The 216th day of the year; Since 216 = 33 + 43 + 53 = 63, it is the smallest cube that's also the sum of three cubes (Plato was among the first to notice this, and mentioned it in Book VIII of Republic). (What is the next cube that is the sum of three cubes?... and how can you be sure there will never be a day that is a cube that is the sum of two cubes?)
216 is also the sum of a twin prime pair (107 + 109).
And for those who are interested in variations on 666, the so called number of the beast, \( 6^{(6^6)} =216 \) mod 360
from which we get the divine equivalent, \( cos(216)^o= \frac{- \phi}{2} \)
Ok, one more 216 to 666 connection from Ben Vitalle. There is a right triangle with legs of 216, 630 and a hypotenuse of (wait for it...... ) 666 Benjamin Vitale @BenVitale
See More Math Facts for every Year Day here
In 1181, supernova seen in Cassiopeia. First observed between August 4 and August 6, 1181, Chinese and Japanese astronomers recorded the supernova now known as SN 1181 in eight separate texts. One of only eight supernovae in the Milky Way observable with the naked eye in recorded history, it appeared in the constellation Cassiopeia and was visible in the night sky for about 185 days.*Wik
Presumed remnant of Super Nova 1181
In 1693, champagne was invented by Dom Perignon.*(I'll drink to that.)
On this day in 1539, Girolamo Cardan wrote to NiccolĂČ Tartaglia in an attempt to understand why his calculations involving the square roots of negative numbers sometimes gave the correct answer. He said that his calculation was as subtle as it is useless.
The first person known to have solved cubic equations algebraically was del Ferro but he told nobody of his achievement. On his deathbed, however, del Ferro passed on the secret to his (rather poor) student Fior. For mathematicians of this time there was more than one type of cubic equation and Fior had only been shown by del Ferro how to solve one type, namely 'unknowns and cubes equal to numbers' or (in modern notation)
đ„
3
+
đ
đ„
=
đ
x
3
+ax=b. As negative numbers were not used this led to a number of other cases, even for equations without a square term. Fior began to boast that he was able to solve cubics and a challenge between him and Tartaglia was arranged in 1535. In fact Tartaglia had also discovered how to solve one type of cubic equation since his friend Zuanne da Coi had set two problems which had led Tartaglia to a general solution of a different type from that which Fior could solve, namely 'squares and cubes equal to numbers' or (in modern notation) x^3 +ax^2 =b. For the contest between Tartaglia and Fior, each man was to submit thirty questions for the other to solve. Fior was supremely confident that his ability to solve cubics would be enough to defeat Tartaglia but Tartaglia submitted a variety of different questions, exposing Fior as an, at best, mediocre mathematician. Fior, on the other hand, offered Tartaglia thirty opportunities to solve the 'unknowns and cubes' problem since he believed that he would be unable to solve this type, as in fact had been the case when the contest was set up. However, in the early hours of 13 February 1535, inspiration came to Tartaglia and he discovered the method to solve 'squares and cubes equal to numbers'. Tartaglia was then able to solve all thirty of Fior's problems in less than two hours. As Fior had made little headway with Tartaglia's questions, it was obvious to all who was the winner. Tartaglia did not take his prize for winning from Fior, however, the honour of winning was enough. *Wik
1597 Galileo wrote Kepler thanking him for the copy of Kepler’s Mysterium cosmographicum, which openly advocated the Copernican theory. Galileo admits he is also a Copernican. See 13 October 1597. *VFR Thanks to The Renaissance Mathematicus, for pointing out that when he received this letter, Kepler had never heard of Galileo. Galileo was completely unknown outside of Northern Italy at this point of his life. See more detail of this interesting story here.
1753 Euler, in a letter to Christian Goldbach, claimed that he had a proof of Fermat’s Last Theorem for the case n = 3. He gave no proof in that letter and none was published until 1770 when he published his Elements of Algebra in Russian.*VFR Euler's proof was wrong, but other methods that Euler developed can be used to provide a correct proof.
1810 Gauss married his second wife, Minna Waldeck, who bore him two sons and a daughter. *VFR Sons Charles and Eugene both emigrated to America and died in Missouri. Therese died in Dresden. An interesting story about Eugene and his relations with his father and history in America is told here which I believe is the work of a Kevin Brown.
