Thursday, 21 January 2016

On This Day in Math - January 21


The whole of the developments and operations of analysis are now capable of being executed by machinery. ... As soon as an Analytical Engine exists, it will necessarily guide the future course of science.
C. Babbage

The 21st day of the year; To tile a square out of integer sided squares requires a minimum of 21 squares. (technically, this is true for what are called "simple" squared squares, one where no subset of the squares forms a rectangle or square. See the solution here) (btw: There are no cubed cubes!)
There are 21 possible ways to draw 5 circles that touch all the points on a 5x5 lattice.  *

21 repeated twenty-one times, following 1, forms a smoothly undulating palindromic prime
121212121212121212121212121212121212121 is prime
Blackjack primes are separated by exactly 21 consecutive composite numbers. Note that the pair {1129, 1151} is the smallest example.(Can you find more?) *Prime Curios


1472, the great daylight comet of 1472 passed within 10.5 million km of earth.*TIS (Johannes Müller von Königsberg (Regiomontanus) is said to have observed this comet)

1609 Modern astronomy dates all astronomical events using the Julian Day Count a system of dating that was first conceived by a Renaissance historian and Bible chronologist, Joseph Justus Scalier, who died on this day. The Julian Day Number (JDN) is the integer assigned to a whole solar day in the Julian day count starting from noon Greenwich Mean Time, with Julian day number 0 assigned to the day starting at noon on January 1, 4713 BC. At noon on the date of his death, the Julian Day 2308756 would have began. *Wik For a few details about his life see this post at the Renaissance Mathematicus.

1665 Samuel Pepys, having acquired a copy of Hooke’s Micrographia the day before, stays up to read it, “Before I went to bed I sat up till two o'clock in my chamber reading of Mr. Hooke's Microscopicall Observations, the most ingenious book that ever I read in my life.” *Pepy’s Diary

1807, the London Institution received a royal charter signed by King George III, to "promote the diffusion of Science, Literature, and the Arts, by means of Lectures and Experiments, and by easy access to an extensive collection of books, both ancient and modern, in all languages." The full name in the charter was the "London Institution for the Advancement of Literature and The Diffusion of Useful Knowledge." The first president was Sir Francis Baring. Its incorporation came after the Royal Society (1663) and Royal Institution (1800). The institution had an extensive lecture program. Instruction in practical chemistry was given in its laboratory, and significant chemistry research was done there through the 19th century. *TIS

1840, Charles Wheatstone and William F. Cooke were granted the earliest English alphabetic telegraph patent. Wheatstone made contributions to a broad range of fields in the mid 19th century. The ABC telegraph was popular in England and Europe because it did not require a trained telegraphist to read or send the messages. The operator simply rotates a wheel to the desired letter. During rotation the instrument sends out the proper number of electric pulses to an electromagnetically controlled pointer on a remote synchronized slave receiver with a similarly lettered wheel which moves to the sender's letter. Electric telegraphs of the 1840-50's are of special historic importance as the earliest practical application of serial binary coded digital communication. *TIS

1888 Babbage's Analytical Engine Passes the First Test
The Analytical Engine of Charles Babbage was never completed in his lifetime, but his son Henry Provost Babbage built the mill portion of the machine from his father's drawings, and on January 21, 1888 computed multiples of pi to prove the adequacy of the design. Perhaps this represents the first successful test of a portion of a modern computer. Recently a portion of his earlier machine, the Difference Engine, was sold at auction by Christies of London to the Powerhouse Museum in Sydney, Australia.*CHM

1954, the first atomic submarine, the U.S.S. Nautilus, was launched at Groton, Connecticut. Nautilus' nuclear propulsion system was a landmark in the history of naval engineering and submersible craft. All vessels previously known as "submarines" were in fact only submersible craft. Because of the nuclear power plant, the Nautilus could stay submerged for months at a time, unlike diesel-fueled subs, whose engines required vast amounts of oxygen. Nautilus demonstrated her capabilities in 1958 when she sailed beneath the Arctic icepack to the North Pole. Scores of nuclear submarines followed Nautilus, replacing the United States' diesel boat fleet. After patrolling the seas until 1980, the Nautilus is back home at Groton. *TIS

1979 Pluto moves closer to the sun than Neptune. *VFR Pluto is usually farther from the Sun. However, its orbit "crosses" inside of Neptune's orbit for 20 years out of every 248 years. Pluto last crossed inside Neptune's orbit on February 7, 1979, and temporarily became the 8th planet from the Sun. Pluto crossed back over Neptune's orbit again on February 11, 1999 to resume its place as the 9th planet from the Sun for the next 228 years (well, now it is now one of five known "dwarf planets").

