Saturday, 24 February 2018

On This Day in Math - February 24

3D Lichtenberg Figures *Wik

Information is the resolution of uncertainty.
~Claude Shannon

The 55th day of the year; 55 is the largest triangular number that appears in the Fibonacci Sequence. (Is there a largest square number?)
55 is also a Kaprekar Number: 55² = 3025 and 30 + 25 = 55 (Thanks to Jim Wilder)

And speaking of 52, Everyone knows that 32 + 42 = 52, but did you know that 332 + 442 = 552 But after that, there could be no more.... right? I mean, that's just too improbable, so why is he stil l going on like this? You don't think......Nah.

55 is the only year day that is both a non-trivial base ten palindrome and also a palindrome in base four.


1582 Pope Gregory XIII promulgated his calendar reform in the papal bull Inter gravissimus (Of the gravest concern). It took effect (in Italy and some other Catholic countries) October 5, 1582 (Julian Thursday, 4 October 1582, being followed by Gregorian Friday, 15 October 1582)

1616 Inquisition qualifiers deny teaching of Heliocentric view . On February 19, 1616, the Inquisition had asked a commission of theologians, known as qualifiers, about the propositions of the heliocentric view of the universe. On February 24 the Qualifiers delivered their unanimous report: the idea that the Sun is stationary is "foolish and absurd in philosophy, and formally heretical since it explicitly contradicts in many places the sense of Holy Scripture..."; while the Earth's movement "receives the same judgement in philosophy and ... in regard to theological truth it is at least erroneous in faith."At a meeting of the cardinals of the Inquisition on the following day, Pope Paul V instructed Bellarmine to deliver this result to Galileo, and to order him to abandon the Copernican opinions; should Galileo resist the decree, stronger action would be taken. On February 26, Galileo was called to Bellarmine's residence, and accepted the orders. *Wik

1755 William Hogarth’s satirical print, “An Election Entertainment,” was published. It contains a Tory sign bearing the inscription “Give us our eleven days.” This refers to the fact that eleven dates were removed from the calendar when England converted to the Gregorian calendar on September 14, 1752. *VFR Image here

1772 Lagrange, in a letter to d’Alembert, called higher mathematics “decadent.” *Grabiner, Origins of Cauchy’s Rigorous Calculus, pp. 25, 185

1818 The word Tangram emerged in American vocabulary about this time. According to various dictionaries, the word may be derived from a Chinese word tang, or it may be derived from the obsolete English word trangam, meaning a trinket or a gimcrack. Merriam-Webster says the word is of unknown origin.

Trangam is found in a 1658 dictionary.

On June 1, 1809, the American Citizen reported, “Vast numbers of those ‘tangrams and gimcracks’ are piled up in the office, of every shape and size, making it a great toy shop. [Joel S. Berson]

A classified advertisement in the Franklin Gazette of Feb. 24, 1818, offers “Chinese Tangrams,” which were probably puzzles [Bill Mullins].

According to Wikipedia and another web page, the word tangram was coined by Dr. Thomas Hill in 1848 for his book Geometrical Puzzles for the Young. [Perhaps this is the first use of the word with its modern meaning.] The web page says the device{???}was invented between 1796 and 1802 in China by Yang-cho-chu-shih, who published the book Ch'i ch'iao t'u (Pictures using seven clever pieces). * Jeff Miller
1842 Sylvester resigned his position at the University of Virginia (after only four months), after a dispute with a student who was reading a newspaper in class. Persistent rumors that he killed the student are unfounded. *VFR

1880 The first commercial order of an Edison Lighting system was installed on the newly launched Steamship Columbia. The dynamo and lights were installed by Edison Engineers and first lighting was on May 2, 1880. The event was featured in the May issue of Scientific American. John Roach and Sons had built the ship in their Chester, Pennsylvania ship works and launched it on Feb 24, 1880. *The History of the American Bureau of Shipping.
1881 Cambridge University in England allowed women to officially take university examinations and to have their names posted along with those of the male students. Previously some women were given special permission to take the Tripos Exam. One of these was Charlotte Agnes Scott, who did quite well on the exam. At the award ceremony “The man read out the names and when he came to ‘eighth,’ before he could say the name, all the undergraduates called out ‘Scott of Girton,’ and cheered tremendously, shouting her name over and over again with tremendous cheers and wavings of hats.” [Women of Mathematics. A Biobibliographic Sourcebook (1987), edited by Louise S. Grinstein and Paul J. Campbell, 194-195] *VFR

