
The University of St Andrews awarded Simson an honorary Doctorate of Medicine in 1746.
In 1753 Simson noted that, as the Fibonacci numbers increased in magnitude, the ratio between adjacent numbers approached the golden ratio, whose value is
(1 + √5)/2 = 1.6180 . . . . *SAU

 


1919 Philip Edward Bertrand Jourdain (16 October 1879 – 1 October 1919) was a British logician and follower of Bertrand Russell. He corresponded with Georg Cantor and Gottlob Frege, and took a close interest in the paradoxes related to Russell's paradox, formulating the card paradox version of the liar paradox. He also worked on algebraic logic, and the history of science with Isaac Newton as a particular study. He was London editor for The Monist. *Wik


1924 John Edward Campbell (27 May 1862, Lisburn, Ireland – 1 October 1924, Oxford, Oxfordshire, England) remembered for the Campbell-Baker-Hausdorff theorem which gives a formula for multiplication of exponentials in Lie algebras. *SAU
Campbell made his most notable contribution to mathematics in 1897 by introducing a formula for multiplication of exponentials in Lie algebras. This formula was later elaborated by Henri Poincaré (1899) and Henry Frederick Baker (1902). It was later systematised geometrically by Felix Hausdorff (1906) and became known as Baker-Campbell-Hausdorff formula.

In 1903, Campbell published a book on Introductory Treatise on Lie's Theory of Finite Continuous Transformation Groups where he popularised the ideas of Sophus Lie. He was elected a Fellow of the Royal Society in 1905, and served as president of the London Mathematical Society from 1918 to 1920. He was tutor to the future literary scholar C. S. Lewis in 1917, assisting Lewis with Responsions in mathematics as part of the entrance requirements for Oxford University/. Campbell was the first mathematician from Oxford who was invited, shortly before his death, by the Cambridge University to examine the Cambridge Mathematical Tripos. *Wik




1972 Francisco José Duarte (6 Jan 1883, 1 Oct 1972) Duarte's most important work in mathematics was done in algebra, number theory and mathematical analysis. His first work in mathematics was about which he presented to the Paris Academy of Sciences in 1907. He published papers on the general solution of a diophantine equation of the third degree x3 + y3 + z3 - 3xyz = v3, simplified Kummer's criterion and gave a simple proof of the impossibility of solving the Fermat equation x3 + y3 + z3 = 0 in nonzero integers. He also observed that the interpolation formula of Everett is a consequence of the interpolation formula of Gauss. In 1908 he published an article where he calculated π to 200 decimal places.
His main three books are: Monograph on the numbers π and e. Historical and bibliographical notes (Spanish) (Bol. Acad. Cien. Fis. Mat. Nat. 11(1948)), with 27 chapters on 250 pages, which contains more information on π and e than has ever before been collected in one place; Lessons on Infinitesimal Analysis (Caracas 1943, 606 pp.) (Spanish) containing material from courses in analysis at UCV during his first three or four years there; and Bibliography of Euclid, Archimedes, Newton (Acad. Cien. Fis. Mat. Nat., Caracas 1963, 163 pp.) (Spanish) which was also done in the 19th century.
Many mathematicians are interested in recreational mathematics. Duarte also contributed to that part of mathematics and proposed problems and solutions to the American Mathematical Monthly for several years, and also to the journal Ciencia y Ingenieria (Science and Engineering) published in Mérida. *SAU



1990 John Stewart Bell​ FRS (28 June 1928 – 1 October 1990) was a physicist from Northern Ireland (Ulster), and the originator of Bell's theorem, a significant theorem in quantum physics regarding hidden variable theories.*Wik



1996  Herbert Karl Johannes Seifert (May 27, 1907, Bernstadt – October 1, 1996, Heidelberg) was a German mathematician known for his work in topology. Seifert did other important work related to knot invariants. In 1934 he published results, using surfaces today called Seifert surfaces, which he used to calculate homological knot invariants. Another topic which Seifert worked on was the homeomorphism problem for 3-dimensional closed manifolds. *SAU

a Seifert surface is an orientable surface whose boundary is a given knot or link. Such surfaces can be used to study the properties of the associated knot or link. For example, many knot invariants are most easily calculated using a Seifert surface.







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