Sunday 28 April 2024

On This Day in Math - April 28

  




 
One of the principal objects of theoretical research
in my department of knowledge
is to find the point of view from which
the subject appears in its greatest simplicity.
Willard Gibbs (1839 - 1903)


The 118th day of the year. 118 is the smallest n such that the range n, n + 1, ... 4n/3 contains at least one prime from each of these forms: 4x + 1, 4x - 1, 6x + 1 and 6x - 1.

There are four unique partitions of 118 into three integers that all have the same product.  No smaller example exists.  14 × 50 × 54 = 15 × 40 × 63 = 18 × 30 × 70 = 21 × 25 × 72 = 37800.

118 plus the sum of its digits is a power, 2^7

And there are 118 partitions of the number 16.

118 in base six is "Pi-like", 314

EVENTS

1664 Trinity College, Cambridge awards a scholarship to Isaac Newton to study for his Master's Degree, thus ending his period as a lowly sizar earning his tuition by cleaning up after wealthier students. Within months his formal education would be put on hold as the college closed under the assault of the plague.




1673 Leeuwenhoeck writes his first letter to the Royal Society, which would be published the next month, May 19, in Philosophical Transactions number 94, "A Specimen of Some Observations Made by a Microscope, Contrived by M. Leewenhoeck in Holland, Lately Communicated by Dr. Regnerus de Graaf." Constantijn Huygens, who lived not far from Delft, visited Leeuwenhoek and read the letter. A week before Leeuwenhoek sent it, Huygens sent his own letter to Robert Hooke that acted as a cover letter and recommendation similar to de Graaf's letter in April. Over the rest of Leeuwenhoeck's life, the Society would publish 116 articles containing excerpts from 113 letters. *lensonleeuwenhoek



1686 Newton shows the handwritten copy of his Principia to the Royal Society. *VFR
 28 April 1686 "Dr. Vincent presented a manuscript treatise entitled Philosophiae Naturalis principia mathematica, and dedicated to the Society by Mr. Isaac Newton,..." Minutes of the RS written by Halley clerk to the Society. (It was actually only the manuscript of Book I) *Thony Christie



1693 Leibniz, in a letter to L’Hopital, explains his discovery of determinants. This work was fifty years before that of Cramer who was the real driving force in the development of determinants. Leibniz’s work had no influence because it was not published until 1850 in his Mathematische Schriften. [Smith, Source Book, p. 267] *VFR
Leibniz was convinced that good mathematical notation was the key to progress so he experimented with different notation for coefficient systems. His unpublished manuscripts contain more than 50 different ways of writing coefficient systems which he worked on during a period of 50 years beginning in 1678. Only two publications (1700 and 1710) contain results on coefficient systems and these use the same notation as in his letter to de l'Hôpital mentioned above.
Leibniz used the word 'resultant' for certain combinatorial sums of terms of a determinant. He proved various results on resultants including what is essentially Cramer's rule. He also knew that a determinant could be expanded using any column - what is now called the Laplace expansion. As well as studying coefficient systems of equations which led him to determinants, Leibniz also studied coefficient systems of quadratic forms which led naturally towards matrix theory. In the 1730's Maclaurin wrote Treatise of algebra although it was not published until 1748, two years after his death. It contains the first published results on determinants proving Cramer's rule for 2 X 2 and 3X 3 systems and indicating how the 4 X 4 case would work. Cramer gave the general rule for n X  n systems in his book Introduction to the analysis of algebraic curves (1750). It arose out of a desire to find the equation of a plane curve passing through a number of given points. The rule appears in an Appendix to the book but no proof is given] *SAU (edited and corrected with suggestions by Dave Renfro)
Dave adds:   a 715 page book (xxiii + 680 + xii pages), which is freely available on the internet. Cramer's rule itself appears in Appendix 2 (pp. 657-676). Cramer's book itself was motivated by Newton's work in classifying cubic curves, and I believe he was one of three mathematicians that devoted an extensive study to Newton's classification in the 1700s. (I don't remember who the other two were, but I believe one of them was Euler.) There is an excellent annotated and translation of Newton's work published in 1860 and freely available on the internet:

"Sir Isaac Newton's Enumeration of Lines of the Third Order, Generation of
Curves by Shadows, Organic Description of Curves, and Construction of
Equations by Curves", Translated from the Latin, with notes and examples,
by C.R.M. Talbot, 1860.
http://books.google.com/books?id=6I97byFB3v0C

http://name.umdl.umich.edu/ABQ9451.0001.001
Thanks again to Dave for the corrections.




