## Monday 1 July 2024

### On This Day in Math - July 1

Mathematics, rightly viewed, possesses not only truth, but supreme beauty
a beauty cold and austere, like that of sculpture,
without appeal to any part of our weaker nature,
without the gorgeous trappings of painting or music,
yet sublimely pure, and capable of a stern perfection such as only the greatest art can show.
The true spirit of delight, the exaltation,
the sense of being more than Man,
which is the touchstone of the highest excellence,
is to be found in mathematics as surely as in poetry.

--BERTRAND RUSSELL,

The 182nd day of the year; there are 182 connected bipartite graphs with 8 vertices. *What's So Special About This Number

The 182nd prime (1091) is the smaller of a pair of twin primes (the 40th pair, actually) *Math Year-Round ‏@MathYearRound(Students might convince themselves that it was not necessary to say it was the smaller of the pair.)

Language time:

182= 13 x 14, is called a pronic, promic, or heteromecic and even an oblong number. Pronic Numbers are numbers that are the product of two consecutive integers; 2, 6, 12, 20, ..(doubles of triangular numbers).  Pronic seems to be a misspelling of promic, from the Greek promekes, for rectangular, oblate or oblong. Neither pronic nor promic seems to appear in most modern dictionaries. Richard Guy pointed out to the Hyacinthos newsgroup that pronic had been used by Euler in series one, volume fifteen of his Opera, so the mathematical use of the "n" form has a long history.

Oblong is from the Latin ob (excessive) + longus (long). The word oblong is also commonly used as an alternate name for a rectangle. In his translation of Euclid's "Elements", Sir Thomas Heath translates the Greek word eteromhkes[hetero mekes - literally "different lengths"] in Book one, Definition 22 as oblong. . "Of Quadrilateral figures, a square is that which is both equilateral and right-angled; an oblong that which is right angled but not equilateral...". (note that with this definition, a square is not a subset of rectangles.)

While literally every small (less than 945) odd number is deficient, 182 is the 91st even number, and only the 48th even number to be deficient. In all then up to 182, there are 139 deficient numbers, and only 41 that are abundant (6 and 28 are perfect). "The natural numbers were first classified as either deficient, perfect or abundant by Nicomachus in his Introductio Arithmetica (circa 100 CE)".*Wikipedia

The regular polygon with 182 sides, has exterior angles at each vertex of less than 2 degree. Coxeter called all these evenly sided, 2*n,  polygons zonagons and said that they could be divided into n(n-1)/2 parallelograms, and in the case of regular polygons, they will all be rhoumbi (but not all identical rhombi), so the 2*91 = 182 sided zonagon will have 91*45=4095 rhombi (too many to make a good image, so here is an Octadecagon with only 36 from the nice people at Wikipedia)  (these disections can be done in a multitude of ways, so I just picked a pretty one).

EVENTS

1349 Sometimes, a little astronomical knowledge can be a dangerous thing, even to those who possess it. A tale from medieval England is passed down from the chronicles of the scholar Thomas Bradwardine of a witch who attempted to force her will on the people through knowledge of an impending eclipse. Bradwardine, who had studied astronomical predictions of Arabian astronomers, saw through the ruse, and matched the prediction of the July 01, 1349 A.D. lunar eclipse with a more precise one of his own. No word survives as to the fate of the accused, but one can only suspect banishment or worse.*listosaur.com

Thomas Bradwardine (c. 1300 – 26 August 1349) was an English cleric, scholar, mathematician, physicist, courtier and, very briefly, Archbishop of Canterbury. As a celebrated scholastic philosopher and doctor of theology, he is often called Doctor Profundus (medieval epithet, meaning "the Profound Doctor").

Chaucer in The Nun's Priest's Tale (line 476) ranks Bradwardine with Augustine and Boethius.

1694 Opening of the University of Halle in Germany. Georg Cantor later taught there. *VFR

1770 – Lexell's Comet passed closer to the Earth than any other comet in recorded history, approaching to a distance of 0.0146 a.u . or six times the distance from the Earth to the Moon. OnThisDay & Facts ‏@NotableHistory Discovered by astronomer Charles Messier, The comet has not been seen since 1770 and is considered a lost comet.