1896  Henri Becquerel read a report to the French Academy of Sciences of his investigation of the phosphorescent rays of some “double sulfate of uranium and potassium” crystals. He reported that he placed the crystals on the outside of a photographic plate wrapped in sheets of very thick black paper and exposed the whole to the sun for several hours. When he developed the photographic plate, he saw a black silhouette of the substance exposed on the negative. When he placed a coin or metal screen between the uranium crystals and the wrapped plate, he saw images of those objects on the negative. He did not yet know yet that the sun is not necessary to initiate the rays, nor did he yet realize that he had accidentally discovered radioactivity. He would learn more from a further accidental discovery on 26 Feb 1896.*TIS

1920 As part of the National Education Association’s annual meeting, 127 mathematics teachers from 20 states met in Cleveland, Ohio, for the “purpose of organizing a National Council of Mathematics Teachers.” *VFR

1931, the Fields Medal was established to recognize outstanding contributions to mathematics. It was conceived since there was no Nobel Prize for mathematicians. Although John Charles Fields probably thought of the medal at some earlier time, the first recorded mention of it was made on 24 Feb 1931 in minutes of a committee meeting. He was chairman of the Committee of the International Congress which had been set up by the University of Toronto to organize the 1924 Congress in Toronto. After the event, Fields proposed that income of $2,500 remaining from that convention would be designated for two medals to be awarded at future International Mathematical Congresses. In 1936, the first awards were made in Oslo.*TIS

In 1968, Nature carried the announcement of the discovery of a pulsar (a pulsating radio source). The first pulsar was discovered by a graduate student, Jocelyn Bell, on 28 Nov 1967, then working under the direction of Prof. Anthony Hewish. The star emitted radio pulses with clock-like precision. It was observed at the Mullard Radio Astronomy Observatory, Cambridge University, England. A special radio telescope, was used with 2,048 antennae arrayed across 4.4 acres. Pulsars prompted studies in quantum-degenerate fluids, relativistic gravity and interstellar magnetic fields. *TIS [Before the nature of the signal was determined, the researchers, Bell and her Ph.D supervisor Antony Hewish, somewhat seriously considered the possibility of extraterrestrial life, "We did not really believe that we had picked up signals from another civilization, but obviously the idea had crossed our minds and we had no proof that it was an entirely natural radio emission. It is an interesting problem - if one thinks one may have detected life elsewhere in the universe how does one announce the results responsibly? Who does one tell first?" The observation was given the half-humorous designation Little green men 1, until researchers Thomas Gold and Fred Hoyle correctly identified these signals as rapidly rotating neutron stars with strong magnetic fields.] Read the details in her own words here.

2009 Comet Lulin, a non-periodic comet, makes its closest approach to Earth, peaking in brightness between magnitude +4 and magnitude +6. *Wik


1663 Thomas Newcomen (24 Feb 1663 (Newcomen was baptised OTD unfortunately there is no mention of his birth date in the baptism record); 5 Aug 1729 at age 66) English engineer and inventor of the the world's first successful atmospheric steam engine. His invention of c.1711 came into use by 1725 to pump water out of coal mines or raise water to power water-wheels. On each stroke, steam filled a cylinder closed by a piston, then a spray of water chilled and condensed the steam in the cylinder creating a vacuum, then atmospheric pressure pushed the piston down. A crossbeam transferred the motion of the piston to operating the pump. This was wasteful of fuel needed to reheat the cylinder for the next stroke. Despite being slow and inefficient, Newcomen's engine was relied on for the first 60 years of the new steam age it began, perhaps the single most important invention of the Industrial Revolution. *TIS

1709 Jacques de Vaucanson (24 Feb 1709; 21 Nov 1782 at age 73) French inventor of automata - robot devices of later significance for modern industry. In 1737-38, he produced a transverse flute player, a pipe and tabor player, and a mechanical duck, which was especially noteworthy, not only imitating the motions of a live duck, but also the motions of drinking, eating, and "digesting." He made improvements in the mechanization of silk weaving, but his most important invention was ignored for several decades - that of automating the loom by means of perforated cards that guided hooks connected to the warp yarns. (Later reconstructed and improved by J.-M. Jacquard, it became one of the most important inventions of the Industrial Revolution.) He also invented many machine tools of permanent importance. *TIS