1811 Thomas Jefferson writes to Nicolas G. Dufief, to thank him for a French Dictionary, and adds, " I am anxious to get a copy of La Croix’s Cours de Mathematiques, (I believe it is in 7. vols) *Natl. Archives
1922 Every telephone in North America was silent for one minute at sunset marking the time funeral services were taking place for Alexander Graham Bell. He was laid to rest in a tomb blasted in the solid rock at the peak of Beinn Bhreagh Mountain on his estate in Nova Scotia, Canada. A watch tower had been built there years earlier by the inventor. His coffin was made in the inventor's own workshop by his laboratory staff. In a memory of the famous inventor, all the switchboards and switching stations of AT&T and the Bell System in the U.S. and Canada suspended service to the 13 million telephones then installed. Bell had died two days earlier on 2 Aug 1922. *TIS
1755 Nicolas-Jacques ContĂ© (4 August 1755 – 6 December 1805) French inventor who devised a method of manufacturing pencil leads by mixing a finely powdered graphite with finely ground clay particles, baked, and used encased in wood. His innovation was prompted when imported plumbago supplies were disrupted by war. He was the first to use graphite - and that is still used as the basis for making pencil leads today. Using different ratios of clay to graphite varies the hardness of the pencil lead. He was commissioned by Napoleon as chief of the balloon corps in Egypt, where he invented ways to improvise tools and machines necessary to provide bread, cloth, munitions, surgical instruments and engineers' tools. As a youth, he had worked as a portrait painter. He lost his left eye in a chemistry laboratory accident*TIS
Conté invented the modern pencil lead at the request of Lazare Nicolas Marguerite Carnot. The French Republic was at that time under economic blockade and unable to import graphite from Great Britain, the main source of the material. Carnot asked Conté to create a pencil that did not rely on foreign imports. After several days of research, Conté had the idea of mixing powdered graphite with clay and pressing the material between two half-cylinders of wood. Thus was formed the modern pencil. Conté received a patent for the invention in 1795 and formed la Société Conté to make them. He also invented the conté crayon named after him, a hard pastel stick used by artists.*Wik
The oldest pencil
During renovation work this unusual pencil was discovered between the roof joists of a house dating back to the 17th century. Evidently the carpenter had forgotten it there. It is the oldest surviving example of a pencil.
1805 Sir William Rowan Hamilton (Many think the correct birthdate is August 3 but his gravestone has Aug 4. The confusion arises from the fact he was born very near midnight.) Irish mathematician in the fields of optics, geometrics, and classical mechanics. By age 12, Hamilton had already learned fourteen languages when he met the American, Zerah Colburn, who could perform amazing mental arithmetical feats, and they joined in competitions. It appears that losing to Colburn sparked Hamilton's interest in mathematics. At 15, he began studied the works of LaPlace and Newton so by age 17 had become the greatest living mathematician. He contributed to the development of optics, dynamics, and algebra. His invention of the calculus of quaternions enabled a three-dimensional algebra or geometry which provided a basis for the later development of quantum mechanics. *TIS
Hamilton describes his memory of the discovery of the Quaternions to his son,
"Every morning in the early part of the above-cited month, on my coming down to breakfast, your (then) little brother, William Edwin, and yourself, used to ask me, `Well, papa, can you multiply triplets?' Whereto I was always obliged to reply, with a sad shake of the head: `No, I can only add and subtract them. But on the 16th day of the same month (Oct) - which happened to be Monday, and a Council day of the Royal Irish Academy - I was walking in to attend and preside, and your mother was walking with me along the Royal Canal, to which she had perhaps driven; and although she talked with me now and then, yet an undercurrent of thought was going on in my mind which gave at last a result, whereof it is not too much to say that I felt at once the importance. An electric circuit seemed to close; and a spark flashed forth the herald (as I foresaw immediately) of many long years to come of definitely directed thought and work by myself, if spared, and, at all events, on the part of others if I should even be allowed to live long enough distinctly to communicate the discovery. Nor could I resist the impulse - unphilosophical as it may have been - to cut with a knife on a stone of Brougham Bridge, as we passed it, the fundamental formula which contains the Solution of the Problem, but, of course, the inscription has long since mouldered away. A more durable notice remains, however, on the Council Books of the Academy for that day (October 16, 1843), which records the fact that I then asked for and obtained leave to read a Paper on `Quaternions,' at the First General Meeting of the Session; which reading took place accordingly, on Monday, the 13th of November following.'' *from Hamilton By Sir Robert Stawell Ball.
Quaternion plaque on Brougham (Broom) Bridge, Dublin, which says:
Here as he walked by on the 16th of October 1843 Sir William Rowan Hamilton in a flash of genius discovered the fundamental formula for quaternion multiplication
i^2 = j^2 = k^2 = ijk = −1 & cut it on a stone of this bridge.
1834 John Venn born (4 August 1834 – 4 April 1923) in Hull, England. He is best known for the diagrams that he presented in his Symbolic Logic (1881). Leibniz was the ïŹrst to systematically use geometric diagrams to represent syllogisms, and Euler developed the ideas, but Venn gets the credit for his book popularized them. *VFR He was a fellow of Gonville and Caius and there is a stained glass window memorial there in the dining hall, which I had the pleasure of visiting with Professor Anthony Edwards.
