Sunday 24 May 2020

On This Day in Math - May 24

 Hence no force, however great, 
can stretch a cord, however fine,
into a horizontal line 
which is accurately straight:
there will always be a bending downwards.
~William Whewell

The 145th day of the year; 145= 1! + 4! + 5!. There are only four such numbers in base ten. 1, 2 and 145 are three of them, what's the fourth? Such numbers are called factorions, a term created by Cliff Pickover in 1995  (**answer at bottom of post)

145 is the result of 34 + 43, making it a Leyland number. a number of the form xy + yx where x and y are integers greater than 1. They are named after the British number theorist, Paul Leyland. (There are ten days of the year that are Leyland numbers)

Prime Curios points out several curiosities related to 145, The 145th prime number is 829 and their concatenation, 145829 is prime. And the largest prime factor of 145, is 1+4+5+8+2+9. and 149 is congruent to 1 in mod 8, mod 2, and mod 9.

More Math facts for this date here 


997 Al-Bırunı in Kath and Abul-Wafa in Baghdad simultaneously watch a lunar eclipse. The time obtained by this prearranged cooperation allowed them to determine the difference in longitude between the cities. *VFR

1032 The renowned Arab scientist Ibn Sina noted, “I saw Venus as a spot on the surface of the sun,” This is the first known record of witnessing the transit of Venus. The first recorded observation of a transit of Venus was made by Jeremiah Horrocks from his home at Carr House in Much Hoole, near Preston in England, on 4 December 1639. Kepler predicted the 1761 transit of Venus, the first such prediction in Western recorded history, and one that inspired several astronomical expeditions. *Sky and Telescope (A.M.S ‏@amoshaye pointed out that he was NOT Arabic, {Persian I believe}. It was once common to lump mid-eastern scholars who wrote in Arabic as Arabian. I write in English, but am not English, a fact that I, and all of England are equally grateful for.)

1543 An advance copy of his work De revolutionibus orbium coelestium was presented to Copernicus. On the same day he died. *VFR

1547 Ferrari replied to Tartaglia’s letter of 21 April 1547 by sending 31 challenge problems of his own. Tartaglia solved all but the five dealing with cubic equations. *VFR  For more on this "math wars" story, see this Renaissance Mathematicus blog.

1626 Manhattan bought from the Indians for \( $24 \) *VFR {In 1626 Peter Minuit bought Manhattan island from the local Indians for a load of cloth, beads, hatchets, and other odds and ends then worth 60 Dutch guilders. Estimated to have been worth  \($24 \) Dollars at a much later time. If we convert that to silver prices at the time, you could purchase about 18 Troy ounces of Silver.. Today the price of silver is about  \($35 \) per ounce, so .. not such a good investment in that sense... }

1683 The Ashmolean, Britain's first Museum, first opened to the public on 24 May 1683. *Ashmolean (in full the Ashmolean Museum of Art and Archaeology) on Beaumont Street, Oxford, England, is the world's first university museum. Its first building was built in 1678–1683 to house the cabinet of curiosities Elias Ashmole gave Oxford University in 1677. *Wik

1727 Euler arrived at St. Petersburg for the first time on 24 May 1727, only seven days after the Russian empress Katherine I, the wife of Peter I (an adopted daughter of Ernst Glilck, the provost of Marienburg, now Aliiksne) died, and he worked at the St. Petersburg Academy of Sciences until 1741 when he moved to
Berlin, there to stay until 1766. *Historia Mathematica

1844 Samuel F. B. Morse dispatched the first telegraphic message over an experimental line from Washington, D.C., to Baltimore. The message, taken from the Bible, Numbers 23:23 and recorded on a paper tape had been suggested to Morse by Annie Ellsworth, the young daughter of a friend. {Nice to have influential friends, she was the teenage daughter of the Commissioner of Patents. Congress appropriated $30,000  for a telegraph wire to be strung the 80 miles between Washington and Baltimore}..Morse sent the message from the chamber of the Supreme Court, then in the United States Capitol, to his assistant Albert Vail at the Mount Clair depot in Baltimore in 1844.*Library of Congress

A photo of the actual paper tape with raised dots and dashes in the Library of Congress is here. Across the top of this artifact of his historic achievement Morse has given credit to Annie Ellsworth for suggesting the message.

Wolfram alpha will let you convert any message to Morse code, or from Morse code by typing [Morse code "input"] to encode, or Morse Code message to decode.

