## Thursday 23 November 2023

### On This Day in Math - November 23

Whereas Nature does not admit of more than three dimensions ...
it may justly seem very improper to talk of a solid ...
drawn into a fourth, fifth, sixth, or further dimension.

~John Wallis

The 327th day of the year; 327 is the largest number n so that n, 2n, and 3n together contain every digit from 1-9 exactly once. (Students might search for a smaller number with that quantity) *What's Special About This Number

and from Jim Wilder @wilderlab:
For day 327: 327 is a perfect totient number- φ(327)=216, φ(216)=72, φ(72)=24, φ(24)=8, φ(8)=4, φ(4)=2, φ(2)=1, and 216+72+24+8+4+2+1=327.

327 cannot be written as the sum of three squares.   Gauss found that this is only true for numbers of the form 4^k (8n-1), such as 7, 15, 23, .... but also 28, 60, 92, ...  and 112, 240, etc.

EVENTS

1654 From 10:30 to 12:30 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. *VFR
Shortly after his death in 1662 a servant was sorting through Pascal’s clothes and noticed something sewn into a coat that Pascal had often worn.  Out of curiosity the servant cut open the cloth and found a parchment, inside of which was a faded piece of paper.  The parchment and the paper both contained, in Pascal’s handwriting, nearly the same words. The papers, containing a confusing list of religious phrases drawn from seemingly non-related Bible verses, are often    called Pascals amulet or memorial.
The common historical narrative is that Pascal never discussed his nigh of religious re-dedication, which led to his giving up all work in mathematics until a brief period in 1658-1659 when he wrote out his discoveries about the cycloid formed by the path a point on the edge of a rolling circle.  In particular he gave a method for determining the area under a circular arc.
Another famous incident in Pascals life was a near fatal accident that happened at the Neuilly-sur-Seine bridge where the horses plunged over the parapet and the carriage nearly followed them. Fortunately, the reins broke and the coach hung halfway over the edge.  Many historians doubt this incident ever happened, but others have linked it to the same date as his religious ectasy and suggest he took the accident as a warning from God that led to his "Night of Fire."  One historian wrote"On this day, November 23, 1654, Pascal's horses bolted and plunged off a bridge. Pascal was thrown into the roadway. He saw this as a warning directly from God. That night he experienced a Christian conversion that would cause his outstanding scientific work to take second place in his pursuits. Light flooded his room. He recognized Jesus, the Word. For the rest of his life Pascal carried around a piece of parchment sewn into his coat--a parchment inscribed with ecstatic phrases…"
"Incidentally, speaking of revelations, about ten years after Pascal’s death, Leibniz was reading Pascal’s 1659 paper on the area under a circular arc, and “a light suddenly burst upon him”.  At this moment, looking at Pascal’s diagram, Leibniz realized that the tangent (derivative) was determined by dividing by the difference between the ordinates, and the quadrature (integral) was determined by multiplying by that same difference, and that, therefore, these two operations were the reciprocals of each other, i.e., the fundamental theorem of calculus.
It was right there in the diagram, but apparently Pascal didn’t see it.  Leibniz wrote to James Bernoulli that “sometimes Pascal seemed to have had a bandage over his eyes”. *Mathpages.com

1670 James Gregory writes to John Collins, with the first use of what will come to be called the Newton-Gregory interpolation formula. He includes in the letter two enclosures showing how to apply his method to series for sines and logarithms. *Thomas Harriot’s Doctrine of Triangular Numbers, Beery & Stedall, pg 51-52

1706 Jakob Hermann writes to Leibniz about proof that Machin's series converges to pi. *My uncredited notes (sorry)

1821 Thomas Jefferson writes to West Point Instructor Claudius Crozet to thank him for the gift of a copy of his A Treatise on Descriptive Geometry and praised the book, and the author. Jefferson pronounced Crozet, "by far the best mathematician in the United States." *Natl. Archives, Wik (Crozet is sometimes credited with introducing the blackboard into the US, but it seems to have been common at West Point before his arrival there.)
Crozet was one of the founders of Virginia Military Institute (VMI) at Lexington, Virginia, a major training institution for engineers and militia officers for Virginia and the South. When VMI opened in 1839, Crozet was the architect of the college's academic program and military organization. At its first meeting, the members of the VMI Board of Visitors elected Crozet president of the Board, a position he held for six years (while remaining the state's Chief Engineer).
Crozet died in January 1864 at the residence of his daughter and son-in-law, as the Confederacy was losing the Civil War, but more than a year before its defeat. He was initially buried near his wife and children in Shockoe Hill Cemetery, but in 1942 his remains were reinterred in the Virginia Military Institute cemetery.
Crozet's grave on the campus of the Virginia Military Institute, in Lexington, Virginia