1804 Heinrich Friedrich Emil Lenz (24 Feb 1804, 10 Feb 1865 at age 61) was the Russian physicist who framed Lenz's Law to describe the direction of flow of electric current generated by a wire moving through a magnetic field. Lenz worked on electrical conduction and electromagnetism. In 1833 he reported investigations into the way electrical resistance changes with temperature, showing that an increase in temperature increases the resistance (for a metal). He is best-known for Lenz's law, which he discovered in 1834 while investigating magnetic induction. It states that the current induced by a change flows so as to oppose the effect producing the change. Lenz's law is a consequence of the, more general, law of conservation of energy. *TIS

1868 James Ireland Craig (24 Feb 1868 in Buckhaven, Fife, Scotland - 26 Jan 1952 in Cairo, Egypt) graduated from Edinburgh and Cambridge. He taught at Eton and Winchester and then went to work on the Nile Survey for the Egyptian government. He made some significant inventions in map projections. He was killed when a mob attacked the Turf Club in Cairo.*SAU

1878 Felix Bernstein born. In 1895 or 1896, while still a Gymnasium student, he volunteered to read the proofs of a paper of Georg Cantor on set theory. In the process of doing this the idea came to him one morning while shaving of how to prove what is now called the Cantor/Bernstein theorem: If each of two sets is equivalent to a subset of the other, then they are equivalent. *VFR He also worked on transfinite ordinal numbers.*SAU

1909 Max Black​ (24 February 1909, 27 August 1988) was a British-American philosopher and a leading influence in analytic philosophy in the first half of the twentieth century. He made contributions to the philosophy of language, the philosophy of mathematics and science, and the philosophy of art, also publishing studies of the work of philosophers such as Frege. His translation (with Peter Geach) of Frege's published philosophical writing is a classic text. *Wik

1920 K C Sreedharan Pillai (1920–1985) was an Indian statistician who was known for his works on multivariate analysis and probability distributions. Pillai was honoured by being elected a Fellow of the American Statistical Association and a Fellow of the Institute of Mathematical Statistics. He was an elected member of the International Statistical Institute. *Wik Perhaps his best known contribution is the widely used multivariate analysis of variance test which bears his name.*SAU

1946 Gregori Aleksandrovich Margulis (24 Feb 1946 - )Russian mathematician who was awarded the Fields Medal in 1978 for his contributions to the theory of Lie groups, though he was not allowed by the Soviet government to travel to Finland to receive the award. In 1990 Margulis immigrated to the United States. Margulis' work was largely involved in solving a number of problems in the theory of Lie groups. In particular, Margulis proved a long-standing conjecture by Atle Selberg concerning discrete subgroups of semisimple Lie groups. The techniques he used in his work were drawn from combinatorics, ergodic theory, dynamical systems, and differential geometry.*TIS The napkin folding problem is a problem in geometry and the mathematics of paper folding that explores whether folding a square or a rectangular napkin can increase its perimeter. The problem is known under several names, including the Margulis napkin problem, suggesting it is due to Grigory Margulis *Wik

1955 Steven Paul Jobs (24 Feb 1955; 5 Oct 2011 at age 56) U S inventor and entrepreneur who, in 1976, co-founded Apple Inc. with Steve Wozniak to manufacture personal computers. During his life he was issued or applied for 338 patents as either inventor or co-inventor of not only applications in computers, portable electronic devices and user interfaces, but also a number of others in a range of technologies. From the outset, he was active in all aspects of the Apple company, designing, developing and marketing. After the initial success of the Apple II series of personal computers, the Macintosh superseded it with a mouse-driven graphical interface. Jobs kept Apple at the forefront of innovative, functional, user-friendly designs with new products including the iPad tablet and iPhone. Jobs was also involved with computer graphics movies through his purchase (1986) of the company that became Pixar *TIS

1967 Brian Paul Schmidt AC, FRS (February 24, 1967, ) is a Distinguished Professor, Australian Research Council Laureate Fellow and astrophysicist at The Australian National University Mount Stromlo Observatory and Research School of Astronomy and Astrophysics and is known for his research in using supernovae as cosmological probes. He currently holds an Australia Research Council Federation Fellowship and was elected to the Royal Society in 2012.[2] Schmidt shared both the 2006 Shaw Prize in Astronomy and the 2011 Nobel Prize in Physics with Saul Perlmutter and Adam Riess for providing evidence that the expansion of the universe is accelerating. *Wik