1798 Napoleon’s ﬂeet reached Alexandria, bearing Monge and Fourier.*VFR

1819 William George Horner’s (1786–1837) method of solving equations is presented to the Royal Society.*VFR In numerical analysis, the Horner scheme (also known as Horner algorithm), named after William George Horner, is an algorithm for the efficient evaluation of polynomials in monomial form. Horner's method describes a manual process by which one may approximate the roots of a polynomial equation. The Horner scheme can also be viewed as a fast algorithm for dividing a polynomial by a linear polynomial with Ruffini's rule. Student's often learn this process as synthetic division.  *Wik

In fact this method was known to Zhu Shijie in China in the thirteenth century.

1847 The United States issued its ﬁrst two postage stamps. They pictured Benjamin Franklin and George Washington respectively [Scott #1-2]. *VFR

1852 Dirichlet delivers a memorial lecture at the Berlin Academy in honor of his close friend Jacobi, calling him the greatest member of the Academy since Lagrange. *VFR

1856 Weierstrass appointed Professor of Mathematics at the Royal Polytechnic School in Berlin. *VFR

In 1858, the Wallace-Darwin theory of evolution was first published at the Linnaean Society in London*. The previous month Charles Darwin received a letter from Alfred Wallace, who was collecting specimens in the East Indies. Wallace had independently developed a theory of natural selection - which was almost identical to Darwin's. The letter asked Darwin to evaluate the theory, and if worthy of publication, to forward the manuscript to Charles Lyell. Darwin did so, almost giving up his clear priority for he had not yet published his masterwork The Origin of Species. Neither Darwin nor Wallace were present for the oral presentation at the Linnaean Society, where geologist Charles Lyell and botanist Joseph Hooker presented both Wallace's paper and excerpts from Darwin's unpublished 1844 essay.*TIS
In his annual report the following May, society president Thomas Bell wrote, “The year which has passed has not, indeed, been marked by any of those striking discoveries which at once revolutionize, so to speak, the department of science on which they bear.” *Futility Closet

1873 From a letter dated July 1, 1873, in the Coast Survey files in the National Archives in Washington. Peirce writes, "Newcomb, in a paper .... says he finds that pendulums hung by springs twist and untwist as they oscillate and says this will affect the time of oscillation."The Charles S. Peirce-Simon Newcomb Correspondence by Carolyn Eisele.

1887 July ?, Nearly a century before anyone thought seriously about wind-powered electricity, a Scotsman named James Blyth built the world’s first wind turbine in his front yard. “When a good breeze was blowing, I stored as much in half a day as gave me light for four evenings,” he wrote.

It was July 1887, and Blyth—an electrical engineer living in Marykirk, a town in northeastern Scotland—used the turbine to power his holiday home. He even offered to light Marykirk’s main street with the excess power, but the villagers, who believed electricity was the work of the devil, rebuffed him.

“[Blyth] was obviously too far forward-thinking for the local villagers, who probably thought he was a wizard,” said Trevor Price, a senior lecturer of environmental and mechanical engineering at the University of South Wales who wrote a short biography of Blyth.

Unlike his contemporary pioneers of wind energy, the American engineer Charles Brush and Danish inventor Poul la Cour, Blyth is less well-remembered—with nary a monument to his name—despite his pride of place as the first person to harness the wind for electricity.  *APS Org

James Blyth’s 1891 design for a wind turbine. The wind, Blyth said, “is to be had everywhere.”

1894 The New York Mathematical Society changed its name to the American Mathematical Society to reﬂect its national charter. [AMS Semicentennial Publications, vol. 1, p. 74]. *VFR

1908 International agreement to use SOS for distress signal signed. An International Radiotelegraphic Convention, ... met in Berlin in 1906. This body signed an international agreement on November 3, 1906, with an effective date of July 1, 1908. An extensive collection of Service Regulations was included to supplement the Convention, and in particular Article XVI adopted Germany's Notzeichen distress signal as the international standard, stating: "Ships in distress shall use the following signal: · · · — — — · · · repeated at brief intervals". *Citizens Compendium

1908  The Chicago Daily News Style Book, dated July 1, 1908, bans the word Scientist.  On the Style Sheet of the Century Magazine it is listed among the "words and phrases to be avoided." It was prohibited by the famous Index Expurgatorius prepared by William Cullen Bryant for the New York Evening Post, and his prohibition is still theoretically in force, but the word is now actually permitted by the Post. * How the term Scientist came to be .