1817 Gauss wrote the astronomer H. W. M. Olbers, “I am becoming more and more convinced that the necessity of our [Euclidean] geometry cannot be proved, at least not by human intellect nor for the human intellect.” [G. E. Martin, Foundations of Geometry and the Non-Euclidean Plane, p. 306] *VFR



1983 Greece issued a stamp portraying Archimedes and his Hydrostatic Principle








1897 In a letter to Fuchs, Dedekind expressed skepticism of a tale about Gauss attempting to light his pipe with a copy of his DA
Schering in Gottingen in response to a note from Fuchs that he had found materials related to Guass' Disquisitiones Arithmetica in the papers of Dirichlet had described a story that he had shared with Kronecker a decade before,
"The piece of Guass's Disquisitiones Arithmeticiae, which is found among Dirichlet's papers, is probably that portion which, as Dirichlet told me himself, he saved from the hand of Gauss when the latter lit his pipe with his manuscript of the Disquisitiones Arithmeticae on the day of his doctoral jubilee."
Dedekind reasoned, if Guass had saved the paper for fifty years he obviously valued it, and that if the anecdote were true, Dirichlet surely would have shared it with him as well.
*Uta Merzbach, An Early Version of Gauss's Disquisitiones Arithmeticae, Mathematical Perspectives, 1981

1930, the first U.S. motion picture of the 1.5 minute totality of an eclipse of the sun was taken from an airplane flying about 18,000 feet over at Honey Lake, California. The flight was sponsored by the U.S. Naval Observatory, and carried out by Lt. Leslie E. Gehres amd Chief Photographer J.M.F. Haase of the U.S. Navy. An attempt made during an earlier eclipse had been made by the same photographer on 10 Sep 1923, but was unsuccessful due to cloudy conditions. A U.S. Navy dirigible was first used to make a motion film of an eclipse on 24 Jan 1925. The dirigible was about 4,500 feet above a point almost 19 miles east of Monauk Point, New York, which it filmed the 2-min 5-sec eclipse. *TIS
Couldn't find the movie or stills from it, but this beauty taken from a commercial flight is pretty.




1949 The phrase "Big Bang" is created. Shortly after 6:30 am GMT on BBC's The Third Program, Fred Hoyle used the term in describing theories that contrasted with his own "continuous creation" model for the Universe. "...based on a theory that all the matter in the universe was created in one big bang ... ". *Mario Livio, Brilliant Blunders
"Suddenly, an explosive expansion began, ballooning our universe outwards faster than the speed of light. This was a period of cosmic inflation that lasted mere fractions of a second — about 10^-32 of a second, according to physicist Alan Guth’s 1980 theory that changed the way we think about the Big Bang forever." *Space.com  


Big Bang Background Radiation *ESA Planck





2004 At 11:50 AM a paper was submitted electronically to the American Mathematical Monthly which purports to be the shortest journal entry ever, essentially two words," n2 + 2 can". After some correspondence back and forth, (the journal suggested, "a line or two of explanatin might help") the paper was accepted as a "filler" in the January 2005 issue. *wfnmc.org

