## Thursday, 17 April 2014

### On This Day in Math - April 17

 Origami Soma Cubes (see Piet Hein, Deaths, 1996)*The New Origami by Steve and Megumi Biddle

A Man of Knowledge like a rich Soil, feeds
If not a world of Corn, a world of Weeds.
~Benjamin Franklin

The 107th day of the year; There is no integer N such that N! has exactly 107 zeros in it. The same is true if we replace 107 by the primes 3, 31, or 43.*Prime Curios (This seems a most remarkable set of facts to me.)
Interestingly, the sum of the first 107 digits of pi is prime, and the sum of the first 107 digits of e is prime. This is trivially true for the first digit of each, but can you find the one (I believe) other number between 1 and 107 for which the sum of the digits of e and pi are both prime?

EVENTS
1397 Geoffrey Chaucer told the Canterbury Tales for the first time at the court of Richard II, *The British Library ‏@britishlibrary
Another significant work of Chaucer's is his Treatise on the Astrolabe, possibly for his own son, that describes the form and use of that instrument in detail and is sometimes cited as the first example of technical writing in the English language. Although much of the text may have come from other sources, the treatise indicates that Chaucer was versed in science in addition to his literary talents. Another scientific work discovered in 1952, Equatorie of the Planetis, has similar language and handwriting compared to some considered to be Chaucer's and it continues many of the ideas from the Astrolabe. Furthermore, it contains an example of early European encryption. The attribution of this work to Chaucer is still uncertain. *Wik

1732 Laura Maria Caterina Bassi defends forty-nine academic theses in public display:
The University of Bologna is the oldest university in Europe and at the beginning of the eighteenth century students were still examined by public disputation, i.e. the candidate was expected to orally defend a series of academic theses. At the beginning of 1732 Bassi took part in a private disputation in her home with members of the university faculty in the presence of many leading members of Bolognese intellectual society. As a result of her performance during this disputation she was elected a member of the prestigious Bologna Academy of Science on 20th March. Rumours of this extraordinary young lady quickly spread and on 17th April she defended forty-nine theses in a highly spectacular public disputation. On 12th May following a public outcry she was awarded a doctorate from the university in a grand ceremony in the city hall of Bologna. Following a further public disputation the City Senate appointed her professor of philosophy at the university, making her the first ever female professor at a European university.
See more at *Thony Christie, The Renaissance Mathematicus

1912 Two days after the sinking of the Titanic a solar eclipse occurred in England and Europe. It was a hybrid event, starting and ending as an annular eclipse, with only a small portion of totality. Totality was visible over the sea between Spain and France, with annularity continued northeast across Europe and Asia.
This eclipse occurred two days after the RMS Titanic sank in the northwestern Atlantic ocean under the darkness of new moon. *Wik
Eclipse poster from the London Underground for the 1912 Eclipse.

1935 Turkey issued a series of semi-postal stamps commemorating the 12th congress of the Women’s International Alliance. One pictured a school teacher. Another was the ﬁrst stamp honoring Marie SkLlodowska Curie. [Scott #B55, B67]*VFR

 *Louis Paul Hennefeld, Out of the Closet

1944 Harvard Mark I Operating:
Harvard University President James Conant writes to IBM founder Thomas Watson Sr. to let him know that the Harvard Mark I, developed in cooperation between the two, was operating smoothly. The project was one of the many examples of wartime collaboration among the federal government, universities, and private corporations. In his letter, Conant noted that the Mark I already was "being used for special problems in connection with the war effort." *CHM

2013 Yitang Zhang announced a proof that there are infinitely many pairs of prime numbers which differ by 70 million or less. This proof is the first to establish the existence of a finite bound for prime gaps, resolving a weak form of the twin prime conjecture. *Wik

