| MONTESSORI GIVING A LESSON IN TOUCHING GEOMETRICAL INSET |
Common sense is not really so common.
~Antoine Arnauld (1612 - 1694) inThe Art of Thinking: Port-Royal Logic
The 60th day of the year; 60 is the smallest composite number which is the order of a simple group.7! is the smallest # with 60 divisors.
There are four Archimedean solids with 60 vertices , : the truncated icosahedron, (shown) the rhombicosidodecahedron, the snub dodecahedron, and the truncated dodecahedron.
Oh, and Pi day is coming up in a couple of weeks, so ... suppose you were scrolling through the digits of pi and wondered how long it would take until you found a string of ten digits that had all ten of 0 through nine in it... Benjamin Vitale @BenVitale thought to find out and :
You can arrange the whole numbers from 1 to 60 into pairs so that the sum of the numbers in each pair is a perfect square; in fact, you can do it in 4,366,714 ways. Here is one of those presented in a pretty fashion using only five squares for the sums. *Gordon Hamilton, Kiran S. Kedlaya, and Henri Picciotto; Square–Sum Pair Partitions(Won the George Polya Prize from MAA for 2016)
EVENTS
1688 On Feb. 29, 1688, Robert Hooke gave a lecture to the Royal Society of London about geological changes that the earth had undergone in its long history. It was one in a series of lectures on geology that Hooke gave over a 30-year span, and which were later printed as "Discourse of Earthquakes" in his Posthumous Works (1705). But this lecture was special, for here Hooke called attention to the importance of fossils in working out the earth's geological history. Shells found in rocks, says Hooke, are "… Records of Antiquity which Nature have left as Monuments and Hieroglyphick Characters of preceding Transactions in the ... Body of the Earth, which are infinitely more evident and certain tokens than any thing of antiquity than can be fetched out of Coins or Medals." Since most of his contemporaries considered fossils to be figured stones that grew in the earth, or lusus naturae, jokes of nature put there to amuse us, Hooke's pronouncement was a remarkable statement, a declaration of his belief that fossils are the remains of once living creatures, and that their location in rocks has to be explained, even if it means turning land into sea and sea into land. His comparison to ancient coins is a wonderful analogy; if we can reconstruct the history of Roman Britain from coins that we find in ruins, why can we not reconstruct the history of the earth from its coins and medals, the fossils in the rocks? *Linda Hall Org
1712 Sweden briefly had a February 30. In planning to switch from the Julian to the Gregorian calendar, the Swedish Empire resolved to omit leap days from 1700 to 1740. It followed through on this plan in 1700, but through error 1704 and 1708 remained leap years. With the time now out of joint, the empire abandoned its plan and returned to the Julian calendar by observing two leap days, February 29 and February 30, in 1712. (Sweden finally converted to the Gregorian calendar in 1753.)
If the original plan had been carried out, a person born on Feb. 29, 1696, would not celebrate a birthday until 1744. As it was, a person born on Feb. 30, 1712, would never celebrate a birthday at all. *Greg Ross, Futility Closet
February 30 existed from 1930–1931 after the Soviet Union introduced a revolutionary calendar in 1929. This calendar featured five-day weeks, 30-day months for every working month, and the remaining five or six days were “monthless” holidays. The abolition of the seven-day week in favor of a five-day week was intended to improve industrial efficiency by avoiding the regular interruption of a non-working day.
1504 On Feb. 29, 1504, Columbus and his men had been shipwrecked in Jamaica for eight months, relying on the local natives to feed them. After six months, the natives cut off the charity. Columbus, who had an astronomical almanac with him, summoned the native leaders and warned that if the natives did not reconsider, God would make the Moon disappear. When, as Columbus had predicted, the Moon became fully eclipsed that night, the natives panicked. *http://listosaur.com (Somewhat skeptical of this story. Did astronomical almanacs this early already include information like this about Jamaica? And since lunar eclipses happen once or twice a year, wouldn't most of these leaders have witnessed more than one?)
Mark Twain seems to have known of this episode, and used it as a basis for a segment of his 1889 novel A Connecticut Yankee in King Arthur's Court. Reversing the Shawnee episode Twain has Hank Morgan, the Yankee in the title (and Bing Crosby in the movie version), hoodwinking the ignorant folk in King Arthur's England by invoking prior knowledge of a solar eclipse due in June of AD 528, even stating the precise time of totality. He used his imagination, though: there was no eclipse around that epoch.