2012 Mountain View, Ca—January 19, 2012—
The Computer History Museum (CHM), the world’s leading institution exploring the history of computing and its ongoing impact on society, today announced its 2012 Fellow Award honorees: Edward A. Feigenbaum, pioneer of artificial intelligence and expert systems; Steve Furber and Sophie Wilson, chief architects of the ARM processor architecture; and Fernando J. Corbató, pioneer of timesharing and the Multics operating system. The four Fellows will be inducted into the Museum’s Hall of Fellows on Saturday, April 28, 2012, at a formal ceremony where Silicon Valley insiders, technology leaders, and Museum supporters will gather to celebrate the accomplishments of the Fellows and their impact on society. This year’s celebration commemorates the 25th Anniversary of the Fellow Awards and will reunite pioneers from more than two decades. *CHM
Mitchell J Feigenbaum - Niels Bohr Institute 2006.




BIRTHS
1765 Sylvestre François Lacroix (April 28, 1765, Paris – May 24, 1843, Paris) was a French mathematician. He displayed a particular talent for mathematics, calculating the motions of the planets by the age of 14. In 1782 at the age of 17 he became an instructor in mathematics at the École Gardes de Marine in Rochefort, France. He returned to Paris and taught courses in astronomy and mathematics at the Lycée. In 1787 he was the co-winner of that year's Grand Prix of the French Académie des Sciences, but was never awarded the prize. The same year the Lycée was abolished and he again moved to the provinces.
In Besançon he taught course in mathematics, physics, and chemistry at the École d'Artillerie. In 1793 he became examiner of the Artillery Corps, replacing Pierre-Simon Laplace in the post. By 1794 he was aiding his old instructor, Gaspard Monge, in creating material for a course on descriptive geometry. In 1799 he was appointed professor at the École Polytechnique. Lacroix produced most of his texts for the sake of improving his courses. The same year he was voted into the newly formed Institut National des Sciences et des Arts. In 1812 he began teaching at the Collège de France, and was appointed chair of mathematics in 1815.
During his career he produced a number of important textbooks in mathematics. Translations of these books into the English language were used in British universities, and the books remained in circulation for nearly 50 years. In 1812 Babbage set up The Analytical Society for the translation of Differential and Integral Calculus and the book was translated into English in 1816 by George Peacock. *Wik He coined the term “analytic geometry.” *VFR



1773 Robert Woodhouse (28 April 1773 – 23 December 1827) was an English mathematician. He was born at Norwich and educated at Caius College, Cambridge, (BA 1795) of which society he was subsequently a fellow. He was elected a Fellow of the Royal Society in December 1802.
His earliest work, entitled the Principles of Analytical Calculation, was published at Cambridge in 1803. In this he explained the differential notation and strongly pressed the employment of it; but he severely criticized the methods used by continental writers, and their constant assumption of non-evident principles. This was followed in 1809 by a trigonometry (plane and spherical), and in 1810 by a historical treatise on the calculus of variations and isoperimetrical problems. He next produced an astronomy; of which the first book (usually bound in two volumes), on practical and descriptive astronomy, was issued in 1812, and the second book, containing an account of the treatment of physical astronomy by Pierre-Simon Laplace and other continental writers, was issued in 1818.
He became the Lucasian Professor of Mathematics in 1820, and subsequently the Plumian professor in the university. As Plumian Professor he was responsible for installing and adjusting the transit instruments and clocks at the Cambridge Observatory. He held that position until his death in 1827.
On his death in Cambridge he was buried in Caius College Chapel.*Wik He was interested in the “metaphysics of the calculus,” i.e., questions such as the proper theoretical foundations of the calculus, the role of geometric and analytic methods, and the importance of notation. *VFR