BIRTHS
1598 Giovanni Battista Riccioli (17 April 1598 – 25 June 1671) Italian astronomer who was the first to observe (1650) a double star (two stars so close together that they appear to be one) - Mizar in Ursa Major, the middle star in the handle of the Big Dipper. He also discovered satellite shadows on Jupiter. In 1651, he assigned the majority of the lunar feature names in current use. He named the more prominent features after famous astronomers, scientists and philosophers, while the large dark and smooth areas he called "seas" or "maria". The lunar seas were named after moods (Seas of Tranquillity, Serenity) or terrestrial phenomena (Sea of Rains, Ocean or Storms) His map was published in Almagestum Novum in1651.*TIS
Riccioli studied seventy-seven objections to the Copernican thesis and after studying them Riccioli said that the weight of argument favored a “geo-heliocentric” hypothesis such as that advocated by the great Danish astronomer Tycho Brahe. Riccioli's preference for Tycho's model illustrates something important about how science is done. While today anti-Copernicans are often portrayed as Einstein characterized them (opposed to rational thinking, opposed to science), Riccioli, perhaps the most prominent of the anti-Copernicans, examined the available evidence diligently and rationally. The conclusion he reached was indeed wrong, but wrong because at that time neither the diffraction of light and the Airy disk, nor the details of the Coriolis effect, were understood. Riccioli's anti-Copernican arguments were so solid that they would become subjects of further investigation in physics, long after the Copernican theory had triumphed over the Tychonic theory.*Christopher M. Graney, Teaching Galileo, Physics Teacher V50,1
An interesting blog about Riccioli is at the Renaissance Mathematicus

1656 William Molyneux (17 April 1656 in Dublin, Ireland - 11 Oct 1698 in Dublin, Ireland) was an Irish scientist and philosopher who worked on optics.After leaving Bologna, Angeli continued his contacts with Cavalieri(who had been his teacher in Bologna) by correspondence, and was entrusted to publish Cavalieri's final work, Exercitationes geometricae sex, since by 1647 Cavalieri's health had deteriorated to such an extent that he was unable to carry out the work himself. Angeli also corresponded with a number of other mathematicians including Torricelli and Viviani. After Cavalieri's death, later in 1647, Angeli was offered his chair of mathematics at the University of Bologna but he was still too modest about his own mathematical achievements to accept the position. He moved to Rome where he devoted himself to both mathematics and religious studies. *SAU

1766 John Leslie (17 April 1766 in Largo, Fife, Scotland - 3 Nov 1832 in Coates (near Largo), Fife, Scotland) Leslie was a successful professor of mathematics, attracting large classes of students and publishing his lectures in popular textbooks such as the three part work Elements of Geometry​, Geometrical Analysis, and Plane Trigonometry (1809). He mixed classical mathematical teaching with some new continental approaches to analysis and algebra particularly in his advanced classes. Leslie became professor in Natural Philosophy in 1819 after the chair fell vacant on Playfair's death. This was not without a battle, for again the Church put up a candidate but, having won a victory in the earlier encounter, this time proved much more straightforward. He gave courses which were filled with experiments on specially made apparatus, for which Leslie himself had paid over half the cost from his own pocket. He soon discovered that one of the main problems of teaching university level physics was the lack of mathematical background of most of his students. He wanted to rectify this by teaching mathematics courses specially tailored for his physics students, but the University of Edinburgh senate prevented him from giving such courses since these topics were deemed the responsibility of the professor of mathematics. *SAU

1798 Étienne Bobillier (April 17, 1798 – March 22, 1840) was a French mathematician. At the age of 19 he was accepted into the École Polytechnique and studied there for a year. However, due to a shortage of money, in 1818 he became an instructor in mathematics at the École des Arts et Métiers in Châlons-sur-Marne. In 1829, he was sent to Angers to be director of studies. The following year he served in the national guard during the 1830 revolution. In 1832 he returned to Châlons after his post was abolished, and was promoted to professor.
In 1836 he began suffering from health problems, but continued teaching; declining to take a leave to recuperate. As a result he died in Châlons at the relatively early age of 41.
He is noted for his work on geometry, particularly the algebraic treatment of geometric surfaces and the polars of curves. He also worked on statics and the catenary. The crater Bobillier on the Moon is named after him.*Wik

1853 Arthur Moritz Schönflies (17 April 1853 in Landsberg an der Warthe, Germany (now Gorzów-Wielkopolski, Poland) - 27 May 1928 in Frankfurt am Main, Germany) worked first on geometry and kinematics but became best known for his work on set theory and crystallography. He classified the 230 space groups in 1891 He studied under Kummer and Weierstrass, and was influenced by Felix Klein.
The Schoenflies problem is to prove that an (n − 1)-sphere in Euclidean n-space bounds a topological ball, however embedded. This question is much more subtle than initially appears. *Wik *SAU

