The Boole Window, Lincoln Cathedral.

**My work always tried to unite the true with the beautiful, but when I had to choose one or the other, I usually chose the beautiful.**

~Hermann Weyl

The 343rd day of the year, a Friedman number (named after Erich Friedman, as of 2013 an Associate Professor of Mathematics and ex-chairman of the Mathematics and Computer Science Department at Stetson University, located in DeLand, Florida *Wik), since it can be made up of arithmetical operations of its digits, (3+4)

^{3}= 343. There will be one more Friedman number this year; can you find it?

Interestingly, the speed of sound in dry air at 20 °C (68 °F) is 343 m/s.

343 is the smallest cube ending in 3. It is also the last cube of the year. As a perfect cube, it is also a perfect number of the second kind, the product of its aliquot parts is equal to the number itself. In 1879, E. Lionett defined a perfect number of the second kind as a number for which the product of the aliquot parts is equal to the number itself. So 343 is the 7th perfect number of the second kind. The only values that can be perfect numbers of the second kind are values in the form P*Q for primes P, Q, and P

^{3}.Lagrange's theorem tells us that each positive integer can be written as a sum of four squares (perhaps including zero), but many can be written as the sum of only one or two non-zero squares. The smallest examples of numbers that need at least four are 7, 15, and 23. If you take any number in this sequence, and raise it to an odd positive power, you get another number in the sequence, so now you know that 7

^{3}= 343 is also not expressible as the sum of less than four non-zero squares.

*Prime Curios

**EVENTS**

**1128**“In the third year of Lothar, emperor of the Romans, in the twenty-eighth year of King Henry of the English…on Saturday, 8 December, there appeared from the morning right up to the evening two black spheres against the sun.” This description of sunspots, and the earliest known drawing of sunspots, appears in John of Worcester’s Chronicle recorded in 1128.

On the night of 13 December 1128, astronomers in Songdo, Korea, witnessed a red vapour that “soared and filled the sky” from the northwest to the southwest. A delay of five days is the average delay between the occurrence of a large sunspot group near the center of the Sun – exactly as witnessed by John of Worcester – and the appearance of the aurora borealis in the night sky at relatively low latitudes *Joe Hanson, itsokaytobesmart.com

(It seems amazing that this is the same date as Harriott's first recorded observations of sunspots.

**1610**Thomas Harriott makes first recorded observations of sunspots using a telescope: ""Decemb. 8 mane ho. That altitude of the sonne being 7 or 8 degrees. It being a frost & a mist. I saw the sonne in this manner. Instrument 10/1 B. I saw it twise of thrise. once with the right ey & other time with the left. In the space of a minutes time. after the sonne was too cleare". Harriot left nearly 200 drawings of sunspots from the period 1610-1612. Interestingly, he does not mention the spots explicitly, even though they are clearly indicated on the drawing. Like the Fabricius father and son team but unlike Galileo and Scheiner, Harriot observed the sun directly through his telescope. His observations were consequently limited to the hour following sunrise, when, as seen from Harriot's residence in Syon, the Sun was greatly dimmed by mist and fog over the river Thames. * paulchar at ucar.edu.

**1864**the Clifton Suspension Bridge spanning the Avon Gorge and the River Avon, designed by Isambard Kingdom Brunel, was openend for the public. Although Brunel was not able to see the bridge in operation anymore during his lifetime, the Clifton Suspension bridge was the first major commission of the famous engineer of the Great Western Railroad and the then largest steamships in the world. *yovisto

**1931**“Prof. Noether’s lectures (she is a woman—a member of a noted mathematical family) are also excellent ... Prof. Noether thinks fast and talks faster. As one listens, one must also think fast—and that is always excellent training. Furthermore, thinking fast is one of the joys of mathematics.” Saunders MacLane, then a student at Gottingen, to his mother. See Emmy Noether, A Tribute to Her Life and Work, ed. by James W. Brewer and Martha K. Smith.