1918 Florian Cajori (1859–1930) appointed professor of the history of mathematics at the University of California, Berkeley, one of the few such chairs in the the world. During the next twelve years he published 159 papers on the history of mathematics. *VFR

1948 The Bell System Technical Journal publishes the first part of Claude Shannon's "A Mathematical Theory of Communication", regarded as a foundation of information theory, introducing the concept of Shannon entropy and adopting the term Bit. *Wik

1964 The New York Times, in a full page ad, announced that Paul Newman and Joanne Woodward would play a game on an elliptical pool table. It had a pocket at one focus so that if the ball passed over the other focus it would bank oﬀ the rail into the pocket. [UMAP Journal, 4(1983), p. 176; Recreational Mathematics Magazine, no. 14, January-February 1964] *
 *The Awesomer

VFR

1980 A method of trisecting any given acute angle Origami is demonstrated. Hisashi Abe invented this idea and published in July, 1980 edition of the Japanese journal "Suugaku Seminar"(Mathematics Seminar). For this method, and more ways to trisect the angle, see this post.
 *Takaya Iwamoto

2001 The last occurrence that there were 3 eclipses in one month, and of which two solar eclipses.
For July 2000 being on 1st a partial solar eclipse, 16th a total lunar eclipse, and 31st a partial solar eclipse. The next occurrence with a month with 3 eclipses will be December 2206 with a partial solar eclipse on 1st and 30th and a total lunar eclipse on 16th. Ref. Fred Espenak 06/00 SEML. *NSEC  It happened in 2020.
The last time we had three eclipses in one lunar month – the period of time between successive new moons or full moons – was in June-July 2020. This period during which eclipses are possible is referred to as an eclipse season. We won’t have three eclipses in one eclipse season again until the year 2029.
watching Ec;ipse in Belfat, Ireland on Marce 20, 2015

2010 Grigori Yakovlevich Perelman turned down the Clay Millineum prize of one million dollars, saying that he considers his contribution to proving the Poincaré conjecture to be no greater than that of Richard Hamilton, who introduced the theory of Ricci flow with the aim of attacking the geometrization conjecture. On March 18 It had been announced that he had met the criteria to receive the first Clay Millennium Prize for resolution of the Poincaré conjecture. *Wik

2015 Michael Elmhirst Cates, becomes the 19th Lucasian Professor of Mathematic at the University of Cambridge. Professor Cates is a physicist and Professor of Natural Philosophy and Royal Society Research Professor at the University of Edinburgh. Previous recognitions for Prof. Cates include Maxwell Medal and Prize (1991), the Paul Dirac Medal and Prize (2009), and the Weissenberg Award (2013). He will assume the chair from another Physicist, Michael Green. He follows a line that began with Isaac Barrow and Isaac Newton and includes Charles Babbage, Paul Dirac, and Stephen Hawking

 *Wik

BIRTHS

1646 Gottfried Wilhelm Leibniz (July 1, 1646 – November 14, 1716) born in Leipzig, Germany. Leibniz occupies a prominent place in the history of mathematics and the history of philosophy. He developed the infinitesimal calculus independently of Isaac Newton, and Leibniz's mathematical notation has been widely used ever since it was published. He became one of the most prolific inventors in the field of mechanical calculators. While working on adding automatic multiplication and division to Pascal's calculator, he was the first to describe a pinwheel calculator in 1685[4] and invented the Leibniz wheel, used in the arithmometer, the first mass-produced mechanical calculator. He also refined the binary number system, which is at the foundation of virtually all digital computers. In philosophy, Leibniz is mostly noted for his optimism, e.g. his conclusion that our Universe is, in a restricted sense, the best possible one that God could have created. Leibniz, along with René Descartes and Baruch Spinoza, was one of the three great 17th century advocates of rationalism. The work of Leibniz anticipated modern logic and analytic philosophy, but his philosophy also looks back to the scholastic tradition, in which conclusions are produced by applying reason to first principles or a priori definitions rather than to empirical evidence. Leibniz made major contributions to physics and technology, and anticipated notions that surfaced much later in biology, medicine, geology, probability theory, psychology, linguistics, and information science. He wrote works on politics, law, ethics, theology, history, philosophy, and philology. Leibniz's contributions to this vast array of subjects were scattered in various learned journals, in tens of thousands of letters, and in unpublished manuscripts. As of 2010, there is no complete gathering of the writings of Leibniz.*Wik
Google Doodle for Leibniz's 372nd birthday in 2018.