1774 Francis Baily (28 April 1774 – 30 August 1844) was an English astronomer. He is most famous for his observations of 'Baily's beads' during an eclipse of the Sun. Bailey was also a major figure in the early history of the Royal Astronomical Society, as one of the founders and president four times.
Baily was born at Newbury in Berkshire in 1774 to Richard Baily. After a tour in the unsettled parts of North America in 1796–1797, his journal of which was edited by Augustus de Morgan in 1856, Baily entered the London Stock Exchange in 1799. The successive publication of Tables for the Purchasing and Renewing of Leases (1802), of The Doctrine of Interest and Annuities (1808), and The Doctrine of Life-Annuities and Assurances (1810), earned him a high reputation as a writer on life-contingencies; he amassed a fortune through diligence and integrity and retired from business in 1825, to devote himself wholly to astronomy.
His observations of "Baily's Beads", during an annular eclipse of the sun on 15 May 1836, at Inch Bonney in Roxburghshire, started the modern series of eclipse expeditions. The phenomenon, which depends upon the irregular shape of the moon's limb, was so vividly described by him as to attract an unprecedented amount of attention to the total eclipse of 8 July 1842, observed by Baily himself at Pavia. *Wik

Postage stamp, Great Britain, 1970, honoring the founding of the Royal Astronomical Society, featuring Francis Baily between William and John Herschel (ianridpath.com)



1831 Peter Guthrie Tait FRSE (28 April 1831 – 4 July 1901) was a Scottish mathematical physicist, best known for the seminal energy physics textbook Treatise on Natural Philosophy, which he co-wrote with Kelvin, and his early investigations into knot theory, which contributed to the eventual formation of topology as a mathematical discipline. His name is known in Graph theory mainly for Tait's conjecture.*Wik (Tait's conjecture states that "Every 3-connected planar cubic graph has a Hamiltonian cycle {along the edges} through all its vertices". His conjecture was proved wrong by counterexample in 1946 by W. T. Tutte. The problem is related to the four color theorem.) He helped develop quaternions, an advanced algebra that gave rise to vector analysis and was instrumental in the development of modern mathematical physics. *TIS
Tait’s work on knots led to a hopeful conjecture that atoms are knotted vortices (of ?) and classifications of knots would correspond to different elements. *Ted Courant
Below is The First Seven Orders of Knottiness"-table compiled by P.G. Tait in 1884 with a big hat-tip to Ben Gross@bhgross144 .




1854 Phoebe Sarah Hertha Ayrton (28 April 1854 – 23 August 1923), was a British engineer, mathematician, physicist, and inventor. Known in adult life as Hertha Ayrton, born Phoebe Sarah Marks, she was awarded the Hughes Medal by the Royal Society for her work on electric arcs and ripples in sand and water.
In 1880, Ayrton passed the Mathematical Tripos, but Cambridge did not grant her an academic degree because, at the time, Cambridge gave only certificates and not full degrees to women. Ayrton passed an external examination at the University of London, which awarded her a Bachelor of Science degree in 1881.
In 1899, she was the first woman ever to read her own paper before the Institution of Electrical Engineers (IEE). Her paper was entitled "The Hissing of the Electric Arc". Shortly thereafter, Ayrton was elected the first female member of the IEE; the next woman to be admitted to the IEE was in 1958. She petitioned to present a paper before the Royal Society but was not allowed because of her sex and "The Mechanism of the Electric Arc" was read by John Perry in her stead in 1901. Ayrton was also the first woman to win a prize from the Society, the Hughes Medal, awarded to her in 1906 in honour of her research on the motion of ripples in sand and water and her work on the electric arc. By the late nineteenth century, Ayrton's work in the field of electrical engineering was recognised more widely, domestically and internationally. At the International Congress of Women held in London in 1899, she presided over the physical science section. Ayrton also spoke at the International Electrical Congress in Paris in 1900. Her success there led the British Association for the Advancement of Science to allow women to serve on general and sectional committees. *Wik