1793 Théodore Olivier (21 Jan 1793 in France - 5 Aug 1853 in France) From the 1840's Olivier wrote textbooks. His greatest fame, however, is as a result of the mathematical models which he created to assist in his teaching of geometry. Some of the models were of ruled surfaces, with moving parts to illustrate to students how the ruled surfaces were generated. Others were designed to illustrate the curves of intersection of certain surfaces. In fact Olivier earned quite a good income from selling these models, particularly in the United States.
The United States Military Academy at West Point had 23 mathematical models made for them by Olivier to use as teaching aids:=
These models are built on wooden boxes as bases, have metal supports, and consist of strings suspended from movable arms and arranged to form a variety of geometrical figures. The strings are held in place by lead weights that are concealed by the bases. The models illustrate such things as the intersection of two half cones, the intersection of a plane, hyperbolic paraboloid and a hyperboloid of one sheet, and the intersection of two half cylinders.
Other institutions in the United States such as the Columbia School of Mines also purchased models from Olivier while Princeton had copies of Olivier's models made for them. In 1849 Olivier presented a full set of the range of models he had created to the Conservatoire National des Arts et Métiers. The models had been manufactured by the firm of Pixii, Père et Fils, and later by the firm of Fabre de Lagrange which took over their manufacture. In 1857, four years after Olivier died, Harvard University purchased 24 of Olivier's models from Fabre de Lagrange and after the university received the order Benjamin Peirce gave a series of lectures on the mathematics which they illustrated. These models are still in Harvard's collection of scientific instruments.
Even after giving a complete set of his models to the Conservatoire National des Arts et Métiers, forty models were still in Olivier's possession at the time of his death. These were sold in 1869 to William Gillispie from Union College in Schenectady, east-central New York, United States. Gillispie exhibited the models at Union College which was appropriate since, twenty years earlier, Union College had became one of the first liberal arts colleges in the United States to give engineering courses. When Gillispie died Olivier's models were sold to the college. *SAU

1846 Pieter Hendrik Schoute (January 21, 1846, Wormerveer–April 18, 1923, Groningen) was a Dutch mathematician known for his work on regular polytopes and Euclidean geometry. *Wik Schoute was a typical geometer. In his early work he investigated quadrics, algebraic curves, complexes, and congruences in the spirit of nineteenth-century projective, metrical, and enumerative geometry. Schläfli's work of the 1850's was brought to the Netherlands by Schoute who, in three papers beginning in 1893 and in his elegant two-volume textbook on many-dimensional geometry 'Mehrdimensionale Geometrie' (2 volumes 1902, 1905), studied the sections and projections of regular polytopes and compound polyhedra. ... Alicia Boole Stott (1870-1940), George Boole's third daughter (of five), ... studied sections of four- and higher-dimensional polytopes after her husband showed her Schoute's 1893 paper, and Schoute later (in his last papers) gave an analytic treatment of her constructions. *SAU

1860 David Eugene Smith, Ph.D., LL.D. (January 21, 1860 in Cortland, New York – July 29, 1944 in New York) was an American mathematician, educator, and editor. David Eugene Smith attended Syracuse University, graduating in 1881 (Ph. D., 1887; LL.D., 1905). He studied to be a lawyer concentrating in arts and humanities, but accepted an instructorship in mathematics at the Cortland Normal School in 1884. He also knew Latin, Greek, and Hebrew. He became a professor at the Michigan State Normal College in 1891, the principal at the State Normal School in Brockport, New York (1898), and a professor of mathematics at Teachers College, Columbia University (1901).
Smith became president of the Mathematical Association of America in 1920.[3] He also wrote a large number of publications of various types. He was editor of the Bulletin of the American Mathematical Society; contributed to other mathematical journals; published a series of textbooks; translated Klein's Famous Problems of Geometry, Fink's History of Mathematics, and the Treviso Arithmetic. He edited Augustus De Morgan's Budget of Paradoxes (1915) and wrote many books on Mathematics and Mathematics History. *Wik