1779 John Farrar (July 1, 1779 – May 8, 1853) born at Lincoln, Massachusetts. As Hollis professor of mathematics and natural philosophy at Harvard, he was responsible for a sweeping modernization of the science and mathematics curriculum, including the change from Newton’s to Leibniz’s notation for the calculus. *VFR
Mathematical Treasure: Farrar’s Translation of Lacroix’s Algebra MAA

1788 Jean Victor Poncelet (July 1, 1788 – December 22, 1867) born in Metz, France. He taught engineering and mechanics, but had a hobby of much greater interest—projective geometry. *VFR French mathematician and engineer whose study of the pole and polar lines associated with conic led to the principle of duality. While serving as an engineer in Napoleon's 1812 Russian campaign as an engineer, he was left for dead at Krasnoy, but then captured. During his imprisonment he studied projective geometry and wrote a treatise on analytic geometry. Released in 1814, he returned to France, and in 1822 published Traité des propriétés projectives des figures in which he presented his fundamental ideas of projective geometry such as the cross-ratio, perspective, involution and the circular points at infinity. As a professor of mechanics (1825-35), he applied mechanics to improve waterwheels and was able to double their efficiency.*TIS

1840  Robert Stawell Ball, an Irish astronomer and popular writer, was born July 1, 1840. In 1864, Ball became tutor to the three children of William Parsons, the third Earl of Rosse, who had built the largest telescope in the world on his estate in Ireland, a reflector with a six-foot mirror known as the “Leviathan of Parsonstown,” It was there and then that Ball began his lifetime love affair with astronomy, and he would rise to become professor of astronomy at both Trinity College, Dublin, and the University of Cambridge.

But it is for his popular books on astronomy that Ball is best remembered. He was an outstanding public lecturer on astronomical subjects, and he had a way of turning those lectures into exciting essays that the public loved to read. His most popular work was The Story of the Heavens, which came out in 1885 and went through edition after edition. What distinguishes Ball’s books from the many other popular astronomy books of the period are the illustrations, which were drawn from the latest available images and were often printed in color, which was quite unusual for the time.
 *Linda Hall Org

1848 Emil Weyr (1 July 1848 in Prague, Bohemia (now Czech Republic) - 25 Jan 1894 in Vienna, Austria) His father Frantisek Weyr, was a professor of mathematics at a realschule (secondary school) in Prague from 1855. Emil was four years older than his brother Eduard Weyr who also became a famous mathematician. Emil attended the realschule in Prague where his father taught, then studied at the Prague Polytechnic from 1865 to 1868 where he was taught geometry by Vilém Fiedler.
He studied in Italy with Cremona and Casorati during the academic year 1870-71 returning to Prague where he continued to teach. In 1872 he was elected to be Head of the Union of Czech Mathematicians and Physicists. In 1875 he was appointed as professor of mathematics at the University of Vienna. He, together with his brother Eduard Weyr, were the main members of the Austrian geometric school. They were interested in descriptive geometry, then in projective geometry and their interests turned towards algebraic and synthetic methods in geometry. Among many works Emil Weyr published were Die Elemente der projectivischen Geometrie and Über die Geometrie der alten Aegypter.
Emil Weyr led the geometry school in Vienna throughout the 1880's up until his death. Together with Gustav von Escherich, Emil Weyr founded the important mathematical journal Monatshefte fuer Mathematik und Physik in 1890. The first volumes of the journal contain papers written by his brother Eduard. In 1891 Emil Weyr became one of the first 19 founder members of the Royal Czech Academy of Sciences. *SAU