1868 Georgy Fedoseevich Voronoy (also voronoi)(28 April 1868 – 20 November 1908) introduced what are today called Voronoi diagrams or Voronoi tessellations. Today they have wide applications to the analysis of spatially distributed data, so have become important in topics such as geophysics and meteorology. Although known under different names, the notion occurs in condensed matter physics, and in the study of Lie groups. (Two dimensional diagrams of Voronoi type were considered as early at 1644 by René Descartes and were used by Dirichlet (1850) in the investigation of positive quadratic forms. They were also studied by Voronoi (1907), who extended the investigation of Voronoi diagrams to higher dimensions. They find widespread applications in areas such as computer graphics, epidemiology, geophysics, and meteorology. A particularly notable use of a Voronoi diagram was the analysis of the 1854 cholera epidemic in London, in which physician John Snow determined a strong correlation of deaths with proximity to a particular (and infected) water pump on Broad Street. *Mathworld)  Snow mapped the distance to the nearest water pump for each residence in that area of London.
Voronoi diagram using Euclidean distance *Wik




1900 Jan Hendrik Oort (28 April 1900 – 5 November 1992) was a Dutch astronomer who made significant contributions to the understanding of the Milky Way and who was a pioneer in the field of radio astronomy. His New York Times obituary called him “one of the century's foremost explorers of the universe;” the European Space Agency website describes him as, “one of the greatest astronomers of the 20th century,” and states that he “revolutionised astronomy through his ground-breaking discoveries.” In 1955, Oort’s name appeared in Life Magazine’s list of the 100 most famous living people. He has been described as “putting the Netherlands in the forefront of postwar astronomy.”

Oort determined that the Milky Way rotates and overturned the idea that the Sun was at its center. He also postulated the existence of the mysterious invisible dark matter in 1932, which is believed to make up roughly 84.5% of the total matter in the Universe and whose gravitational pull causes “the clustering of stars into galaxies and galaxies into connecting strings of galaxies.” He discovered the galactic halo, a group of stars orbiting the Milky Way but outside the main disk. Additionally Oort is responsible for a number of important insights about comets, including the realization that their orbits “implied there was a lot more solar system than the region occupied by the planets.”

The Oort cloud, the Oort constants, and the Asteroid, 1691 Oort, were all named after him. *Wik




1906 Kurt Godel (April 28, 1906 – January 14, 1978) Austrian-born US mathematician, logician, and author of Gödel's proof. He is best known for his proof of Gödel's Incompleteness Theorems (1931) He proved fundamental results about axiomatic systems showing in any axiomatic mathematical system there are propositions that cannot be proved or disproved within the axioms of the system. In particular the consistency of the axioms cannot be proved. This ended a hundred years of attempts to establish axioms to put the whole of mathematics on an axiomatic basis.*TIS



1906 Richard Rado FRS(28 April 1906 – 23 December 1989) was a Jewish German mathematician. He earned two Ph.D.s: in 1933 from the University of Berlin, and in 1935 from the University of Cambridge. He was interviewed in Berlin by Lord Cherwell for a scholarship given by the chemist Sir Robert Mond which provided financial support to study at Cambridge. After he was awarded the scholarship, Rado and his wife left for the UK in 1933. He made contributions in combinatorics and graph theory. He wrote 18 papers with Paul Erdős. In 1964, he discovered the Rado graph (The Rado graph contains all finite and countably infinite graphs as induced subgraphs..)
In 1972, he was awarded the Senior Berwick Prize*Wik




1923 Fritz Joseph Ursell FRS (28 April 1923 – 11 May 2012) was a British mathematician noted for his contributions to fluid mechanics, especially in the area of wave-structure interactions.[5] He held the Beyer Chair of Applied Mathematics at the University of Manchester from 1961–1990, was elected Fellow of the Royal Society in 1972 and retired in 1990.
Ursell came to England as a refugee in 1937 from Germany. From 1941 to 1943 he studied at Trinity College, Cambridge, graduating with a bachelor degree in mathematics. *Wik