1874 René-Louis Baire (21 Jan 1874; 5 Jul 1932) French mathematician whose study of irrational numbers and whose concept to divide the notion of continuity into upper and lower semi-continuity greatly influenced the French School of Mathematics. His doctoral thesis led to the solution of the problem of the characteristic property of limited functions of continuous functions and helped establish the theory of functions of real variables.*TIS

1897 Alexander Weinstein (21 Jan 1897 in Saratov, Russia - 6 Nov 1979 in Washington DC, USA) is famed for solving a variety of boundary value problems which have been used in a wide range of applications. Weinstein's method was developed to give accurate bounds for eigenvalues of plates and membranes. In examining singular partial differential equations he introduced a new branch of potential theory and applied the results to many different situations including flow about a wedge, flow around lenses and flow around spindles. *SAU

1908 Bengt Strömgren (21 Jan 1908; 4 Jul 1987) Bengt (Georg Daniel) Strömgren was a Danish astrophysicist who pioneered the present-day knowledge of the gas clouds in space. Researching for his theory of the ionized gas clouds around hot stars, he found relations between the gas density, the luminosity of the star, and the size of the "Strömgren sphere" of ionized hydrogen around it. He surveyed such H II regions in the Galaxy, and he also did important work on stellar atmospheres and ionization in stars. *TIS

1915 Yuri Vladimirovich Linnik (January 8, 1915 – June 30, 1972) was a Soviet mathematician active in number theory, probability theory and mathematical statistics.*Wik

1923 Daniel E. Gorenstein (January 1, 1923 – August 26, 1992) was an American mathematician. He earned his undergraduate and graduate degrees at Harvard University, where he earned his Ph.D. in 1950 under Oscar Zariski, introducing in his dissertation a duality principle for plane curves that motivated Grothendieck's introduction of Gorenstein rings. He was a major influence on the classification of finite simple groups.
After teaching mathematics to military personnel at Harvard before earning his doctorate, Gorenstein held posts at Clark University and Northeastern University before he began teaching at Rutgers University in 1969, where he remained for the rest of his life. He was the founding director of DIMACS in 1989, and remained as its director until his death.[1]
Gorenstein was awarded many honors for his work on finite simple groups. He was recognised, in addition to his own research contributions such as work on signalizer functors, as a leader in directing the classification proof, the largest collaborative piece of pure mathematics ever attempted. In 1972 he was a Guggenheim Fellow and a Fulbright Scholar; in 1978 he gained membership in the National Academy of Sciences and the American Academy of Arts and Sciences, and in 1989 won the Steele Prize for mathematical exposition. *Wik

1609 Joseph Justus Scaliger (5 Aug 1540, 21 Jan 1609) French scholar who was one of the founders of the science of chronology. Like Roger de Losinga, Bishop of Hereford, centuries before, Scaliger recognized that combining the three cycles of the 28-year solar cycle (S), the 19-year cycle of Golden Numbers (G) and the 15-year indiction cycle (I) produced one greater cycle of 7980 years (28×9×15). Scalinger applied this fact, called a Julian cycle, in his attempt to resolve a patchwork of historical eras and he used notation (S, G, I) to characterize years. The year of Christ's birth had been determined by Dionysius Exigus to be the number 9 on the solar cycle, by Golden Number 1, and by 3 of the indiction cycle, thus (9, 1, 3), which was 4713 of his chronological era. Hence, the year (1, 1, 1) was 4713 B.C. (later adopted as the initial epoch for the Julian day numbers).*TIS A formula for converting days to Julian day numbers is here.

1800 Jean-Baptiste Le Roy (15 August 1720;Paris, France - 21 January 1800, Paris) Son of the renowned clockmaker Julien Le Roy, Jean-Baptiste Le Roy was one of four brothers to achieve scientific prominence in Enlightenment France; the others were Charles Le Roy (medicine and chemistry), Julien-David Le Roy (architecture), and Pierre Le Roy(chronometry). Elected to the Académie Royale des Sciences in 1751 as adjoint géomètre, Le Roy played an active role in technical as well as administrative aspects of French science for the next half-century. He was elected pensionnaire mécanicies in 1770 and director of the Academy for 1773 and 1778, and became both a fellow of the Royal Society and a member of the American Philosophical Society in 1773.
Le Roy’s major field of enquiry was electricity, a subject on which European opinion was much divided at mid-century. The most prominent controversy engaged the proponents of the Abbé Nollet’s doctrine of two distinct streams of electric fluids (outflowing and inflowing) and the partisans of Benjamin Franklin’s concept of a single electric fluid. This debate intensified in France in 1753 with an attack on Franklin’s views by Nollet. Le Roy, later a friend and correspondent of Franklin, defended his single-fluid theory and offered considerable experimental evidence in support thereof. He played an important role in the dissemination of Franklin’s ideas, stressing particularly their practical applications, and published many memoirs on electrical machines and theory in the annual Histoires and Mémoires of the Academy and in the Journal de Physique.
A regular contributor to the Encyclopédie, Le Roy wrote articles dealing with scientific instruments. The most important of these included comprehensive treatments of “Horlogerie,” “Télescope,” and “Électrométre” (in which Le Roy claimed priority for the invention of the electrometer). He also promoted the use of lightning rods in France, urged that the Academy support technical education, and was active in hospital and prison reform. After the Revolutionary suppression of royal academies, Le Roy was appointed to the first class of the Institut National (section de mécanique) at its formation in 1795. *