**1947**The Eckert-Mauchly Computer Corporation is incorporated. After a dispute with the administration at the University of Pennsylvania over ENIAC patent rights, J. Presper Eckert and John Mauchly started the company that, after several mergers, produced the Binac for Northrop Aircraft and the Univac. Grace Murray Hopper joined Eckert-Mauchly Computer Corp as a senior mathematician in 1949. In 1950, before completing the UNIVAC, the company became a division of Remington Rand, IBM’s main challenger throughout the 1970s. *CHM

**1948**Prudential Insurance signs a contract to buy a UNIVAC I. *VFR

**BIRTHS**

**1508 Gemma Frisius**(Dec 1508 in Dokkum, Friesland, The Netherlands

- 25 May 1555 in Louvain, Brabant (now Belgium)) He applied his mathematical expertise to geography, astronomy and map making. He became the leading theoretical mathematician in the Low Countries. From 1534 Gemma Frisius began to teach his student Gerardus Mercator and over the following years he cooperated with Gaspard Van der Heyden and Gerardus Mercator. They constructed a terrestrial globe in 1536, and they constructed a celestial globe in the following year.*SAU His real name was Jemme Reinerszoon, which means Jemme son of Reiner. As an author he adopted the humanist name of Gemma Frisius. Gemma is a pseudo Latinised form of Jemme and Frisius is a toponym for Friesland where he was born. *Thony Christie

**1594 Pierre Petit**(8 Dec 1594 in Montluçon, France - 20 Aug 1677 in Lagny-sur-Marne, France) was a French scientist who had a strong influence on the French government. He was one of Mersenne's collaborators. Among many collaborations, Petit worked with Etienne Pascal and his son Blaise Pascal in October 1646 in repeating Torricelli's experiment on the barometric vacuum. *SAU

**1795 Peter Andreas Hansen**(8 Dec 1795; 28 Mar 1874) Danish astronomer whose most important work was the improvement of the theories and tables of the orbits of the principal bodies in the solar system. At Altona observatory he assisted in measuring the arc of meridian (1821). He became the director (1825) of Seeberg observatory, which was removed to Gotha in a new observatory built for him (1857). He worked on theoretical geodesy, optics, and the theory of probability. The work in celestial mechanics for which he is best known are his theories of motion for comets, minor planets, moon and his lunar tables (1857) which were in use until 1923. He published his lunar theory in Fundamenta ("Foundation") in 1838, and Darlegung ("Explanation") in 1862-64.*TIS

**1865 Jacques-Salomon Hadamard**(8 Dec 1865; 17 Oct 1963) French mathematician who proved the prime-number theorem (as n approaches infinity, the limit of the ratio of (n) and n/ln n is 1, where (n) is the number of positive prime numbers not greater than n). Conjectured in the 18th century, this theorem was not proved until 1896, when Hadamard and also Charles de la Vallée Poussin, used complex analysis. Hadamard's work includes the theory of integral functions and singularities of functions represented by Taylor series. His work on the partial differential equations of mathematical physics is important. He introduced the concept of a well-posed initial value and boundary value problem. In considering boundary value problems he introduced a generalisation of Green's functions (1932).*TIS (

*students, I think, find it easier to understand this theorem in the form, as n gets very large*

**1883 Ludwig Berwald**(8 Dec 1883 in Prague, Bohemia (now Czech Republic) - 20 April 1942 in Łódź, Poland)was a Czech mathematician who made important contributions to differential geometry. He wrote 54 papers up to the time of his deportation. A portion of his work set up the basic theory of Finsler geometry and Spray geometry (i.e., differential geometry of path spaces). Many people working in Finsler geometry consider that Ludwig Berwald is the founder of Finsler geometry. Berwald and E Cartan developed a general theory of two-dimensional Finsler spaces. Berwald wrote a series of major papers On Finsler and Cartan geometries.*SAU