1928  Eugene Merle Shoemaker (April 28, 1928 – July 18, 1997)  was an American planetary geologist. Shoemaker initiated and vigorously promoted the intensive geologic training of the astronauts that made them able scientific observers and reporters on moon landings. He was a major investigator of the imaging by unmanned Ranger and Surveyor satellites which, before any Apollo landing, revealed the nature of the Moon's cover of soil and broken rock that he named the regolith. He co-discovered Comet Shoemaker–Levy 9 with his wife Carolyn S. Shoemaker and David H. Levy.  The comet, which collided with Jupiter (1994), was the first observed collision of two solar system bodies. He died in a car crash. In tribute, a small capsule of his ashes were launched in a memorial capsule aboard Lunar Prospector to the moon. *TIS
Comet Shoemaker–Levy 9 (formally designated D/1993 F2) broke apart in July 1992 and collided with Jupiter in July 1994, providing the first direct observation of an extraterrestrial collision of Solar System objects.
Shoemaker–Levy 9, disrupted comet on a collision course
(total of 21 fragments, taken in July 1994)
Gene & Carolyn Shoemaker








DEATHS
1843 William Wallace (23 September 1768, Dysart—28 April 1843, Edinburgh) worked on geometry and discovered the (so-called)
Simson line of a triangle.*SAU In geometry, given a triangle ABC and a point P on its circumcircle, the three closest points to P on lines AB, AC, and BC are collinear. The line through these points is the Simson line of P, named for Robert Simson. The concept was first published, however, by William Wallace.*Wik
 Mary Sommerville was one of his students.  He succeeded John Playfair as Math Chair in Edinburgh. He also invented a complicated type of pantograph called the eidograph.


1903 Josiah Willard Gibbs (February 11, 1839 – April 28, 1903) was an American mathematical physicist and chemist known for contributions to vector analysis and as one of the founders of physical chemistry. In 1863, He was awarded Yale University's first engineering doctorate degree. His major work was in developing thermodynamic theory, which brought physical chemistry from an empirical inquiry to a deductive science. In 1873, he published two papers concerning the fundamental nature of entropy of a system, and established the "thermodynamic surface," a geometrical and graphical method for the analysis of the thermodynamic properties of substances. His famous On the Equilibrium of Homogeneous Substances, published in 1876, established the use of "chemical potential," now an important concept in physical chemistry. *TIS
He is buried at the  Grove Street Cemetery in New Haven Connecticut, USA.

1946 Louis Jean-Baptiste Alphonse Bachelier (March 11, 1870 – April 28, 1946) was a French mathematician at the turn of the 20th century. He is credited with being the first person to model the stochastic process now called Brownian motion, which was part of his PhD thesis The Theory of Speculation, (published 1900).
His thesis, which discussed the use of Brownian motion to evaluate stock options, is historically the first paper to use advanced mathematics in the study of finance. Thus, Bachelier is considered a pioneer in the study of financial mathematics and stochastic processes. *Wik Bachelier is now recognised internationally as the father of financial mathematics, but this fame, which he so justly deserved, was a long time coming. The Bachelier Society, named in his honour, is the world-wide financial mathematics society and mathematical finance is now a scientific discipline of its own. The Society held its first World Congress on 2000 in Paris on the hundredth anniversary of Bachelier's celebrated PhD Thesis, Théorie de la Spéculation *SAU




1986 R H Bing (October 20, 1914, Oakwood, Texas – April 28, 1986, Austin, Texas) He wrote papers on general topology, particularly on metrization; planar sets where he examined in particular planar webs, cuttings and planar embeddings. He worked on topological classification of the 2-sphere, the 3-sphere, pseudo arcs, simple closed curves and Hilbert space. He studied partitions and decompositions of locally connected continua. He considered several different aspects of 3-manifolds including decompositions, maps, approximating surfaces, recognizing tameness, triangulation and the Poincaré conjecture. *SAU Oakwood had a population of 471 at the 2000 census.