1883 Brooklyn Bridge was opened over the East River, New York City, USA, of a breadth of 1,600 feet, navigable water with a single span. What was then regarded as the greatest engineering feat still stands in service today, and remains the world's only stone-towered, steel cabled bridge. Twice the size of the Niagara Suspension Bridge and four times the longest non-extension spans ever attempted, the total length of this colossal structure is 6,927 ft. The road bed is 80 feet wide, and at an elevation of 186 feet above high water. John Roebling, and after his death his son Washington Roebling, worked on its construction for 13 years. *TIS
Contrary to the New York Times Magazine of 27 March 1983, the cables hang in the shape of parabolas, not catenaries. *VFR

1937 A temporary science exhibition called Le Palais de la Decouverte opened its doors in the west wing of the Grand Palais in time for the 1937 International Exposition of Art and Technology in Modern Life, which was to be held in Paris. It was primarily the inspiration of French physicist Jean Perrin, who won the Nobel prize in 1926 for his work on the atom. An interesting mathematical anecdote relates to the museum.
The museum contains a circular room known as the "pi room". On its wall is inscribed 707 digits of the number π. The digits are large wooden characters attached to the dome-like ceiling. The digits were based on an 1853 calculation by English mathematician William Shanks, which included an error in the 528th digit. The error was detected in 1946 and corrected in 1949
Shank's 707 digits was the record at that time, taken from his teacher William Rutherford, whose record was 404 digits.His record, now adjusted to the 528 digits he had right, was the last record of hand computation.  D. F. Ferguson's 1946 calculation of 606 digits was done with a desk top calculating machine.

1961 MIT's Clark Begins Work on LINC Computer :
Wes Clark began his work on LINC, or the Laboratory Instrument Computer, at MIT's Lincoln Laboratory. His plan was to create a computer for biomedical research, that was easy to program and maintain, that could be communicated with while it operated, and that could process biotechnical signals directly. Building on his previous experience in developing the Whirlwind, TX-0, and other early computers, Clark set to work on one of the earliest examples of a "user friendly" machine -- setting the standard for personal computer design in the following decades. *CHM

1965, Hansard, the official record of all English parliamentary debates, recorded in an Appendix the statement by Mr Jay (President of the Board of Trade) saying he was impressed by the case for adoption of the metric system - by a long-term, gradual, voluntary process - and was arranging for the British Standards Institution to investigate. Eventually, as a member of the European Common Market, the transition to the metric system for trade and commerce became obligatory.*TIS

1973 French mathematicians Jean Guilloud and Mlle. Martine Bouyer computed π on a CDC 7600 computer to one million decimal places, the greatest accuracy to (that) date. The value was not verified until September 3, 1973. It is published in a 400 page book. *VFR

1983 Marshall Stone received the National Medal of Science, the nation’s highest scientific honor, “for his original synthesis of analysis, algebra and topology into the new, vital area of functional analysis, in modern mathematics.” Notices AMS, v. 30, p. 485, contains more information. *VFR

2014 NASA predicts a never before seen meteor shower. The shower is the May Camelopardalids (a faint constellation near the North Star), caused by dust from periodic comet 209P/LINEAR. No one has ever seen it before, but this year the Camelopardalids could put on a display that rivals the well-known Perseids of August.
"Some forecasters have predicted more than 200 meteors per hour," *


1544 William Gilbert (24 May 1544 – 30 November 1603)  English scientist, the "father of electrical studies" and a pioneer researcher into magnetism, who spent years investigating magnetic and electrical attractions. Gilbert coined the names of electric attraction, electric force, and magnetic pole. He became the most distinguished man of science in England during the reign of Queen Elizabeth I. Noting that a compass needle not only points north and south, but also dips downward, he thought the Earth acts like a bar magnet. Like Copernicus, he believed the Earth rotates on its axis, and that the fixed stars were not all at the same distance from the earth. Gilbert thought it was a form of magnetism that held planets in their orbits. *TIS  "Gilbert shall live, till Load-stones cease to draw,   Or British Fleets the boundless Ocean awe. ~ John Dryden

1640 John Mayow (24 May 1640 - October 1679 ) English chemist and physiologist who, about a hundred years before Joseph Priestley and Antoine-Laurent Lavoisier, identified spiritus nitroaereus (oxygen) as a distinct atmospheric entity. He further recognized the role of oxygen in the combustion of metals. His medical writings include a remarkably correct anatomical description of respiration. *TIS  {It is said that he observed a mouse in a sealed jar with a candle, and as the candle flame was going out, the mouse fainted...}

1686 Daniel Gabriel Fahrenheit (24 May 1686 – 16 September 1736) German physicist and maker of scientific instruments. He is best known for inventing the alcohol thermometer (1709) and mercury thermometer (1714) and for developing the Fahrenheit temperature scale. He devoted himself to the study of physics and the manufacture of precision meteorological instruments. He discovered, among  other things, that water can remain liquid below its freezing point and that the boiling point of  liquids varies with atmospheric pressure.*TIS

