It requires a very unusual mind to undertake the analysis of the obvious.

~Alfred North Whitehead

### The 364th day of the year; 364 is the total number of gifts in the Twelve Days of Christmas song: 1+(2+1) + (3+2+1) ... which is a series of triangular numbers. The sum of the first n triangular numbers can be expressed as (n+2 Choose 3).

If you put a standard 8x8 chessboard on each face of a cube, there would be 364*(below) squares. Futility closet included this note on such a cube: "British puzzle expert Henry Dudeney once set himself the task of devising a complete knight’s tour of a cube each of whose sides is a chessboard. He came up with this:

If you cut out the figure, fold it into a cube and fasten it using the tabs provided, you’ll have a map of the knight’s path. It can start anywhere and make its way around the whole cube, visiting each of the 364 squares once and returning to its starting point. (*BTW, I've done the arithmetic on this, and that has to be 384 squares, but I didn't notice the discrepancy at first, so it's still here since I don't have a 384th day of the year to post it.)

The number of primes less than 364 = 3*6*4 (is this true for any other number?)

### 364 is the 20th (and last) Hoax number of the year, (the sum of its digits is equal to the sum of the digits of it's distinct prime divisors). Exactly half those 20 numbers, including this one, have a digit sum of 13.

### There are also Smith (or joke) numbers: composite numbers n such that sum of digits of n = sum of digits of prime factors of n (counted with multiplicity).

**EVENTS**

**1610**Galileo in answer to a question from Father Christoph Clavius SJ about why his large aperture was partly covered; answered that he did this for two reasons:

The first is to make it possible to work it more accurately because a large surface is

more easily kept in the proper shape than a smaller one. The other reason is that if

one wants to see a larger space in one glance, the glass can be uncovered, but it is then

necessary to put a less acute glass near the eye and shorten the tube, otherwise the

objects will appear very fuzzy. *Aalbert Vvan Helden, Galileo and the Telescope; Origins of the Telescope - Royal Netherlands Academy of Arts and Sciences, 2010

In

**1873**, the American Metrological Society was formed in New York City to improve systems of weights, measures and money. Its activities eventually extended with a committee considering units of force and energy, and another concerned with the adoption of Standard Time for the U.S. On 30 Dec 1884, at the meeting of the American Metrological Society at Columbia College in New York City, Charles S. Peirce read a paper on the determination of gravity. He also participated in a discussion of the adequacy of the standards of weight and measure in the United States and pointed out some of the deficiencies in the current system. As a result of his revelations, the Society passed a resolution recommending the appointment of a committee to advise Congress on the need for establishing an efficient bureau of standards. *TIS

**1881**The “Four Fours” problem was ﬁrst published in Knowledge a magazine of popular science edited by the astronomer Richard Proctor. The problem is to express whole numbers using exactly four fours and various arithmetical signs. For example 52 = 44 + 4 + 4. This can be done for the integers from 1 to 112, but 113 is a problem. Variations of the game allow use of factorials, square roots, decimal points (such as .4) etc. A good source for further study is here. And if you are interested, before there was a four-fours problem there was a three-threes problem

**1902**Leornard Eugene Dickson married Susan Davis. Later he often said of his honeymoon: “It was a great success, except that I only got two research papers written.” In all he published 18 books and hundreds of articles.*VFR

**1915**A two day meeting in Columbus, Ohio began to found a new mathematical organization. The new organization would be called the Mathematical Organization of America, and took over the publishing of the American Mathematical Monthly which had been in operation for three years. The first president was Professor E. R. Hedrick of the University of Missouri. The Earle Raymond Hedrick lectures were established by the Mathematical Association in America in his honor.

**In 1924**, Edwin Hubble announced the existence of another galactic system in addition to the Milky Way. He had found at least one "island universe," or galaxy of stars, lies outside our own Milky Way. Until then, scientists were not certain whether certain fuzzy clouds of light called "nebulae" that had been seen with telescopes were small clusters of clouds within the Milky Way or separate galaxies. Hubble measured the distance to the Andromeda nebula and showed it to be a hundred thousand times as far away as the nearest stars. This proved it was a separate galaxy, as large as our own Milky Way, but very far away. More galaxies have been found, some a spiral form like the Milky Way; others spheroidal, others without the spiral arms, or of irregular shape.

1952 Harvard mathematician Andrew Gleason received the Newcomb Cleveland Prize, a $1000 financial award, for his contributions toward the solution of Hilbert's Fifth Problem about Lie Groups.