1892 John Couch Adams (5 Jun 1819, 21 Jan 1892) In 1878 he published his calculation of Euler’s constant (Euler-Mascheronie constant) to 263 decimal places. (he also calculated the Bernoulli numbers up to the 62 nd) *VFR The Euler-Mascheronie constant is the limiting value of the difference between the sum of the first n values in the harmonic series and the natural log of n. (not 263 places, but the approximate value is 0.5772156649015328606065...)
He also predicted the location of the then unknown planet of Neptune, but it seems he failed to convince Airy to search for the planet. Independently, Urbanne LeVerrier predicted its locatin in Germany, and then assisted Galle in the Berlin Observatory in locating the planet on 23 September 1846. As a side note, when he was appointed to a Regius position at St. Andrews in Scotland, he was the last professor ever to have to swear and oath of “abjuration and allegience”, swearing fealty to Queen Victoria, and abjuring the Jacobite succession. The need for the oath was removed by the 1858 Universities Scotland Act. Adams made many other contributions to astronomy, notably his studies of the Leonid meteor shower (1866) where he showed that the orbit of the meteor shower was very similar to that of a comet. He was able to correctly conclude that the meteor shower was associated with the comet. *Wik & *TIS

1930 H(ugh) L(ongbourne) Callendar (18 Apr 1863, 21 Jan 1930) was an English physicist famous for work in calorimetry, thermometry and especially, the thermodynamic properties of steam. He published the first steam tables (1915). In 1886, he invented the platinum resistance thermometer using the electrical resistivity of platinum, enabling the precise measurement of temperatures. He also invented the electrical continuous-flow calorimeter, the compensated air thermometer (1891), a radio balance (1910) and a rolling-chart thermometer (1897) that enabled long-duration collection of climatic temperature data. His son, Guy S. Callendar linked climatic change with increases in carbon dioxide (CO2) resulting from mankind's burning of carbon fuels (1938), known as the Callendar effect, part of the greenhouse effect.*TIS

1931 Cesare Burali-Forti (13 August 1861 – 21 January 1931) was an Italian mathematician. He was born in Arezzo, and was an assistant of Giuseppe Peano in Turin from 1894 to 1896, during which time he discovered what came to be called the Burali-Forti paradox of Cantorian set theory.*Wik

1946 Harry Bateman FRS (29 May 1882 – 21 January 1946) was an English mathematician. He first grew to love mathematics at Manchester Grammar School, and in his final year, won a scholarship to Trinity College, Cambridge. There he distinguished himself in 1903 as Senior Wrangler (tied with P.E. Marrack) and by winning the Smith's Prize (1905). He studied in Göttingen and Paris, taught at the University of Liverpool and University of Manchester before moving to the US in 1910. First he taught at Bryn Mawr College and then Johns Hopkins University. There, working with Frank Morley in geometry, he achieved the Ph.D. In 1917 he took up his permanent position at California Institute of Technology, then still called Throop Polytechnic Institute.
Eric Temple Bell says, "Like his contemporaries and immediate predecessors among Cambridge mathematicians of the first decade of this century [1901–1910]... Bateman was thoroughly trained in both pure analysis and mathematical physics, and retained an equal interest in both throughout his scientific career."*Wik

1974 Arnaud Denjoy (5 January 1884 – 21 January 1974 in Paris) a French mathematician born in Auch, Gers. His contributions include work in harmonic analysis and differential equations. His integral was the first to be able to integrate all derivatives. Among his students is Gustave Choquet.*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
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