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

1820  William Chauvenet (24 May 1820, Milford, Pennsylvania - 13 December 1870, St. Paul, Minnesota) was born on a farm near Milford, Pennsylvania, in 1820 and was raised in Philadelphia. Early in life he exhibited a knack for mathematics and all things mechanical, and he attended Yale University. Entering Yale at age 16, he graduated in 1840 with high honors and soon after began his scholarly career by assisting a professor at Girard College in Philadelphia, Pennsylvania in a series of magnetic observations. In 1841 he was appointed professor of mathematics in the U.S. Navy and for a few months served on the U.S. steamer Mississippi, where he taught midshipmen. He later taught at and was instrumental in the establishment of the U.S. Naval Academy at Annapolis, Maryland.*Wik

1903  Władysław Roman Orlicz (May 24, 1903 in Okocim, Austria-Hungary (now Poland) – August 9, 1990 in Poznań, Poland) was a Polish mathematician of Lwów School of Mathematics.  His main interest was topology. *Wik

1909 Karl Heinrich Weise (24 May 1909 in Gera, Thüringen, Germany, 15 April 1990 in Kiel, Germany) Weise's mathematical work was mainly on questions from differential geometry and topology. In 1951, jointly with Robert König, he published the book Mathematische Grundlagen der Höheren Geodäsie und Kartographie.
Weise acted as supervisor of PhD students from a wide range of mathematical fields, a dozen of them went on to become professors, among them Wolfgang Gaschütz (finite groups), Wolfgang Haken (knot theory and the solution of the four-colour-problem), Wilhelm Klingenberg (differential geometry) and Jens Mennicke (topology). Let us look in a little more detail at Weise's influence on one of these students, Wolfgang Haken, who studied mathematics, physics and philosophy at the University of Kiel. Haken attended Heinrich Heesch's talk on his contributions to the Four Colour Problem, but he was most enthused by Weise's lectures on topology. In these lectures, Weise described three long-standing unsolved problems - the Poincaré Conjecture, the Four Colour Problem, and a problem on knot theory. Haken decided to attempt to solve all three problems and began this challenge while studying for a doctorate at Kiel with Weise as his thesis advisor. His thesis, submitted in 1953, was Ein topologischer Satz über die Einbettung (d-1)-dimensionaler Mannigfaltigkeiten in d-dimensionale Mannigfaltigkeiten. He had solved the knot theory problem and this led to his appointment at the University of Illinois in the United States. Eventually, assisted by Kenneth Appel, he solved the Four Colour Problem in 1976 with the aid of computer techniques.
Weise was retired on 30 September1977, and in the following year the Christian Albrechts Universität conferred on him the title of 'Ehrensenator' (honorary senator). *SAU

1914 Federico Cafiero (24 May 1914 in Riposto, Catania, Sicily, 7 May 1980 in Naples, Italy) Cafiero played an important role in building a vigorous mathematical school at Naples which included (in alphabetical order) Luigi Albano, Ugo Barbuti, Antonio Chffi, Paolo De Lucia, Nicola Fedele, Renato Fiorenza, Francesco Guglielmino, Giuseppe Pulvirenti, Giuseppe Santagati and Antonio Zitarosa. We have already seen that Cafiero made contributions to the theory of ordinary differential equations and to the theory of measure and integration.
Two notable awards the Cafiero received for his mathematical contributions were the Tenore prize of the Accademia Pontaniana (awarded in 1953 for his monograph Funzioni additive d'insieme e integrazione negli spazi astratti) and the Golden medal 'Benemeriti della Scuola, della Cultura, dell'Arte' which he received from the President of the Italian Republic in 1976. *SAU


1543 Nicolaus Copernicus (19 February 1473 – 24 May 1543) Polish astronomer who proposed that the planets have the Sun as the fixed point to which their motions are to be referred; that the Earth is a planet which, besides orbiting the Sun annually, also turns once daily on its own axis; and that very slow, long-term changes in the direction of this axis account for the precession of the equinoxes    *TIS     An advance copy of his work De revolutionibus orbium coelestium was presented to Copernicus. On the same day he died. *VFR  Over 450 years after his death, Copernicus was reburied in the cathedral at Frombork on Poland’s Baltic coast. The astronomer whose ideas were once declared heresy by the Vatican—was reburied with full religious honors. 