1880 On Leap Day in 2012, John D Cook at The Endeavor blog posted a tribute from Pirates of Penzance by Gilbert & Sullivan :
"For some ridiculous reason, to which, however, I’ve no desire to be disloyal,
Some person in authority, I don’t know who, very likely the Astronomer Royal,
Has decided that, although for such a beastly month as February, twenty-eight days as a general rule are plenty,
One year in every four, its days shall be reckoned as nine and twenty."
In 1916, Maria Montessori of Rome, Italy, received a U.S. patent for “Cut-Out Geometrical Figure for Didactical Purposes” (No. 1,173,298). Montessori is famous for her educational methods. The patent covered her invention of a plate with recesses into which geometrical shapes can be fitted so the “fundamental principles of geometry may be easily and rapidly taught to young pupils.” The recesses can be filled with, for example, several smaller triangles that fill the larger triangular cavity.*TIS
1924 The first Josiah Willard Gibbs lecture was delivered by Professor M. I. Pupin of Columbia University to an AMS meeting in New York City. In introducing him, AMS president Veblen said “It is hoped that the Willard Gibbs Lecturers will remind the mathematicians of something that we fear they sometimes forget, – the existence of an outside world. It is equally hoped that they will remind the outside world that mathematics is a growing concern, – not a pedantic exercise for the torment of schoolboys, but a living organism growing larger and stronger each year.” See BAMS 30(1924), p. 289. *VFR
In 1936, Nature carried Niels Bohr's “bowl of balls” explanation for the effect of bombarding particles on a nucleus (Vol. 137, p. 344). He followed up in an article in Science (20 Aug 1937, p. 161) explaining that “to understand the typical features of nuclear transmutations initiated by impacts of material particles... A simple mechanical model which illustrates these features of nuclear collisions is ... a shallow basic with a number of billard balls in it. If the bowl were empty, then a ball which was sent in would go down one clope and pass out on the opposite side with its original energy. When, however, there are other balls in the bowl, then the incident one will not be able to pass through freely but will divide its energy first with one of the balls, these two will share their energy ... divided among all the balls.”*TIS
Suspended In Language: Niels Bohrs Life, Discoveries, And The Century He Shaped
by Jim Ottaviani, Leland Purvis and Jeff Parker
1940 Ernest O. Lawrence delivered his 1939 Nobel Prize in Physics banquet speech in Berkeley, California, having arranged to receive the prize there, rather than Sweden, so he would not lose time away from the task of fund raising for his cyclotron research. He was awarded the prize “for the invention and development of the cyclotron and for results obtained with it, especially with regard to artificial radioactive elements.” Lawrence said the discoveries made had “immediate practical significance” as “the new radiations and radioactive substances have opened vistas for all the sciences, especially in medical research and therapy.” He looked forward to a new research frontier using energies above a hundred million volts with “a giant cyclotron perhaps weighing more than 4,000 tons - twenty times larger.”«
1968 British astronomer, Jocelyn Burnell, announced the discovery of a pulsar, a pulsating radio source believed to be a rapidly rotating neutron star. *VFR
BIRTHS
1804 Antoine Hercule Romuald Florence ( 29 Feb 1804; 27 Mar 1879) was a French inventor, photographer and printer who coined the word “photographie” in French (before the use of “photography” in English suggested by John Herschel). Florence pioneered a process of reproducing drawings on paper sensitized with silver salts. He developed his ideas from 1832, before the better known Louis Daguerre. He was then living in Brazil, where he had settled in 1824 after working on board ships. During 1825-30, he had joined a scientific expedition as an illustrator and topographic draftsman. By 1832, his goal was document reproduction (in publications as illustrations) rather than portraits. He never published his discoveries to the larger scientific world in Europe, and his name was forgotten in history. In 1976, a Brazilian historian, Boris Kossoy, uncovered Florence's work, and studied his notes. Kossoy presented the results of his research at a photography symposium in 1976, and in a book published in 1980.*TIS
Photocopy of a diploma made using Florence's photographic technique, ca. 1833
1840 John Phillip Holland (29 Feb 1840; 12 Aug 1914 )Irish inventor known as the “father of the modern submarine,” who designed and built the first underwater vessel accepted by the U.S. Navy. In 1873, he emigrated to the U.S. where, with financial support from the Irish Fenian Society (who hoped to use submarines against England), he built the Fenian Ram, a small sub that proved a limited success in a test run. In 1895, his J.P. Holland Torpedo Boat Company received a contract from the U.S. Navy to build a submarine, and in 1898 a successful Holland, the first truly practical submarine, was launched. The U.S. government ordered six more; similar orders came from England, Japan, and Russia. Holland’s final years were marked by litigation with his financial backers.*TIS
Holland stands in the hatch of a submarine.