**1919 Julia B Robinson**(8 Dec 1919 in St Louis, Missouri, USA - 30 July 1985 in USA)worked on computability, decision problems and non-standard models of arithmetic. " What I really am is a mathematician. Rather than being remembered as the first woman this or that, I would prefer to be remembered, as a mathematician should, simply for the theorems I have proved and the problems I have solved. "

A year after Robinson's death, her husband set up the Julia B Robinson Fellowship Fund to provide fellowships for graduate students in mathematics at Berkeley. When Raphael Robinson died in January 1995 almost all his estate went into the Fellowship Fund. *SAU

**DEATHS**

**1632 Albert Girard**(1595 in St Mihiel, France - 8 Dec 1632 in Leiden, Netherlands). He introduced the abbreviations sin, tan, and sec for the trigonometric functions. *VFR

With the aid of trigonometric tables Girard solved equations of the third degree having three real roots. For those having only one root he indicated, beside Cardano's rules, an elegant method of numerical solution by means of trigonometric tables and iteration.

He was the first to give a geometric interpretation of negative quantities, writing, "The negative solution is explained in geometry by moving backward, and the minus sign moves back when the + advances." Girard is also famed for being the first to formulate the (now well-known) inductive definition fn+2 = fn+1 + fn for the Fibonacci sequence, and stating that the ratios of terms of the Fibonacci sequence tend to the golden ratio, which appear in this 1634 publication. *SAU

Glen Van Brummelen states in Heavenly Mathematics that Girard was also the first to use the symbol for cube root in his 1629 Invention nouvelle.. It was not adopted by others until Michel Rolle used it in 1690 in Traité d'Algèbre.*Cajori

**1632 Philippe van Lansberge**(25 Aug 1561 in Ghent, Netherlands (now Belgium)

Died: 8 Dec 1632 in Middelburg, Netherlands) was a Flemish clergyman who wrote on mathematics and astronomy. He calculated π to 28 places by a new method.*SAU

**1864 George Boole**(2 Nov 1815, 8 Dec 1864)English mathematician who helped establish modern symbolic logic and an algebra of logic, now called Boolean algebra. By replacing logical operations by symbols, Boole showed that the operations could be manipulated to give logically consistent results. Boole's logical algebra is essentially an algebra of classes, being based on such concepts as complement and union of classes. The study of mathematical or symbolic logic developed mainly from his ideas, and is basic to the design of digital computer circuits. Boolean also algebras find important applications in such diverse fields as topology, measure theory, probability and statistics. Boole also wrote important works on differential equations and other branches of mathematics. *TIS George Boole died from a feverish cold, or perhaps pneumonia, he got after walking two miles from his home in Queen’s College at Cork, Ireland, in a drenching rain to teach his class. [Eves, Circles, 289◦] *VFR

**1894 Pafnuty Lvovich Chebyshev**(4 May 1821, 8 Dec 1894) Russian mathematician who founded the St. Petersburg mathematical school (sometimes called the Chebyshev school), who is remembered primarily for his work on the theory of prime numbers, including the determination of the number of primes not exceeding a given number. He wrote about many subjects, including the theory of congruences in 1849, probability theory, quadratic forms, orthogonal functions, the theory of integrals, the construction of maps, and the calculation of geometric volumes. Chebyshev was also interested in mechanics and studied the problems involved in converting rotary motion into rectilinear motion by mechanical coupling. The Chebyshev parallel motion is three linked bars approximating rectilinear motion. *TIS

(

*I always loved the little jingle by Nathan Fine, "Chebyshev said, and I say it again. There is always a prime between n and 2n."*)

**1896 Ernst Engel**(26 Mar 1821, 8 Dec 1896) German statistician, the head of the Prussian Statistical Bureau (1860-82), known for the "Engel curve," or Engel's law, which states that the proportion of expenditure on food will fall as income rises, i.e. food is a necessary good. Engel's law applies to goods as a whole. Demand for food, clothing and shelter - and for most manufactured products - doesn't keep pace with increases in incomes. Engel curves are useful for separating the effect of income on demand from the effects of changes in relative prices. Engel also examined the relationship between the size of the Prussian rye harvest and the average price of rye over a number of years prior to 1860, probably the first empirical study of the relationship between price and supply. *TIS