1659 Georg Ernst Stahl (22 October 1659 – 24 May 1734 [NS}) was a German chemist, physician and philosopher. He was a supporter of vitalism, and until the late 18th century his works on phlogiston were accepted as an explanation for chemical processes
Stahl used the works of Johann Joachim Becher to help him come up with explanations of chemical phenomena. The main theory that Stahl got from J. J. Becher was the theory of phlogiston. This theory did not have any experimental basis before Stahl. He was able to make the theory applicable to chemistry.[4] Becher's theories attempted in explaining chemistry as comprehensively as seemingly possible through classifying different earths according to specific reactions. Terra pinguis was a substance that escaped during combustion reactions, according to Becher.[10] Stahl, influenced by Becher's work, developed his theory of phlogiston.People who dismiss Phlogiston theory as early ignorance should read The Renaissance Mathematicus blog, The Phlogiston Theory – Wonderfully wrong but fantastically fruitful.

1843  Sylvestre François Lacroix (April 28, 1765, Paris – May 24, 1843) was the writer of important textbooks in mathematics and through these he made a major contribution to the teaching of mathematics throughout France and also in other countries. He published a two volume text Traité de calcul differéntiel et du calcul intégral (1797-1798) which is perhaps his most famous work. In the first of these volumes Lacroix introduces for the first time the expression "analyic geometry" writing:-
There exists a manner of viewing geometry that could be called géométrie analytique, and which would consist in deducing the properties of extension from the least possible number of principles, and by truly analytic methods.
He expanded his masterpiece to three volumes for the second edition published between 1810 and 1819.
 Lacroix's texts had an influence beyond France,... and it was through English translations of Traité élémentaire de calcul differéntiel et du calcul intégral by Babbage, Peacock and Herschel that the 'new continental mathematics' entered universities in Britain. It is interesting that Lacroix held the view that algebra and geometry:-
... should be treated separately, as far apart as they can be, and that the results in each should serve for mutual clarification, corresponding, so to speak, to the text of a book and its translation.
His texts appeared in many editions for over 50 years .  *SAU

1896 Luigi Menabrea (4 Sept 1809 in Chambéry, Savoy, France - 24 May 1896 in St Cassin (near Chambéry), France) was a French-born soldier and engineer who made contributions to elasticity theory and became prime-minister of Italy. *SAU

1904 Cecil John Alvin Evelyn (25 August 1904 in London, England, 24 May 1976 in Deptford, Kent, England) He graduated with a B.A. in 1927. At Oxford he had become friendly with Hubert Linfoot who was one year older than Evelyn. Linfoot graduated in 1926 but had remained at Oxford undertaking research advised by G H Hardy. Both Evelyn and Linfoot were interested in number theory at this time and they worked together.
Between 1929 and 1933, Evelyn and Linfoot produced six joint papers, all with the title On a problem in the additive theory of numbers.
A book was to be Evelyn's final mathematical publication. He published the book (with G B Money-Coutts and J A Tyrrell) The seven circles theorem and other new theorems (1974) which was translated into French and published as (with G B Money-Coutts and J A Tyrrell) Le théorème des sept cercles (1975). R D Nelson, Ampleforth College, York, writes :-
This elegant book will please all geometers, amateur and professional, and deserves a place in every library. Using a variety of essentially elementary methods, the authors present and prove a number of new or little known theorems in plane geometry. To emphasise the aesthetic appeal of these results and to assist the argument in places, over forty of its pages carry diagrams of high quality. The book has three independent sections but the style of writing is uniform. The authors invite and sometimes require the co-operation of the reader as he works through the book and, in this way, they prepare him for the intricacies of the final and most difficult section. The first part re-introduces an algebra of vectors, due to Silberstein, in which the laws of addition and equivalence are such that few of the usual properties are obvious. For example, associativity of addition requires two applications of Desargues' theorem for its proof. No use is made of this algebra. The second section opens with a delightful new theorem concerning seven Pascal lines derived from a heptagon inscribed in a conic. This is followed by a number of extensions and generalisations of the theorems of Pascal and Brianchon. ... Finally there are four new theorems about closed chains of six circles ... In the first theorem each circle touches a seventh, in the second the circles alternately touch a pair of parallel lines, in the third each circle touches two of the sides of a triangle and in the fourth each circle touches two out of three fixed circles making a configuration of nine circles in all. The first theorem, beautifully proved by inversion, gives the book its title.

The remarkable thing about this book is that the theorem of the title is an elementary geometry theorem which appears to have been first discovered by the authors of this book. The theorem concerns six circles, all inside and touching a seventh circle. These six circles all touch each other. Join each of the six points on the outer circle where the six inner circles touch it, to the point of contact directly opposite it. The theorem states that these three lines are concurrent. *SAU

*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell

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