## Friday, 17 June 2016

### On This Day in Math - June 17

By keenly confronting the enigmas that surround us, and by considering and analyzing the observations that I have made, I ended up in the domain of mathematics, Although I am absolutely without training in the exact sciences, I often seem to have more in common with mathematicians than with my fellow artists.

M. C. Escher, Quoted in To Infinity and Beyond, E Maor (Princeton 1991)

The 169th day of the year; 169 is the smallest square which is prime when rotated 180o (691)  What is the next one?

And from Jim Wilder, 169 is the reverse of 961. The same is true of their square roots... √169=13 and √961=31
or stated another way, 169 = 132 and in reverse order 312 = 961

An interesting loop sequence within Pi. If you search for 169, it appears at position 40. If you then search for 40, it appears at position 70. Search for 70, ... 96, 180, 3664, 24717, 15492, 84198, 65489, 3725, 16974, 41702, 3788, 5757, 1958, 14609, 62892, 44745, 9385, 169, *Pi Search page

169 is the only year day which is both the difference of consecutive cubes, and a square: $8^3-7^3 =169=13^2$

The first successful dissection of a square into smaller squares was of a square with 169 units on a side. 1907-1914 S. Loyd published The Patch Quilt Puzzle. A square quilt made of 169 square patches of the same size is to be divided into the smallest number of square pieces by cutting along lattice lines. The answer, which is unique, is composed of 11 squares with sides 1,1,2,2,2,3,3,4,6,6,7 within a square of 13. It is neither perfect nor simple. Gardner states that this problem first appeared in 1907 in a puzzle magazine edited by Sam Loyd. David Singmaster lists it as first appearing in 1914 in Cyclopedia by Loyd but credits Loyd with publishing Our Puzzle Magazine in 1907 - 08. This puzzle also appeared in a publication by Henry Dudeney as Mrs Perkins Quilt. Problem 173 in Amusements in Mathematics. 1917

EVENTS

1713  Leibniz replies from Vienna to Johan (I) Bernoulli's letter of June 7th informing him of the book from London accusing Leibniz of "plagiary".  "I have not yet seen the little English book directed against me. .... it appears that he (Newton) no more knew our calculus than Apollonius knew the algebraic calculus of Viete and Descartes." In this letter he will deny being the author of a critical review of Newton's tracts in the Arcta Eruditorum. (A lie.) *The Correspondence of Isaac Newton

1867 Nobel invented dynamite. It is from this invention that he earned the fortune that he used to endow the Nobel Prizes.*VFR

1870  Benjamin Pierce, Superintendent U. S. Coast Survey, sends letter of introduction for his son to August De Morgan, "I presume upon the unseen brotherhood of science to introduce to you my son Charles S. Peirce Esq. who is a devoted student of Logic and I think that he has original thoughts which you may regard as deserving your consideration. He carries with him a memoir which he has written upon one of the subjects of your own learned investigations... " *Universidad de Navarra

1928,  Amelia Earhart  embarked on a trans-Atlantic flight from Newfoundland to Wales; she was  the first woman to fly across the Atlantic Ocean, though as a passenger  in a plane piloted by Wilmer Stultz. In 1932, she became the first  woman to fly solo across that ocean.

BIRTHS

1714  César-François Cassini de Thury (17 June 1714 – 4 September 1784), French astronomer and geodesist (Cassini III), who continued surveying work he began while assisting his father, Jacques Cassini (Cassini II), resulting in the first topographical map of France produced by modern principles. His grandfather, Giovanni Domenico Cassini  (Cassini I) discovered four satellites of Saturn, a band on planet's  surface, and that its ring was subdivided. Cassini I was the first to  assume effective direction (1671) of the new observatory established by  the Académie Royale des Sciences in Paris, which his descendants in turn  continued. Cassini III was the first official director of the  observatory when the post was created by the king in 1771. His son was  Jean-Dominique Cassini (Cassini IV) *TIS

 Victorian picture "Leviathan of Parsonstown" *Wik
1800  William Parsons class="st">(17 June 1800 – 31 October 1867), 3rd Earl of Rosse was an Irish astronomer  who built the largest reflecting telescope of the 19th century. He  learned to polish metal mirrors (1827) and spent the next few years  building a 36-inch telescope. He later completed a giant 72-inch  telescope (1845) which he named "Leviathan," It remained the largest  ever built until decades after his death. He was the first to resolve  the spiral shape of objects - previously seen as only clouds - which  were much later identified as galaxies independent of our own Milky Way  galaxy and millions of light-years away. His first such sighting was  made in 1845, and by 1850 he had discovered 13 more. In 1848, he found  and named the Crab Nebula (because he thought it resembled a crab), by which name it is still known.*TIS