1991 Paul Ernest Klopsteg (May 30, 1889 – April 28, 1991) was an American physicist. The asteroid 3520 Klopsteg was named after him and the yearly Klopsteg Memorial Award was founded in his memory.
He performed ballistics research during World War I at the US Army's Aberdeen Proving Grounds in Maryland. He applied his knowledge of ballistics to the study of archery.
He was director of research at Northwestern University Technical Institution. From 1951 through 1958 he was helped organize the National Science Foundation and was an associate director of the National Science Foundation and was president of the American Association for the Advancement of Science from 1958 through 1959.*Wik





1999 Arthur Leonard Schawlow (May 5, 1921 – April 28, 1999) was an American physicist. He is best remembered for his work on lasers, for which he shared the 1981 Nobel Prize in Physics with Nicolaas Bloembergen and Kai Siegbahn.
In 1991 the NEC Corporation and the American Physical Society established a prize: the Arthur L. Schawlow Prize in Laser Science. The prize is awarded annually to "candidates who have made outstanding contributions to basic research using lasers."
In 1951, he married Aurelia Townes, younger sister to physicist Charles Hard Townes, and together they had three children; Arthur Jr., Helen, and Edith. Arthur Jr. was autistic, with very little speech ability.
Schawlow and Professor Robert Hofstadter at Stanford, who also had an autistic child, teamed up to help each other find solutions to the condition. Arthur Jr. was put in a special center for autistic individuals, and later Schawlow put together an institution to care for people with autism in Paradise, California. It was later named the Arthur Schawlow Center in 1999, shortly before his death on the 29th of April 1999.
Schawlow died of leukemia in Palo Alto, California.*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


Saturday 27 April 2024

Parabolas, Tangents, and the Wallace-Simson Line

 Re-post from 2012, because of several visitors who ask questions that led me to refer them here.  Thought it worth re-posting.


The oft-called Simson line was attributed to Simson by Poncelet, but is now frequently known as the Wallace-Simson line since it does not actually appear in any work of Simson. (Oh go on, ask your teacher, so WHY do we still call it the Simson line at all?)
The Wallace for whom the line should more probably be named is William Wallace FRSE (23 September 1768, Dysart—28 April 1843, Edinburgh; the Scottish mathematician and astronomer who invented the eidograph, a more complicated version of the pantograph used to make scale images of drawings. He was a protegee of John Playfair, and teacher to Mary Somerville. He wrote about the line in 1799. He is also not credited for his 1807 proof of a result about polygons with an equal area, which has become the Bolyai–Gerwien theorem. He was also one of the first in England/Scotland to promote the calculus as taught on the Continent.  


The theorem says that if a triangle is inscribed in a circle, then if perpendiculars are dropped from a point on this circumcircle to the three sides of the triangle (extended as needed) the feet of these perpendiculars will lie on a straight line. It works the other way too. If you draw a straight line cutting all three sides of the triangle, perpendiculars drawn at these points of intersection will be concurrent at a point on the circumcircle.  (With dynamic geometry software, it is relatively easy for students/teachers to create a single line through three sides of a triangle, then construct perpendiculars to the three intersections and make their intersection a traceable point, the rotate the line about ther middle point of the three to get the circumcircle.)

I mentioned recently in a description of David Well's new book, Games and Mathematics, that I keep finding out new stuff. Well, he pointed out a connection between the Wallace line (he uses Simson, but I believe he knows better) and tangents of a parabola.

If you find three tangents to parabola and construct the circumcircle to the triangle formed by their mutual intersections, the circumcircle will pass through the focus of the parabola.
Tricky and cool, but what does that have to do with the the Wallace line? Well if you drop a perpendicular from the focus to ANY tangent, the foot of the perpendicular will always fall on the line tangent to the parabola at the vertex. The tangent at the vertex is a Wallace line for any triangle formed by three tangents to a parabola.


 

On This Day in Math - April 27

   




I believe that we do not know anything for certain,
but everything probably.
~ Christiaan Huygens


The 117th day of the year; 117 can be written as the difference of prime squares (112 - 22) or prime cubes (53 - 23). *Prime Curios (Can you find another number which can be expressed as both the difference of squared primes and cubed primes?)