**1968** The front page of The New York Times reveals Bill Anders' "Earthrise" for the first time, albeit in black and white. (It was one of 13 photographs released by NASA the previous evening.) *Chasing The Moon: The Book

In **1982**, a second full moon of the month was visible. Known as a "blue moon," the name does not refer to its color, but it is a rare event, giving rise to the expression, "once in a blue moon" came from. This blue blue moon was more special as a total lunar eclipse also occurred (U.S.). Although there were 41 blue moons in the twentieth century, this was one of four during an eclipse of the moon, and the only total eclipse of a blue moon in the twentieth century. A blue moon happens every 2.7 years because of a disparity between our calendar and the lunar cycle. The lunar cycle is the time it takes for the moon to revolve around the earth, is 29 days, 12 hours, and 44 minutes. *TIS The next blue moon will occur on September 30 of 2012.

**1985**Version 3.2 of the IBM PC-DOS operating system is announced

PC-DOS, IBM's version of the DOS operating system used on the IBM PC, released Version 3.2 on this date. The system required 128KB RAM and was available on either one 720KB disk or two 51/4” disks. DOS has remained in use since the introduction of the IBM PC in 1981, with PC-DOS 200 being the latest release in 1998. *CHM

**BIRTHS**

**1850 John Milne**(30 Dec 1850; 30 Jul 1913) English seismologist who invented the horizontal pendulum seismograph (1894) and was one of the European scientists that helped organize the seismic survey of Japan in the last half of the 1800's. Milne conducted experiments on the propagation of elastic waves from artificial sources, and building construction. He spent 20 years in Japan, until 1895, when a fire destroyed his property, and he returned home to the Isle of Wight. He set up a new laboratory and persuaded the Royal Society to fund initially 20 earthquake observatories around the world, equipped with his seismographs. By 1900, Milne seismographs were established on all of the inhabited continents and he was recognized as the world's leading seismologist. He died of Bright's disease.*TIS

**1897 Stanisław Saks**(December 30, 1897 – November 23, 1942) was a Polish mathematician and university tutor, known primarily for his membership in the Scottish Café circle, an extensive monograph on the Theory of Integrals, his works on measure theory and the Vitali-Hahn-Saks theorem.*wIK

**1931 Sir John (Theodore) Houghton**(30 Dec 1931, ) Welsh meteorologist who began in the late 1960's drawing attention to the buildup of carbon dioxide in the earth's atmosphere and its result of global warming, now known as the greenhouse effect. As director-general (1983) of the British Meteorological Office, he began tracking changing climate patterns. In 1990, he co-chaired a team of scientists working for the United Nations that produced the first comprehensive report on the science of climate change. This led to the 1997 U.N. Conference on Climate Change, in Kyoto, Japan. The Kyoto Protocol that resulted there was a treaty among industrialized and developed nations to combat global warming by voluntarily adhering to progressively stiffening emissions-reduction standards.*TIS

**1934 John N. Bahcall**(30 Dec 1934, ) American astrophysicist who pioneered the development of neutrino astrophysics in the early 1960s. He theorized that neutrinos (subatomic particles that have no charge and exceedingly weak interaction with matter) can be used to understanding how stars shine. They are emitted by the sun and stars during the fusion energy creation process, and most are able to pass through the Earth without being stopped. He calculated the expected output of neutrinos from the sun, which created an experimental challenge to explain the unexpected result. He won the National Medal of Science (1998) for both his contributions to the planning and development of the Hubble Space Telescope and his pioneering research in neutrino astrophysics.*TIS

**DEATHS**

**1691 Robert Boyle**(25 Jan 1627, 30 Dec 1691) Anglo-Irish chemist and natural philosopher noted for his pioneering experiments on the properties of gases and his espousal of a corpuscular view of matter that was a forerunner of the modern theory of chemical elements. He was a founding member of the Royal Society of London. From 1656-68, he resided at Oxford where Robert Hooke, who helped him to construct the air pump. With this invention, Boyle demonstrated the physical characteristics of air and the necessity of air for combustion, respiration, and the transmission of sound, published in New Experiments Physio-Mechanical, Touching the Spring of the Air and its Effects (1660). In 1661, he reported to the Royal Society on the relationship of the volume of gases and pressure (Boyle's Law).*TIS