1863 Augustus Edward Hough Love (17 Apr 1863; 5 Jun 1940 at age 77) British geophysicist and mathematician who discovered a major type of earthquake wave that was subsequently named for him. Love assumed that the Earth consists of concentric layers that differ in density and postulated the occurrence of a seismic wave confined to the surface layer (crust) of the Earth which propagated between the crust and underlying mantle. His prediction was confirmed by recordings of the behaviour of waves in the surface layer of the Earth. He proposed a method, based on measurements of Love waves, to measure the thickness of the Earth's crust. In addition to his work on geophysical theory, Love studied elasticity and wrote A Treatise on the Mathematical Theory of Elasticity, 2 vol. (1892-93). *TIS (Hard to imagine the newsperson announcing that "Love waves caused the collapse of multiple buildings in San Francisco on this day in 1906.")

1918 Matteo Bottasso (17 April 1878 in Chiusa di Pesio (Cuneo), Italy - 4 Oct 1918 in Messina, ItalyMessina, Italy)was an Italian mathematician who used the vector calculus in studying problems in geometry, mechanics and physics. *SAU

DEATHS
485 Proclus Diadochus (8 Feb 411 in Constantinople (now Istanbul), Byzantium (now Turkey) - 17 April 485 in Athens, Greece) was a Greek philosopher who became head of Plato's Academy and is important mathematically for his commentaries on the work of other mathematicians. *SAU

1761 Thomas Bayes (1702, 17 Apr 1761) English theologian and mathematician who was the first to use probability inductively and who established a mathematical basis for probability inference (a means of calculating, from the frequency with which an event has occurred in prior trials, the probability that it will occur in future trials). This became the basis of a statistical technique, now called Bayesian estimation, for calculating the probability of the validity of a proposition on the basis of a prior estimate of its probability and new relevant evidence. Later statisticians cite disadvantages of the method that include the different ways of assigning prior distributions of parameters and the possible sensitivity of conclusions to the choice of distributions. *TIS British mathematician and Presbyterian minister, known for having formulated a special case of Bayes' theorem, which was published posthumously. Bayes died in Tunbridge Wells, Kent. He is interred in Bunhill Fields Cemetery in London where many Nonconformists are buried. Bayesian probability is the name given to several related interpretations of probability, which have in common the application of probability to any kind of statement, not just those involving random variables. "Bayesian" has been used in this sense since about 1950.

1787 Wenceslaus Johann Gustav Karsten (15 Dec 1732 in Neubrandenburg, Mecklenburg-Strelitz, Germany - 17 April 1787 in Halle, Germany) He wrote an important article in 1768 Von den Logarithmen vermeinter Grössen in which he discussed logarithms of negative and imaginary numbers, giving a geometric interpretation of logarithms of complex numbers as hyperbolic sectors, based on the similarity of the equations of the circle and of the equilateral hyperbola. *SAU

1790 Benjamin Franklin, (17 Jan 1706; 17 Apr 1790) American printer and publisher, author, inventor and scientist, and diplomat. He become widely known in European scientific circles for his reports of electrical experiments and theories. He invented a type of stove, still being manufactured, to give more warmth than open fireplaces and the lightning rod, bifocal eyeglasses also were his ideas. Grasping the fact that by united effort a community may have amenities which only the wealthy few can get for themselves, he helped establish institutions people now take for granted: a fire company (1736), a library (1731), an insurance company (1752), an academy (1751), and a hospital (1751). In some cases these foundations were the first of their kind in North America. *TIS When he observed a balloon launch by the Montgolﬁer brothers he was asked of what use it was. He replied: Of what use is a new born baby? *VFR
While traveling on a ship, Franklin had observed that the wake of a ship was diminished when the cooks scuttled their greasy water. He studied the effects at Clapham common on a large pond there. "I fetched out a cruet of oil and dropt a little of it on the water...though not more than a teaspoon full, produced an instant calm over a space of several yards square." He later used the trick to "calm the waters" by carrying "a little oil in the hollow joint of my cane." *W. Gratzer, Eurekas and Euphorias, pgs 80,81