1860 Herman Hollerith (29 Feb 1860, 17 Nov 1929) American inventor of a tabulating machine that was an important precursor of the electronic computer. For the 1890 U.S. census, he invented several punched-card machines to automate the sorting of data. The machine which read the cards used a pin going through a hole in the card to make an electrical connection with mercury placed beneath. The resulting electrical current activated a mechanical counter. It saved the United States 5 million dollars for the 1890 census by completing the analysis of the data in a fraction of the time it would have taken without it and with a smaller amount of manpower than would have been necessary otherwise. In 1896, he formed the Tabulating Machine Company, a precursor of IBM. *TIS
1928 Caleb Vance Haynes, Jr (born February 29, 1928)) is an American archeologist and geologist who was active (1996-2004) in the effort to keep the remains of prehistoric Kennewick Man for academic purposes, rather than letting the Army Corps of Engineers repatriate them to a modern Indian tribe. Haynes was one of eight scientists that sued on 16 Oct 1996 for the right to study the bones. He provided the court deciding the matter with arguments that because the bones had been carbon dated to be about 9,000 years old, the remains could not be a direct ancestor of any modern tribe. The court's judgment was that Kennewick Man did not meet the definition of a native American, as used in the Native American Graves and Protection Act. The almost complete skeleton of Kennewick Man, found beside the Columbia River in Kennewick, Washington (28 Jul 1996), is one of the very few specimens available to understand the peopling of America in that era, and offers great value to science.« *TIS
Haynes coined the term "black mat" for a layer of 10,000-year-old swamp soil seen in many North American archaeological studies.
Haynes was elected in 1990 to the National Academy of Sciences. From 1996 to 2004, Haynes worked to keep the Kennewick Man discovery available for science. Currently an emeritus Regents' professor at the University of Arizona, Haynes is still active in the School of Anthropology.*Wik
1932 Gene Howard Golub (February 29, 1932 – November 16, 2007), Fletcher Jones Professor of Computer Science (and, by courtesy, of Electrical Engineering) at Stanford University, was one of the preeminent numerical analysts of his generation.
Credits. *Wik
DEATHS
1744 John Theophile Desaguliers (12 Mar 1683, 29 Feb 1744 at age 60)French-English chaplain and physicist who studied at Oxford, became experimental assistant to Sir Isaac Newton. As curator at the Royal Society, his experimental lectures in mechanical philosophy and electricity (advocating, substantiating and popularizing the work of Isaac Newton) attracted a wide audience. In electricity, he coined the terms conductor and insulator. He repeated and extended the work of Stephen Gray in electricity. He proposed a scheme for heating vessels such as salt-boilers by steam instead of fire. He made inventions of his own, such as a planetarium, and improvements to machines, such as Thomas Savery's steam engine (by adding a safety valve, and using an internal water jet to condense the steam in the displacement chambers) and a ventilator at the House of Commons. He was a prolific author and translator. *TIS
1932 Giuseppe Vitali (26 August 1875 – 29 February 1932) was an Italian mathematician who worked in several branches of mathematical analysis. He was the first to give an example of a non-measurable subset of real numbers, see Vitali set. His covering theorem is a fundamental result in measure theory. He also proved several theorems concerning convergence of sequences of measurable and holomorphic functions. Vitali convergence theorem generalizes Lebesgue's dominated convergence theorem. Another theorem bearing his name gives a sufficient condition for the uniform convergence of a sequence of holomorphic functions on an open domain D⊂ℂ to a holomorphic function on D. This result has been generalized to normal families of meromorphic functions, holomorphic functions of several complex variables, and so on. *Wik
1960 Teiji Takagi (21 April 1875 in Kazuya Village (near Gifu), Japan - 29 Feb 1960 in Tokyo, Japan) Takagi worked on class field theory, building on Heinrich Weber's work.*SAU
He is best known for proving the Takagi existence theorem in class field theory. The Blancmange curve, the graph of a nowhere-differentiable but uniformly continuous function, is also called the Takagi curve after his work on it.
He was also instrumental during World War II in the development of Japanese encryption systems.
Credits
*VFR = V Frederick Rickey, USMA
*TIS= Today in Science History
*Wik = Wikipedia
*SAU=St Andrews Univ. Math History
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
No comments:
Post a Comment