1832 Sir William Crookes, OM, FRS (17 June 1832 – 4 April 1919) was a British chemist and physicist who attended the Royal College of Chemistry, London, and worked on spectroscopy. He was a pioneer of vacuum tubes, inventing the Crookes tube.*Wik

1898 Maurits Cornelius Escher (17 June 1898 – 27 March 1972)   an artist whose works have included a considerable mathematical content.  He is known for his often mathematically inspired woodcuts, lithographs, and mezzotints. These feature impossible constructions, explorations of infinity, architecture, and tessellations. *Wik

1903 Sir. William Valance Douglas Hodge Jun 17, 2011 – 1903born.*VFR  Hodge also wrote, with Daniel Pedoe, a three-volume work Methods of Algebraic Geometry, on classical algebraic geometry, with much concrete content — illustrating though what Élie Cartan  called 'the debauch of indices', in its component notation. According  to Atiyah, this was intended to update and replace H. F. Baker's Principles of Geometry. *Wik

1906 Samuel Stanley Wilks (June 17, 1906 – March 7, 1964) was an American mathematician and academic who played an important role in the development of mathematical statistics, especially in regard to practical applications.
Born in Little Elm, Texas (Little Elm was once a quiet farm town, and today is one of the fastest growing municipalities in Texas) and raised on a farm, Wilks was educated at the University of Iowa, where he acquired his Ph.D. under Everett F. Linquist; his thesis dealt with a problem of statistical measurement in education, and was published in the Journal of Educational Psychology. Wilks became an instructor in mathematics at Princeton University in 1933; in 1938 he assumed the editorship of the journal Annals of Mathematical Statistics in place of Harry C. Carver. Wilks assembled an advisory board for the journal that included major figures in statistics and probability, among them Ronald Fisher, Jerzy Neyman, and Egon Pearson.
Wilks was named professor of mathematics and director of the Section of Mathematical Statistics at Princeton in 1944, and became chairman of the Division of Mathematics at the University in 1958. He was noted for his work on multivariate statistics and unit-weighted regression.
From the start of his career, Wilks favored a strong focus on practical applications for the increasingly abstract field of mathematical statistics; he also influenced other researchers, notably John Tukey, in a similar direction. Drawing upon the background of his thesis, Wilks worked with the Educational Testing Service in developing the standardized tests like the SAT that have had a profound effect on American education. He also worked with Walter Shewhart on statistical applications in quality control in manufacturing.
During World War II he was a consultant with the Office of Naval Research. Both during and after the War he had a profound impact on the application of statistical methods to all aspects of military planning.
The American Statistical Association named its Wilks Memorial Award in his honor.
Wilks' lambda distribution is a probability distribution related to two independent Wishart distributed variables. It is important in multivariate statistics and likelihood-ratio tests. *Wik

1908 Gunnar Af Hallstrom born. He determined the congruence axioms which Hilbert used in his famous axiomatization of geometry. *VFR

1919  William Kaye Estas  (June 17, 1919 – August 17, 2011) American psychologist, a leader in bringing mathematical methods into  psychological research, who was awarded the National Medal of Science in  1997 for "his fundamental theories of cognition and learning that  transformed the field of experimental psychology. His pioneering methods  of quantitative modeling and an insistence on rigor and precision  established the standard for modern psychological science." In his early  professional research he partnered with another pioneering psychologist  B. F. Skinner in studying animal learning and behavior. The  quantitative method they devised to measure emotional reactions is still  widely used today. From 1979, Estes focused on investigating human  memory and classification learning.

DEATHS

1994 Frank Yates FRS (May 12, 1902 – June 17, 1994) was one of the pioneers of 20th century statistics.   He was born in Manchester. He spent two years teaching mathematics to secondary school pupils before heading to Africa where he was mathematical advisor on the Gold Coast Survey. He returned to England due to ill health and met and married a chemist, Margaret Forsythe Marsden, the daughter of a civil servant.  This marriage was dissolved in 1933 and he later married Pauline Penn,  previously the partner of the well-known architect. After her death in  1976 he married Ruth Hunt, his long-time secretary.
In 1931 Yates was appointed assistant statistician at Rothamsted Experimental Station by R.A. Fisher. In 1933 he became head of statistics when Fisher went to University College London. At Rothamsted he worked on the design of experiments, including contributions to the theory of analysis of variance and originating Yates' algorithm and the balanced incomplete block design.
During World War II he worked on what would later be called operational research.
After the war he worked on sample survey design and analysis. He became an enthusiast of electronic computers, in 1954 obtaining an Elliott 401 for Rothamsted and contributing to the initial development of statistical computing. In he was awarded the Guy Medal in Gold of the Royal Statistical Society, and in 1966 he was awarded the Royal Medal of the Royal Society. He retired from Rothamsted to become a Senior Research Fellow at Imperial College London. He died in 1994, aged 92, in Harpenden.*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