1906 Jean Dieudonn´e (1 July 1906 – 29 November 1992) born. *VFR French mathematician and educator known for his writings on abstract algebra, functional analysis, topology, and his theory of Lie groups. Dieudonné was one of the two main contributors to the Bourbaki series of texts. He began his mathematical career working on the analysis of polynomials. He worked in a wide variety of mathematical areas including general topology, topological vector spaces, algebraic geometry, invariant theory and the classical groups. *TIS

1916 Iosif Samuilovich Shklovsky ( sometimes transliterated Josif, Josif, Shklovskii, Shklovskij) (1 July 1916 – 3 March 1985) was a Soviet astronomer and astrophysicist. He is remembered for work in theoretical astrophysics and other topics, as well as for his 1962 book on extraterrestrial life, the revised and expanded version of which was co-authored by American astronomer Carl Sagan in 1966 as Intelligent Life in the Universe.
He showed, in 1946, that the radio-wave radiation from the Sun emanates from the ionized layers of its corona, and he developed a mathematical method for discriminating between thermal and nonthermal radio waves in the Milky Way. He is noted especially for his suggestion that the radiation from the Crab Nebula is due to synchrotron radiation, in which unusually energetic electrons twist through magnetic fields at speeds close to that of light. Shklovsky proposed that cosmic rays from supernova explosions within 300 light years of the sun could have been responsible for some of the mass extinctions of life on earth.
In 1959, Shklovsky examined the orbital motion of Mars's inner satellite Phobos. He concluded that its orbit was decaying, and noted that if this decay was attributed to friction with the Martian atmosphere, then the satellite must have an exceptionally low density. In this context, he voiced a suggestion that Phobos might be hollow, and possibly of artificial origin. This interpretation has since been refuted by more detailed study, but the apparent suggestion of extraterrestrial involvement caught the public imagination, though there is some disagreement as to how seriously Shklovsky intended the idea to be taken. However, Shklovsky and Carl Sagan argued for serious consideration of "paleocontact" with extraterrestrials in the early historical era, and for examination of myths and religious lore for evidence of such contact.
He won the Lenin Prize in 1960 and the Bruce Medal in 1972. Asteroid 2849 Shklovskij and the crater Shklovsky (on the Martian moon Phobos) are named in his honor. He was a Corresponding Member of Soviet Academy of Sciences since 1966.

1923 Herman Chernoff (born July 1, 1923) is an American applied mathematician, statistician and physicist. He was formerly a professor at University of Illinois Urbana-Champaign, Stanford, and MIT, currently emeritus at Harvard University.
Chernoff studied at Townsend Harris High School and earned a B.S. in mathematics from the City College of New York in 1943. He attended graduate school at Brown University, earning an M.Sc. in applied mathematics in 1945, and a Ph.D. in applied mathematics in 1948 under the supervision of Abraham Wald.
Chernoff became a fellow of the American Academy of Arts and Sciences in 1974, and was elected to the National Academy of Sciences in 1980. In 1987, he was selected for the Wilks Memorial Award by the American Statistical Association, and in 2012, he was made an inaugural fellow of the American Mathematical Society.

Chernoff turned 100 on July 1, 2023.

DEATHS

1912  Harriet Quimby (May 11, 1875 – July 1, 1912) Harriet Quimby of Coldwater, Michigan, the first American woman to earn a pilot's license, on August 1, 1911, when she earned license #37 from the Aero Club of America. She later becomes the first woman to fly an airplane across the English Channel.  Her accomplishment received little media attention, however, as the sinking of the Titanic ocean liner the day before riveted the interest of the public and filled newspapers.

The Vin Fiz Company, a division of Armour Meat Packing Plant of Chicago, recruited Quimby as the spokesperson for the new grape soda, Vin Fiz  in April 1912. Her distinctive purple aviator uniform and image graced many of the advertising pieces of the day.