He also gave me directions to Venn's grave site at the Trumpington Parish Extension cemetery. His grave was so covered with vines that I would have never found it except my very psychic wife, Jeannie, stops by a clump of brambles and says, "I think this is it.." Sure enough, after clearing away the vines, we managed to expose the grave site, which includes Venn, his wife, his son, and his daughter-in-law.
1837 Birthdate of E. L. W. Maximilian Curtze, (4 August 1837 in Ballenstedt- February 1903) expert on medieval mathematical texts. His work was aided by his excellent knowledge of the current mathematical literature, unusual talent for languages, and skill in deciphering hard-to-read handwriting. *VFR
1893 Francis Dominic Murnaghan (1873–1976) was an Irish mathematician, former head of the mathematics department at Johns Hopkins University. His name is attached to developments in group theory and mathematics applied to continuum mechanics (Murnaghan and Birch–Murnaghan equations of state).*SAU
1909 Saunders Mac Lane (4 August 1909 – 14 April 2005) was an American mathematician who co-founded category theory with Samuel Eilenberg.
After a thesis in mathematical logic, his early work was in field theory and valuation theory. He wrote on valuation rings and Witt vectors, and separability in infinite field extensions. He started writing on group extensions in 1942, and in 1943 began his research on what are now called Eilenberg–MacLane spaces K(G,n), having a single non-trivial homotopy group G in dimension n. This work opened the way to group cohomology in general.
After introducing, via the Eilenberg–Steenrod axioms, the abstract approach to homology theory, he and Eilenberg originated category theory in 1945. He is especially known for his work on coherence theorems. A recurring feature of category theory, abstract algebra, and of some other mathematics as well, is the use of diagrams, consisting of arrows (morphisms) linking objects, such as products and coproducts. According to McLarty (2005), this diagrammatic approach to contemporary mathematics largely stems from Mac Lane (1948). Mac Lane also coined the term Yoneda lemma for a lemma which is an essential background to many central concepts of category theory and which was discovered by Nobuo Yoneda.
Mac Lane had an exemplary devotion to writing approachable texts, starting with his very influential A Survey of Modern Algebra, coauthored in 1941 with Garrett Birkhoff. From then on, it was possible to teach elementary modern algebra to undergraduates using an English text. His Categories for the Working Mathematician remains the definitive introduction to category theory.
Mac Lane supervised the Ph.Ds of, among many others, David Eisenbud, William Howard, Irving Kaplansky, Michael Morley, Anil Nerode, Robert Solovay, and John G. Thompson.
Mac Lane and Samuel Eilenberg at a conference in July 1992
1912 Aleksandr Danilovic Aleksandrov 4 Aug 1912 in Volyn, Ryazan, Russia - 27 July 1999) "approached the differential geometry of surfaces [by extending the notion of objects studied], extending the class of regular convex surface with the class of all convex surface .... To solve concrete problems Aleksandrov had to replace the Gaussian geometry of regular surfaces with a more general theory. In the first place the intrinsic properties (ie, the properties appear as a result of measurements carried out surface) of an arbitrary convex surface has been studied, and methods to be found for verification of theorems on the connection between the real and external properties of convex surfaces. Aleksandrov constructed a theory of intrinsic geometry on the convex basis. Due to the depth of this theory, the importance of its applications and the breadth of his statement, Aleksandrov comes second only to Gauss in the history of the development of the theory of surfaces." *from Math.info
In 1921, a facsimile was transmitted by radio across the Atlantic Ocean using the Belinograph invented by Eduard Belin. A written message from the managing editor of the New York Times was scanned by the equipment and sent by radio from Annapolis, Md., within seven minutes to Belin's laboratories at La Malmaison, France. The image received demonstrated that thereafter photographs could be scanned for radio transmission in the same way. The method was already in use within Europe sending photographs by wire. The original, wrapped on a rotating cylinder was scanned by a light beam reflected onto a photcell to convert the variations in the received intensity to electrical signals forwarded by radio or telephone wires.
1950 Jacqueline Anne ( Barton) Stedall (4 August 1950; Romford, Essex, U.K.–27 September 2014; Painswick, Gloucestershire) was a well-known historian of mathematics. Although her career as a researcher, scholar and university teacher lasted less than 14 years, it was greatly influential. Her nine books, more than 20 articles, input to the online edition of the manuscripts of Thomas Harriot, journal editorships and contributions to Melvyn Bragg’s Radio 4 program In Our Time showed her exceptional breadth of scholarship.
Jackie Stedall came to Oxford in October 2000 as Clifford-Norton Student in the History of Science at Queen’s College. She held degrees of BA (later MA) in Mathematics from Cambridge University (1972), MSc in Statistics from the University of Kent (1973), and PhD in History of Mathematics from the Open University (2000). She also had a PGCE in Mathematics (Bristol Polytechnic 1991). In due course she became Senior Research Fellow in the Oxford Mathematical Institute and at Queen’s College, posts from which, knowing that she was suffering from incurable cancer, she took early retirement in December 2013.