1728 Charles René Reyneau (11 June 1656 in Brissac, Maine-et-Loire, France - 24 Feb 1728 in Paris, France) was a French mathematician who published an influential textbook on the newly invented calculus.*SAU (He) "undertook to reduce into one body, for the use of his scholars, the principal theories scattered here and there in Newton, Descartes, Leibnitz, Bernoulli, the Leipsic Acts, the Memoirs of the Paris Academy, and in other works; treasures which by being so widely dispersed, proved much less useful than they otherwise might have been. The fruit of this undertaking, was his “Analyse Demontree,” or Analysis Demonstrated, which he published in 1708. He gave it the name of “Analysis Demonstrated,” because he demonstrates in it several methods which had not been handled by the authors of them, with sufficient perspicuity and exactness. The book was so well approved, that it soon became a maxim, at least in France, that to follow him was the best, if not the only way, to make any extraordinary progress in the mathematics and he was considered as the first master, as the Euclid of the sublime geometry." (From the 1812 Chalmer's Biography, vol. 26, p. 151)

1799 Georg Christoph Lichtenberg (1 Jul 1742, 24 Feb 1799 at age 56). German physicist and satirical writer, best known for his aphorisms and his ridicule of metaphysical and romantic excesses. At Göttingen University, Lichtenberg did research in a wide variety of fields, including geophysics, volcanology, meteorology, chemistry, astronomy, and mathematics. His most important were his investigations into physics. Notably, he constructed a huge electrophorus and, in the course of experimentations, discovered in 1777 the basic principle of modern xerographic copying; the images that he reproduced are still called "Lichtenberg figures." These are radial patterns formed when sharp, pointed conducting bodies at high voltage get near enough to insulators to discharge electrically, or seen on persons struck by lightning. *TIS

1810 Henry Cavendish (10 Oct 1731; 24 Feb 1810) English chemist and physicist who conducted experiments with diverse interests in his private laboratory. Most notably, he determined the mass and density of the Earth. He investigated the properties of hydrogen and carbon dioxide, including comparing their density to that of air. Cavendish also showed that water was a compound and measured the specific heat of various substances. His manuscripts (published 1879) revealed discoveries he made in electrostatics before Coulomb, Ohm and Faraday - including deducing the inverse square law of electrostatic attraction and repulsion. He also found specific inductive capacity. His family name is attached to the Cavendish Laboratory (founded 1871, funded by a later family member) at Cambridge University. *TIS Cavendish was supposedly so shy that for his only portrait the artist painted his coat from a hook in the hall, then painted Cavendish body from memory. *"Shock and Awe", BBC broadcast on the history of electricity

1812 Étienne-Louis Malus (23 Jun 1775, 24 Feb 1812 at age 36) He served in Napoleon's corps of engineers, fought in Egypt, and contracted the plague during Napoleon's aborted campaign in Palestine. Posted to Europe after 1801, he began research in optics. In 1808, he discovered that light rays may be polarized by reflection, while looking through a crystal of Iceland spar at the windows of a building reflecting the rays of the Sun. He noticed that on rotating the crystal the light was extinguished in certain positions. Applying corpuscular theory, he argued that light particles have sides or poles and coined the word "polarization." *TIS He studied geometric systems called ray systems, closely connected to Julius Plücker's line geometry. He conducted experiments to verify Christiaan Huygens' theories of light and rewrote the theory in analytical form. His discovery of the polarization of light by reflection was published in 1809 and his theory of double refraction of light in crystals, in 1810.
Malus attempted to identify the relationship between the polarising angle of reflection that he had discovered, and the refractive index of the reflecting material. While he deduced the correct relation for water, he was unable to do so for glasses due to the low quality of materials available to him (most glasses at that time showing a variation in refractive index between the surface and the interior of the glass). It was not until 1815 that Sir David Brewster was able to experiment with higher quality glasses and correctly formulate what is known as Brewster's law.
Malus is probably best remembered for Malus' law, giving the resultant intensity, when a polariser is placed in the path of an incident beam. His name is one of the 72 names inscribed on the Eiffel tower.*Wik