1823 Janos Bolyai wrote to his father “I have made such wonderful discoveries that I am myself lost in astonishment.” This refers to his discovery of Non-Euclidean Geometry that was published in 1833. *Kline, Mathematics. The Loss of Certainty, p. 83 via *VFR
Carl Friedrich Gauss, on reading the Appendix, wrote to a friend saying "I regard this young geometer Bolyai as a genius of the first order." To Farkas Bolyai, however, Gauss wrote: "To praise it would amount to praising myself. For the entire content of the work...coincides almost exactly with my own meditations which have occupied my mind for the past thirty or thirty-five years." In 1848 Bolyai learned that Nikolai Ivanovich Lobachevsky had published a similar piece of work in 1829. Though Lobachevsky published his work a few years earlier than Bolyai, it contained only hyperbolic geometry. Working independently, Bolyai and Lobachevsky pioneered the investigation of non-Euclidean geometry.
In addition to his work in geometry, Bolyai developed a rigorous geometric concept of complex numbers as ordered pairs of real numbers. Although he never published more than the 24 pages of the Appendix, he left more than 20,000 pages of mathematical manuscripts when he died.

1834 Astronomer Royal Airy Replies to suggestion that he begin a mathematical search for undiscovered planet that would be Neptune by the Reverend T.J. Hussey.
Hussey had mentioned in his letter how he has heard of a possible planet beyond Uranus and looked for it using a reflector telescope, but to no avail. He presented the idea of using mathematics as a tool in the search but admitted to Airy that he would not be of much help in that regard. On November 23rd Airy writes back to the reverend and admits he too has been preoccupied with a possible planet. He had observed that Uranus' orbit deviated the most in 1750 and 1834, when it would be at the same point. This was strong evidence for an object pulling on the planet, but Airy felt that until more observations were made no mathematical tools would be of help
*from http://theoriginal1701.hubpages.com/hub/The-Drama-of-Neptunes-Discovery

In 1889, the first jukebox was installed when an entrepreneur named Louis Glass and his business associate, William S. Arnold, placed a coin-operated Edison cylinder phonograph in the Palais Royale Saloon in San Francisco. The machine, an Edison Class M Electric Phonograph with oak cabinet, had been fitted locally in San Francisco with a coin mechanism invented and soon patented by Glass and Arnold. This was before the time of vacuum tubes, so there was no amplification. For a nickel a play, a patron could listen using one of four listening tubes. Known as "Nickel-in-the-Slot," the machine was an instant success, earning over $1000 in less than half a year. *TIS "Rockin' like it's 1889" 1924 New York Times publishes Hubble's new universe: Between 1922–1923, Hubble's observations had proved conclusively that these nebulae were much too distant to be part of the Milky Way and were, in fact, entire galaxies outside our own. This idea had been opposed by many in the astronomy establishment of the time, in particular by the Harvard University-based Harlow Shapley. (Shapley wrote sarcastically that Hubble's letter informing him of his results was “the most entertaining piece of literature I have seen for a long time.” ) Despite the opposition, Hubble, then a thirty-five year old scientist, had his findings first published in The New York Times on November 23, 1924, and then more formally presented in the form of a paper at the January 1, 1925 meeting of the American Astronomical Society. Hubble's findings fundamentally changed the scientific view of the universe.*Wik 1982 Vatican City issued a set of three stamps commemorating the 400th anniversary of the Gregorian Calendar. The image on the Vatican stamp is from the tomb of Pope Gregory XIII in St. Peter's Basilica. The tomb, the work of Camillo Rusconi, includes a relief showing Clavius kneeling before the Pope, presenting his work as the Pope promulgates the new calendar in 1582. *VFR 1982 Poland issued stamps honoring the mathematicians StanisLlaw Zaremba (1863–1942), WacLlaw Sierpi´nski (1882–1969), Zygmunt Janiszewski (1888–1920), and Stefan Banach (1892-1945). [Scott #2542-5]. *VFR 1992 "Computer industry on the skids" With IBM projected to lose$5 billion in 1992, Business Week describes the computer business as "an industry on the skids." The magazine cited layoffs at most established computer companies, such as IBM, as well as newer firms like Sun Microsystems Inc., as evidence that the industry was saturated. A solution, the article concluded, would be for each business to find its proper niche.*CHM