**1695 Sir Samuel Morland**(born 1625, 30 Dec 1695) English mathematician and inventor of mechanical calculators. His first machine added and subtracted English money using eight dials that were moved by a simple stylus. Another could multiply and divide using 30 discs with numbers marked around the edge - circular versions of Napier's linear bones. Five more discs handled finding square and cube roots. His third machine made trigonometric calculations. Morland built a speaking trumpet (1671) he claimed would allow a conversation to be conducted over a distance of 3/4 mile. By 1675, he had developed various pumps for domestic, marine and industrial applications, such as wells, draining ponds or mines, and fire fighting. He also designed iron stoves for marine use, and improved barometers. *TIS

**1883 John Henry Dallmeyer**(6 Sep 1830, 30 Dec 1883) German-born British inventor and manufacturer of lenses and telescopes. He introduced improvements in both photographic portrait and landscape lenses, in object glasses for the microscope, and in condensers for the optical lantern. Dallmeyer made photoheliographs (telescopes adapted for photographing the Sun) for Harvard observatory (1864), and the British government (1873). He introduced the "rapid rectilinear" (1866) which is a lens system composed of two matching doublet lenses, symmetrically placed around the focal aperture to remove many of the aberrations present in more simple constructions. He died on board a ship at sea off New Zealand. *TIS

**1932 Eliakim Hastings Moore**(January 26, 1862 – December 30, 1932) was an American mathematician. He discovered mathematics through a summer job at the Cincinnati Observatory while in high school. When the University of Chicago opened its doors in 1892, Moore was the first head of its mathematics department, a position he retained until his death in 1931. His first two colleagues were Bolza and Maschke. The resulting department was the second research-oriented mathematics department in American history, after Johns Hopkins University.

Moore first worked in abstract algebra, proving in 1893 the classification of the structure of finite fields (also called Galois fields). Around 1900, he began working on the foundations of geometry. He reformulated Hilbert's axioms for geometry so that points were the only primitive notion, thus turning Hilbert's primitive lines and planes into defined notions. In 1902, he further showed that one of Hilbert's axioms for geometry was redundant. Independently, the twenty year old R.L. Moore (no relation) also proved this, but in a more elegant fashion than E. H. Moore used. When E. H. Moore heard of the feat, he arranged for a scholarship that would allow R.L. Moore to study for a doctorate at Chicago. E.H. Moore's work on axiom systems is considered one of the starting points for metamathematics and model theory. After 1906, he turned to the foundations of analysis. The concept of closure operator first appeared in his 1910 Introduction to a form of general analysis. He also wrote on algebraic geometry, number theory, and integral equations.

At Chicago, Moore supervised 31 doctoral dissertations, including those of George Birkhoff, Leonard Dickson, Robert Lee Moore (no relation), and Oswald Veblen. Birkhoff and Veblen went on to forge and lead the first-rate departments at Harvard and Princeton, respectively. Dickson became the first great American algebraist and number theorist. Robert Moore founded American topology. According to the Mathematics Genealogy Project, as of January 2011, E. H. Moore had over 14,900 known "descendants."

Moore convinced the New York Mathematical Society to change its name to the American Mathematical Society, whose Chicago branch he led. He presided over the AMS, 1901–02, and edited the Transactions of the American Mathematical Society, 1899–1907. He was elected to the National Academy of Sciences, the American Academy of Arts and Sciences, and the American Philosophical Society.

The American Mathematical Society established a prize in his honor in 2002. *Wik

**1947 Alfred North Whitehead**(15 Feb 1861, 30 Dec 1947) English mathematician and philosopher, who worked in logic, physics, philosophy of science and metaphysics. He is best known for his work with Bertrand Russell on one of probably the most famous books of the century, Principia Mathematica (1910-13) to demonstrate that logic is the basis for all mathematics. In physics (1910-24) his best known work was a theory of gravity, that competed with Einstein's general relativity for many decades. In his later life from 1924 onward at Harvard, he worked on more general issues in philosophy rather than mathematics, including the development of a comprehensive metaphysical system which has come to be known as process philosophy. *TIS

**1956 Heinrich Scholz**(December 17 1884 in Berlin , December 30 1956 in Muenster, Westphalia ) was a German logician, philosopher and theologian. *Wik

**1982 Philip Hall**(11 April 1904 in Hampstead, London, England - 30 Dec 1982 in Cambridge, Cambridge shire, England) Hall was the main impetus behind the British school of group theory and the growth of group theory to be one of the major mathematical topics of the 20th Century was largely due to him.*SAU

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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