1844 Antoine-André-Louis Reynaud (12 Sept 1771, 24 Feb 1844) Reynaud published a number of extremely influential textbooks. He published a mathematics manual for surveyors as well as Traité d'algèbre, Trigonométrie rectiligne et sphérique, Théorèmes et problèmes de géométrie and Traité de statistique. His best known texts, however, were his editions of Bézout's Traité d'arithmétique which appeared in at least 26 versions containing much original work by Reynaud.
It appears that Reynaud became interested in algorithms when he was working with de Prony. At this time de Prony was very much involved in trying to get his logarithmic and trigonometric tables published and it seems to have made Reynaud think about analysing algorithms. Certainly Reynaud, although his results in this area were rather trivial, must get the credit for being one of the first people to give an explicit analysis of an algorithm, an area of mathematics which is of major importance today. *SAU

1856 Nikolai Ivanovich Lobachevsky (December 1, 1792 – February 24, 1856 (N.S.); November 20, 1792 – February 12, 1856 (O.S.)) was a Russian mathematician and geometer, renowned primarily for his pioneering works on hyperbolic geometry, otherwise known as Lobachevskian geometry. William Kingdon Clifford called Lobachevsky the "Copernicus of Geometry" due to the revolutionary character of his work. *Wik  A yahoo recording of the classic Tom Lehrer song about Lobachevsky is here with lyrics. Lehrer has stated there is no accusation of Lobachevsky plagiarizing anything, and his name was chosen for the rhythmic characteristics.

1871 Julius Ludwig Weisbach (10 August 1806 in Mittelschmiedeberg (now Mildenau Municipality), Erzgebirge, 24 February 1871, Freiberg) was a German mathematician and engineer. He studied with Carl Friedrich Gauss in Göttingen and with Friedrich Mohs in Vienna. He wrote an influential book for mechanical engineering students, called Lehrbuch der Ingenieur- und Maschinenmechanik, which has been expanded and reprinted on numerous occasions between 1845 and 1863. *Wik He wrote fourteen books and 59 papers he wrote on mechanics, hydraulics, surveying, and mathematics. It is in hydraulics that his work was most influential, with his books on the topic continuing to be of importance well into the 20th century. *SAU

1923 Edward Williams Morley (29 Jan 1838; 24 Feb 1923) American chemist who is best known for his collaboration with the physicist A.A. Michelson in an attempt to measure the relative motion of the Earth through a hypothetical ether (1887). He also studied the variations of atmospheric oxygen content. He specialized in accurate quantitative measurements, such as those of the vapor tension of mercury, thermal expansion of gases, or the combining weights of hydrogen and oxygen. Morley assisted Michelson in the latter's persuit of measurements of the greatest possible accuracy to detect a difference in the speed of light through an omnipresent ether. Yet the ether could not be detected and the physicists had seriously to consider that the ether did not exist, even questioning much orthodox physical theory. *TIS

1933 Eugenio Bertini (8 Nov 1846 in Forli, Italy - 24 Feb 1933 in Pisa, Italy) was an Italian mathematician who worked in projective and algebraic geometry. His work in algebraic geometry extended Cremona's work. He studied geometrical properties invariant under Cremona transformations and used the theory to resolve the singularities of a curve. A paper by Kleiman studies what the authors calls the two fundamental theorems of Bertini. These two fundamental theorems are among the ones most used in algebraic geometry. The first theorem is a statement about singular points of members of a pencil of hypersurfaces in an algebraic variety. The second theorem is about the irreducibility of a general member of a linear system of hypersurfaces. *SAU

Memorial in childhood
home of Gaylord, Mi
2001 Claude Shannon (30 April 1916 in Petoskey, Michigan, USA - 24 Feb 2001 in Medford, Massachusetts, USA) founded the subject of information theory and he proposed a linear schematic model of a communications system. His Master's thesis was on A Symbolic Analysis of Relay and Switching Circuits on the use of Boole's algebra to analyse and optimise relay switching circuits. *SAU While working with John von Neumann on early computer designs, (John) Tukey introduced the word "bit" as a contraction of "binary digit". The term "bit" was first used in an article by Claude Shannon in 1948. Among several statues to Shannon, one is erected in his hometown of Gaylord, Michigan. The statue is located in Shannon Park in the center of downtown Gaylord, which was Shannon's boyhood home. Shannon Park is the former site of the Shannon Building, built and owned by Claude Shannon's father.

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
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