BIRTHS

1221 Alfonso X of Castile (23 Nov 1221; 4 Apr 1284) Spanish monarch and astronomer who encouraged the preparation of revised planetary tables (1252), published on the day of his accession to the throne as king of Castile and León. These "Alfonsine Tables," a revision and improvement of the Ptolemaic tables, were the best available during the Middle Ages; they were not replaced by better ones for over three centuries. The astronomical data tabulating the positions and movements of the planets was compiled by about 50 astronomers he had assembled for this purpose. He questioned the complexity of the Ptolemaic model centuries before Copernicus. "If the Lord Almighty had consulted me before embarking on the Creation, I would have recommended something simpler." He also wrote a commentary on alchemy. *TIS

1616 John Wallis (23 Nov 1616, 28 Oct 1703) British mathematician who introduced the infinity math symbol $\mathrm{\infty }$. Wallis was skilled in cryptography and decoded Royalist messages for the Parliamentarians during the Civil War. Subsequently, he was appointed to the Savilian Chair of geometry at Oxford in 1649, a position he held until his death more than 50 years later. Wallis was part of a group interested in natural and experimental science which became the Royal Society, so Wallis is a founder member of the Royal Society and one of its first Fellows. Wallis contributed substantially to the origins of calculus and was the most influential English mathematician before Newton. *TIS

1820 Isaac Todhunter (23 Nov 1820 in Rye, Sussex, England - 1 March 1884 in Cambridge, England) Todhunter is best known for his textbooks and his writing on the history of mathematics. Among his textbooks are Analytic Statics (1853), Plane Coordinate Geometry (1855), Examples of Analytic geometry in Three Dimensions (1858). He also wrote some more elementary texts, for example Algebra (1858), Trigonometry (1859), Theory of Equations (1861), Euclid (1862), Mechanics (1867) and Mensuration (1869).
Among his books on the history of mathematics are A History of the Mathematical Theory of Probability from the Time of Pascal to that of Laplace (1865, reprinted 1965) and History of the Mathematical Theories of Attraction (1873). *SAU

1837 Johannes Diederik van der Waals (23 Nov 1837; 9 Mar 1923) Dutch physicist, winner of the 1910 Nobel Prize for Physics for his research on the gaseous and liquid states of matter. He was largely self-taught in science and he originally worked as a school teacher. His main work was to develop an equation (the van der Waals equation) that - unlike the laws of Boyle and Charles - applied to real gases. Since the molecules do have attractive forces and volume (however small), van der Waals introduced into the theory two further constants to take these properties into account. The weak electrostatic attractive forces between molecules and between atoms are called van der Waals forces in his honour. His valuable results enabled James Dewar and Heike Kamerlingh-Onnes to work out methods of liquefying the permanent gases. *TIS

1853 George Bruce Halsted (23 Nov 1853 in Newark, New Jersey, USA - 16 March 1922 in New York, USA) His main interests were the foundations of geometry and he introduced non-euclidean geometry into the United States, both through his own research and writings as well as by his many important translations. Halsted gave commentaries on the work of Lobachevsky, Bolyai, Saccheri and Poincaré and made translations of their works into English. His work on the foundations of geometry led him to publish Demonstration of Descartes's theorem and Euler's theorem in the Annals of Mathematics in 1885. His other main interest was in mathematical education and, as a mathematics educator, he criticised the careless way that mathematics was presented in the textbooks of the time. He contributed over ninety article to the American Mathematical Monthly and wrote many biographies of mathematicians such as Lambert, Farkas Bolyai, Lobachevsky, De Morgan, Sylvester, Chebyshev, Cayley, Hoüel and Klein. *SAU
Halsted introduced conics after the manner of a Steiner conic, here shown from a projectivity composed of two perspectivities