1847 Francois-Joseph Servois (19 July 1768 in Mont-de-Laval (N of Morteau), Doubs, France - 17 April 1847 in Mont-de-Laval, Doubs, France) He worked in projective geometry, functional equations and complex numbers. He introduced the word pole in projective geometry. He also came close to discovering the quaternions before Hamilton.
Servois introduced the terms "commutative" and "distributive" in a paper describing properties of operators, and he also gave some examples of noncommutativity. Although he does not use the concept of a ring explicitly, he does verify that linear commutative operators satisfy the ring axioms. In doing so he showed why operators could be manipulated like algebraic magnitudes. This work initiates the algebraic theory of operators.
Servois was critical of Argand's geometric interpretation of the complex numbers. He wrote to Gergonne telling him so in November 1813 and Gergonne published the letter in the Annales de mathématiques in January 1814. Servois wrote:- I confess that I do not yet see in this notation anything but a geometric mask applied to analytic forms the direct use of which seems to me simple and more expeditious.
Considered as a leading expert by many mathematicians of his day, he was consulted on many occasions by Poncelet while he was writing his book on projective geometry Traité des propriétés projective. *SAU

1942 Jean-Baptiste Perrin (30 Sep 1870, 17 Apr 1942 at age 71) was a French physicist who, in his studies of the Brownian motion of minute particles suspended in liquids, verified Albert Einstein's explanation of this phenomenon and thereby confirmed the atomic nature of matter. Using a gamboge emulsion, Perrin was able to determine by a new method, one of the most important physical constants, Avogadro's number (the number of molecules of a substance in so many grams as indicated by the molecular weight, for example, the number of molecules in two grams of hydrogen). The value obtained corresponded, within the limits of error, to that given by the kinetic theory of gases. For this achievement he was honoured with the Nobel Prize for Physics in 1926. *TIS

1977 Richard Dagobert Brauer (10 Feb 1901; 17 Apr 1977 at age 76) German-American mathematician and educator, a pioneer in the development of algebra theory. He worked with Weyl on several projects including a famous joint paper on spinors (published in 1935 in the American Journal of Mathematics). This work provided a background for Paul Dirac's theory of the spinning electron within the framework of quantum mechanics. With Nesbitt, Brauer introduced the theory of blocks (1937). Brauer used this to obtain results on finite groups, particularly finite simple groups, and the theory of blocks would play a big part in much of Brauer's later work. Starting with his group-theoretical characterisation of the simple groups (1951), he spent the rest of his life formulating a method to classify all finite simple groups. *TIS

1996 Piet Hein (December 16, 1905 – April 17, 1996) was a Danish scientist, mathematician, inventor, designer, author, and poet, often writing under the Old Norse pseudonym "Kumbel" meaning "tombstone". His short poems, known as gruks or grooks (Danish: Gruk), first started to appear in the daily newspaper "Politiken" shortly after the Nazi occupation in April 1940 under the pseudonym "Kumbel Kumbell"
The Soma cube is a solid dissection puzzle invented by Piet Hein in 1933 during a lecture on quantum mechanics conducted by Werner Heisenberg. Seven pieces made out of unit cubes must be assembled into a 3x3x3 cube. The pieces can also be used to make a variety of other 3D shapes. Piet Hein created the superellipse which became the hallmark of modern Scandinavian architecture.
In addition to the thousands of grooks he wrote, Piet Hein devised the games of Hex, Tangloids, Morra, Tower, Polytaire, TacTix, Nimbi, Qrazy Qube, Pyramystery, and the Soma cube. He advocated the use of the superellipse curve in city planning, furniture making and other realms. He also invented a perpetual calendar called the Astro Calendar and marketed housewares based on the superellipse and Superegg. *Wik My Favorite of his grooks is this one:
Problems worthy
of attack
prove their worth
by hitting back.

2006 Gloria Olive (8 June 1923 in New York City, USA - 17 April 2006 in Dunedin, New Zealand) Much of Olive's research was on applications of generalised powers. She published papers such as Binomial functions and combinatorial mathematics (1979), A combinatorial approach to generalized powers (1980), Binomial functions with the Stirling property (1981), Some functions that count (1983), Taylor series revisited (1984), Catalan numbers revisited (1985), A special class of infinite matrices (1987), and The ballot problem revisited (1988). Some of her work on binomial functions overlaps that of Gian-Carlo Rota's "polynomials of binomial type". She has had a special interest in the polynomials which are generated by her generalised powers, and hopes that someone will prove or disprove her conjecture, now about 30 years old, that all their zeros lie on the unit circle. This conjecture has now been verified for infinitely many special cases. *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