**1933 John Joly**(1 Nov 1857, 8 Dec 1933) Irish geologist, physicist and inventor whose interests spanned several fields. Using Edmond Halley's method of measuring the degree of salinity of the oceans, and then by examining radioactive decay in rocks, he estimated Earth's age at 80-90 million years (1898). Later, he revised this figure to 100 million years. He published Radioactivity and Geology (1909) in which he demonstrated that the rate of radioactive decay has been more or less constant through time. He also developed a method for extracting radium (1914) and pioneered its use for cancer treatment, and invented a constant- volume gas thermometer, a photometer, and a differential steam calorimeter for measuring the specific heat capacity of gases at constant volume. *TIS

**1955 Hermann Weyl**(9 Nov 1885, 8 Dec 1955)German-American mathematician whose widely varied contributions in mathematics linked pure mathematics and theoretical physics. He made significant contributions to quantum mechanics and the theory of relativity. He attempted to incorporate electromagnetism into the geometric formalism of general relativity. Weyl published Die Idee der Riemannschen Fläche (1913) which united analysis, geometry and topology. He produced the first guage theory in which the Maxwell electromagnetic field and the gravitational field appear as geometrical properties of space-time. He evolved (1923-38) the concept of continuous groups using matrix representations. Applying group theory to quantum mechanics he set up the modern subject.

(

*My favorite Weyl quote, "God exists since mathematics is consistent, and the devil exists since its consistency cannot be proved."*) *TIS

**1961 Francesco Severi**(13 April 1879 – 8 December 1961) was an Italian mathematician.

Severi was born in Arezzo, Italy. He is famous for his contributions to algebraic geometry and the theory of functions of several complex variables. He became the effective leader of the Italian school of algebraic geometry. Together with Federigo Enriques, he won the Bordin prize from the French Academy of Sciences.

He contributed in a major way to birational geometry, the theory of algebraic surfaces, in particular of the curves lying on them, the theory of moduli spaces and the theory of functions of several complex variables. He wrote prolifically, and some of his work has subsequently been shown to be not rigorous according to the then new standards set in particular by Oscar Zariski and David Mumford. At the personal level, according to Roth (1963) he was easily offended, and he was involved in a number of controversies. He died in Rome of cancer.*Wik

**1966 Arthur Byron Coble**(November 3, 1878, Williamstown, Pennsylvania – December 8, 1966) was an American mathematician. He did research on finite geometries and the group theory related to them, Cremona transformations associated with the Galois theory of equations, and the relations between hyperelliptic theta functions, irrational binary invariants, the Weddle surface and the Kummer surface. He was President of the American Mathematical Society from 1933 to 1934.*Wik

**1973 Griffith Conrad Evans**(May 11, 1887 – December 8, 1973) was a mathematician working for much of his career at the University of California, Berkeley. He is largely credited with elevating Berkeley's mathematics department to a top-tier research department,[1] having recruited many notable mathematicians in the 1930s and 1940s.*Wik

**1986 Harrison (Scott) Brown**(26 Sep 1917, Sheridan, Wyoming, 8 Dec 1986) was an American geochemist known for his role in isolating plutonium for its use in the first atomic bombs and for his studies regarding meteorites and the Earth's origin. He was one of 67 concerned Manhattan Project scientists at Oak Ridge to sign a July 1945 petition to the President, which said, in part, "...Therefore we recommend that before this weapon be used without restriction in the present conflict, its powers should be adequately described and demonstrated, and the Japanese nation should be given the opportunity to consider the consequences of further refusal to surrender." *TIS (

*I like that he graduated from Galileo HS in San Francisco*)

2012 Barry S. Altman (founder of Commodore USA and designer of the C64x), died on December 8, 2012. *Commodore USA

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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