1887 Henry Gwyn Jeffreys Moseley (23 Nov 1887; 10 Aug 1915) English physicist who experimentally demonstrated that the major properties of an element are determined by the atomic number, not by the atomic weight, and firmly established the relationship between atomic number and the charge of the atomic nucleus. He began his research under Ernest Rutherford while serving as lecturer at the Univ. of Manchester. Using X-ray photographic techniques, he determined a mathematical relation between the radiation wavelength and the atomic numbers of the emitting elements. Moseley obtained several quantitative relationships from which he predicted the existence of three missing elements (numbers 43, 61, and 75) in the periodic table, all of which were subsequently identified. Moseley was killed in action during WW I.*TIS
Moseley in the Balliol-Trinity Laboratories in 1910

1917 Elizabeth Scott (November 23, 1917 – December 20, 1988) was an American mathematician specializing in statistics.
Scott was born in Fort Sill, Oklahoma. Her family moved to Berkeley, California when she was 4 years old. She attended the University of California, Berkeley where she studied mathematics and astronomy. There were few options for further study in astronomy, as the field was largely closed to women at the time, so she completed her graduate studies in mathematics. "It was a profession not quite ready to welcome women." She received her Ph.D. in 1949, and received a permanent position in the Department of Mathematics at Berkeley in 1951.
She wrote over 30 papers on astronomy and 30 on weather modification research analysis, incorporating and expanding the use of statistical analyses in these fields. She also used statistics to promote equal opportunities and equal pay for female academics.
In 1957 Elizabeth Scott noted a bias in the observation of galaxy clusters. She noticed that for an observer to find a very distant cluster, it must contain brighter than normal galaxies and must also contain a large number of galaxies. She proposed a correction formula to adjust for (what came to be known as) the "Scott effect".
The Committee of Presidents of Statistical Societies awards a prize in her honour to female statisticians.*Wik

DEATHS

1604 Francesco Barozzi (in Latin, Franciscus Barocius) (9 August 1537 – 23 November 1604) was an Italian mathematician, astronomer and humanist. Barozzi helped in the general reappraisal of the geometry of Euclid, and corresponded with numerous mathematicians, including the German Jesuit Christopher Clavius. His original works include Cosmographia in quatuor libros distributa summo ordine, miraque facilitate, ac brevitate ad magnam Ptolemaei mathematicam constructionem, ad universamque
astrologiam institutens (1585), which he dedicated to the Duke of Urbino. This work concerns the cosmography and mathematic systems of Ptolemy. Barozzi also discussed 13 ways of drawing a parallel line in his Admirandum illud geometricum problema tredecim modis demonstratum quod docet duas lineas in eodem plano designare, quae nunquam invicem coincidant, etiam si in infinitum protrahantur: et quanto longius producuntur, tanto sibiinuicem propiores euadant (1586).
In his Opusculum: in quo una Oratio et due Questiones, altera de Certitude et altera de Medietate Mathematicarum continentur, Barozzi stressed that "the certitude of mathematics is contained in the syntactic rigor of demonstrations." Barozzi dedicated this work to Daniele Barbaro.
He also wrote Rythmomachia (1572), which he dedicated to Camille Paleotti, a Senator of Bologna, a work that is based on the mathematical game of the same name, also known as "The Philosophers' Game."
As an antiquarian, he copied many Greek inscriptions on Crete. His collection of inscriptions was later inherited by his nephew Iacopo Barozzi (1562–1617), who edited and expanded it. This collection was later acquired in 1629 by the University of Oxford. They are wide-ranging in date and subject-matter and can still be found in the Bodleian Library.*Wik

1817 James Glenie (Oct 1750 in Leslie, Fife, Scotland - 23 Nov 1817 in Chelsea, London, England ) He was an artillery officer when his regiment was sent out to North America in 1775 at the start of the American War of Independence. During his time in North America with the army Glenie worked on mathematics. In fact, even before being sent to North America, he had discovered what he called the antecedental calculus in 1774. The was an attempt to base Newton's fluxional calculus on the binomial theorem rather than on the concept of motion. He published a number of papers on this and other topics; The division of right lines, surfaces and solids being published in the Philosophical Transactions of the Royal Society in 1776 while The general mathematical laws which regulate and extend proportion universally was published in the same journal in the following year. In 1778 the Royal Society published Glenie's paper on the antecedental calculus. In addition to these papers he had also published a book on gunnery entitled The History of Gunnery with a New Method of Deriving the Theory of Projectiles in 1776. For his achievements in mathematics and its applications he was elected a fellow of the Royal Society on 18 March 1779 while he was still based with the army in Quebec.
He died in poverty. *SAU