This was her fifth career. Following her studies at Cambridge and Canterbury she had been three years a statistician, four years Overseas Programmes Administrator for War on Want, seven years a full-time parent, and eight years a schoolteacher before she became an academic. *Obituaries at The Guardian, Oxford Mathematics, and Wik
1812 Georg KlĂŒgel (August 19, 1739 – August 4, 1812) was a German mathematician who wrote a Dictionary of Mathematics.*SAU
1874 Ludwig Otto Hesse (22 April 1811 – 4 August 1874) worked on the development of the theory algebraic functions and the theory of invariants. He is remembered particularly for introducing the Hessian determinant.*SAU
1900 (Jean-Joseph-) Ătienne Lenoir (12 January 1822 - 4 August 1900) was a Belgian inventor who devised the world's first commercially successful internal-combustion engine. He moved to Paris where his work with electro-plating led him to other electrical inventions, among them a railway telegraph. Lenoir patented his first engine in 1860. Looking much like a double-acting steam engine, it fired an uncompressed charge of air and illuminating gas with an ignition system of his own design. One of these engines powered a road vehicle in 1863; another ran a boat. Because of improved designs by Nikolaus Otto and other inventors, the Lenoir engine became obsolete and only about 500 Lenoir engines were built. The Lenoir engine wasn't efficient enough, and the inventor died poor. *TIS
1906 Joseph Tilly was a Belgian soldier who published works on non-Euclidean geometry.*SAU
1920 Karl Friedrich Wilhelm Rohn (January 25, 1855 - August 4, 1920) In 1884 Rohn was promoted to extraordinary professor at Leipzig, then in 1887 he became a full professor at Technische Hochschule in Dresden where he held the chair of descriptive geometry. Felix Klein lectured during his visit to the United States in Evanston between 28 August and 9 September 1893. During these lectures he spoke about various models of the Kummer surface. He said that Rohn's work on this topic was the most significant. One of Rohn's models for the Kummer surface uses the generating lines on a hyperboloid of one sheet. He then took four lines from each of the two sets of generators, shaded the alternate regions, and then glued a copy of the shaded regions to the original along the boundary. In this way he produced a closed surface without boundary having sixteen real nodal points. He published this construction in 1881 and gave more details in an 1887 paper. Burau writes : In these early writings he demonstrated his ability to work out connections between geometric and algebraic- analytic relations. In the following years, Rohn further developed these capacities and became an acknowledged master in all questions concerning the algebraic geometry of the real P2 and P3, where it is possible to overlook the different figures. This concerns forms of algebraic curves and surfaces up to degree four, linear and quadratic congruences, and complexes of lines in P3. Gifted with a strong spatial intuition, Rohn possessed outstanding ability to select geometric facts from algebraic relations.
His love of geometry is also illustrated by his beautiful thread models which were especially produced to excite the curiosity of the uninitiated. Rohn constructed models of surfaces and space curves that he was studying, particularly in the early part of his career. In 1884 the Jablonowski Society proposed as prize problem asking for essays on the general surface of order 4, extending the work of SchlÀfli, Klein and Zeuthen on cubic surfaces; they awarded the prize to Rohn for his essay in 1886. He made important contributions to the theory of quartic surfaces, in particular of ruled quartics and quartics with a triple point. He also showed that the maximum number of separated ovals possible for a quartic surface is ten. He published Die FlÀchen vierter Ordnung hinsichtlich ihrer Knotenpunkte und ihrer Gestaltung: Gekrönte Preisschrift (1886). Rohn was made rector of the Technical University of Dresden during 1900-01. As rector he gave a speech on 23 April 1900 to celebrate the birthday of His Majesty the King. His speech was entitled Die Entwickelung der Raumanschauung im Unterricht and it was published by the Technical University of Dresden in 1900. In Dresden, Rohn gave the course 'Darstellende Geometrie' in the summer of 1904. It was the last session that he lectured at Dresden for in the following year he was appointed to the University of Leipzig. From 1 April 1905 until his death, Rohn held the chair of mathematics at the University of Leipzig. *SAU
1945 Gerhard Gentzen (November 24, 1909, Greifswald, Germany – August 4, 1945, Prague, Czechoslovakia) invented a 'natural deduction' which provided a logic closer to mathematical reasoning than the systems proposed by Frege, Russell and Hilbert.*SAU He had his major contributions in the foundations of mathematics, proof theory, especially on natural deduction and sequent calculus. *Wik
2009 Professor James "Jim" Wiegold (15 April 1934 – 4 August 2009) was a Welsh mathematician. He earned a PhD at the University of Manchester in 1958, studying under Bernhard Neumann, and is most notable for his contributions to group theory.*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
No comments:
Post a Comment