1957 Donald McIntosh (Banffshire, 13 January 1868 – Invernesshire, 1 July 1957) graduated from the University of Aberdeen and taught at George Watson's Ladies College in Edinburgh. He was appointed a Director of Education. He became Secretary of the EMS in 1899 and President in 1905. *SAU

1963 Bevan Braithwaite Baker (1890 in Edinburgh, Scotland - 1 July 1963 in Edinburgh, Scotland) graduated from University College London. After service in World War I he became a lecturer at Edinburgh University and was Secretary of the EMS from 1921 to 1923. He left to become Professor at Royal Holloway College London. *SAU

1971 Sir William Lawrence Bragg (31 Mar 1890; 1 Jul 1971 at age 81) was an Australian-English physicist and X-ray crystallographer who at the early age of 25, shared the Nobel Prize for Physics in 1915 (with his father, Sir William Bragg). Lawrence Bragg formulated the Bragg law of X-ray diffraction, which is basic for the determination of crystal structure: nλ = 2dsinθ which relates the wavelength of x-rays, λ, the angle of incidence on a crystal, θ, and the spacing of crystal planes, d, for x-ray diffraction, where n is an integer (1, 2, 3, etc.). Together, the Braggs worked out the crystal structures of a number of substances. Early in this work, they showed that sodium chloride does not have individual molecules in the solid, but is an array of sodium and chloride ions. *TIS

1983 Richard Buckminster Fuller (July 12, 1895 – July 1, 1983) was a U.S. engineer and architect who developed the geodesic dome, the only large dome that can be set directly on the ground as a complete structure, and the only practical kind of building that has no limiting dimensions (i.e., beyond which the structural strength must be insufficient). Fuller also invented a wide range of other paradigm-shifting machines and structural systems. He was especially interested in high-strength-to-weight designs, with a maximum of utility for minimum of material. His designs and engineering philosophy are part of the foundation of contemporary high-tech design aesthetics. He held over 2000 patents.*TIS
Fuller died on July 1, 1983, 11 days before his 88th birthday. During the period leading up to his death, his wife had been lying comatose in a Los Angeles hospital, dying of cancer. It was while visiting her there that he exclaimed, at a certain point: "She is squeezing my hand!" He then stood up, had a heart attack, and died an hour later, at age 87. His wife of 66 years died 36 hours later. They are buried in Mount Auburn Cemetery in Cambridge, Massachusetts
This is another one who died within two weeks of his date of birth. I must organize data on this...

 The Montreal Biosphère by Buckminster Fuller, 1967

1965 Dudley Weldon Woodard (October 3, 1881 – July 1  {or 15?}, 1965) was a Galveston-born American mathematician and professor, and the second African-American to earn a PhD in mathematics; the first was Woodard's mentor Elbert Frank Cox, who earned a PhD from Cornell in 1925).

He received his B.A. degree from Wilberforce University in Ohio (1903), his B.S. degree (1906) and M.Sc. degree (1907) at the University of Chicago. He taught collegiate mathematics in Tuskegee for many years, until finally he earned his PhD at the University of Pennsylvania (1928). His doctoral thesis was entitled, On Two-Dimensional Analysis Situs with Special Reference to the Jordan Curve Theorem, and was advised by John R. Kline.

During his lifetime, he published three papers. The second of these, The Characterization of the Closed N-Cell in Fundamenta Mathematicae, 13 (1929), is, according to Scott Williams, Professor of Mathematics at the State University of New York-Buffalo, the first paper published in an accredited mathematics journal by an African American.[4][6] He also published a study for the Committee of twelve for the advancement of the interests of the Negro race on Jackson, Mississippi in 1909, a textbook, Practical Arithmetic (1911), and an article on geometry teaching at Tuskegee in 1913.

Woodard was a respected mathematician, professor and mentor to his students at Howard University in Washington DC, where he established the masters program in mathematics. One of his best known students was William Waldron Schieffelin Claytor, who later took his PhD at the University of Pennsylvania (1933), also under Woodard's former advisor, John R. Kline.

Woodard retired in 1947, after having become chairman of the mathematics department. He died on July 1, 1965, at his home in Cleveland, Ohio, aged 83.

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