1826 Johann Elert Bode (19 Jan 1747, 23 Nov 1826) German astronomer best known for his popularization of Bode's law. In 1766, his compatriot Johann Titius had discovered a curious mathematical relationship in the distances of the planets from the sun. If 4 is added to each number in the series 0, 3, 6, 12, 24,... and the answers divided by 10, the resulting sequence gives the distances of the planets in astronomical units (earth = 1). Also known as the Titius-Bode law, the idea fell into disrepute after the discovery of Neptune, which does not conform with the 'law' - nor does Pluto. Bode was director at the Berlin Observatory, where he published Uranographia (1801), one of the first successful attempts at mapping all stars visible to the naked eye without any artistic interpretation of the stellar constellation figures. *TIS

1844 Thomas Henderson (28 Dec 1798, 23 Nov 1844) Scottish astronomer, the first Scottish Astronomer Royal (1834), who was first to measure the parallax of a star (Alpha Centauri, observed at the Cape of Good Hope) in 1831-33, but delayed publication of his results until Jan 1839. By then, a few months earlier, both Friedrich Bessel and Friedrich Struve had been recognized as first for their measurements of stellar parallaxes. Alpha Centauri can be observed from the Cape, though not from Britain. It is now known to be the nearest star to the Sun, but is still so distant that its light takes 4.5 years to reach us. As Scottish Astronomer Royal in 1834, he worked diligently at the Edinburgh observatory for ten years, making over 60,000 observations of star positions before his death in 1844.*TIS

1864 Friedrich Georg Wilhelm von Struve (15 Apr 1793, 23 Nov 1864) German-Russian astronomer, one of the greatest 19th-century astronomers and the first in a line of four generations of distinguished astronomers. He founded the modern study of binary (double) stars. In 1817, he became director of the Dorpat Observatory, which he equipped with a 9.5-inch (24-cm) refractor that he used in a massive survey of binary stars from the north celestial pole to 15°S. He measured 3112 binaries - discovering well over 2000 - and cataloged his results in Stellarum Duplicium Mensurae Micrometricae (1837). In 1835, Czar Nicholas I persuaded Struve to set up a new observatory at Pulkovo, near St. Petersburg. There in 1840 Struve became, with Friedrich Bessel and Thomas Henderson, one of the first astronomers to detect parallax. *TIS

1910 Octave Chanute(18 Feb 1832, 23 Nov 1910) U.S. aeronaut whose work and interests profoundly influenced Orville and Wilbur Wright and the invention of the airplane. Octave Chanute was a successful engineer who took up the invention of the airplane as a hobby following his early retirement. Knowing how railroad bridges were strengthened, Chanute experimented with box kites using the same basic strengthening metod, which he then incorporated into wing design of gliders. Through thousands of letters, he drew geographically isolated pioneers into an informal international community. He organized sessions of aeronautical papers for the professional engineering societies that he led; attracted fresh talent and new ideas into the field through his lectures; and produced important publications. *TIS The town of Chanute, Kansas is named after him, as well as the former Chanute Air Force Base near Rantoul, Illinois, which was decommissioned in 1993. The former Base, now turned to peacetime endeavors, includes the Octave Chanute Aerospace Museum, detailing the history of aviation and of Chanute Air Force base. He was buried in Springdale Cemetery, Peoria, Illinois. *Wik
Chanute's 1896 biplane hang glider is a trailblazing design adapted by the Wright brothers, who "contrived a system consisting of two large surfaces on the Chanute double-deck plan.

1942 Stanisław Saks (December 30, 1897 – November 23, 1942) was a Polish mathematician and university tutor, known primarily for his membership in the Scottish Café circle, an extensive monograph on the Theory of Integrals, his works on measure theory and the Vitali-Hahn-Saks theorem.*Wik

1942 Stanisław Zaremba (October 3, 1863 – November 23, 1942) was a Polish mathematician. His research in differential equations, applied mathematics, classical analysis, particularly on harmonic analysis, was widely recognized. He was a mathematician who contributed to the success of the Polish School of Mathematics through his teaching and organizational skills as well as through his research. Zaremba wrote a number of university textbooks and monographies.*Wik

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