117 is the smallest possible length for the longest side of a Heronian tetrahedron (one whose sides are all integers, and all surface areas and volume are rational). The other edges are 51, 52, 53, 80, & 84. (Are the areas / volume integral?)
*Mathworld.Wolfram



An Euler brick, named after Leonhard Euler, is a cuboid whose edge and face diagonals all have integer lengths. A primitive Euler brick is an Euler brick whose edge lengths are relatively prime.The smallest Euler brick, discovered by Paul Halcke in 1719, has edges(a,b,c) = (44, 117, 240) and face diagonals 125, 244, and 267.



EVENTS

1521 In the Philippines, Magellan became involved in a tribal war in which he was killed. His remaining ships returned to Spain in September of 1522 without their leader. *VFR

1610 Martin Horky writes to Kepler saying that Galileo's telescope was admirable for terrestrial observations,but completely failed to show others what the latter claimed for the heavens. *John McCafferty

1657 Christiaan Huygens published De ratiociniis in ludo aleae. *VFR [Download of English version printed in London in pdf]  
 In 1655 he made his first visit to Paris. He informed the mathematicians in Paris including Boulliau of his discovery and in turn Huygens learnt of the work on probability carried out in a correspondence between Pascal and Fermat. On his return to Holland Huygens wrote a small work De Ratiociniis in Ludo Aleae on the calculus of probabilities, the first printed work on the subject.




1740 The French Academie des Sciences announced that their prize on the ebb and flow of the tides would be shared between Leonhard Euler, Daniel Bernoulli, Antoine Cavalleri, one of the last of the Cartesians, and Colin Maclaurin, then Professor of Mathematics at the University of Edinburgh. [Niccol´o Guiciardini, The Development of Newtonian Calculus in Britain 1700–1800 (1989), p. 69.] *VFR

1783 In a letter to A. M. Lorgna, Gian Francesco Malfatti gave the polar equation concerning the squaring of the circle. [DSB 9, 55] Does this refer to the polar equation of the spiral of Archimedes, r = aθ? *VFR  
Malfatti and Lorgna were two of the founders of the "Società Italiana delle Scienze" (1782) and Malfatti was active in academic reform, especially in the Napoleonic period.  He is remembered for the Malfetti problem, finding three circles in a triangle that include the largest area.  Malfatti applied the distinction that circles had to all be mutually tangent and tangent to two sides of the triangle.  Later this solution was chipped apart as better solutions were found by not having the three circles all be cotangent.  
*wik 



In 1871, the American Museum of Natural History opened to the public in New York City. With a series of exhibits, the Museum's collection Went on view for the first time in the Central Park Arsenal, the Museum's original home, on the eastern side of Central Park. The museum began from the efforts of Albert Smith Bickmore, one-time student of Harvard zoologist Louis Agassiz, who was successful in his proposal to create a natural history museum in Central Park, New York City, with the support of William E. Dodge, Jr., Theodore Roosevelt, Sr., Joseph Choate, and J. Pierpont Morgan. The Governor of New York, John Thompson Hoffman, signed a bill officially creating the American Museum of Natural History on 6 Apr 1869. *TIS



1865 King George V of Hanover visited Gottingen and ordered a commemorative plate placed at the room in which Gauss had died ten years before.

In 1895, Professor Charles F. Marvin, a future chief of the Weather Bureau, began experimenting with kites for routine use in the Bureau. In 1896 he perfected his kite meteorograph, an instrument capable of measuring and recording temperature, pressure and humidity. These measurements were recorded by pens tracings on paper, or on a smoked copper sheet, which was attached to a clock rotated drum. i
n 1898, the first Weather Bureau kite was launched from Topeka, Kansas, and by the end of the year, 16 additional kite stations were attempting daily, early morning, simultaneous observations. The kites were large "box types" with dimensions of 8 feet long, 7 feet wide and 3 feet high. As many as seven kites would be attached to the kite wire during and observation. These kites were placed at regular intervals with the second 1500 feet behind the first, the third 2000 feet behind the second and from there on a spacing of 2500 feet.*TIS



1938 Lev D Landau, head of the Theoretical Division at the Institute for Physical Problems in Russia, was arrested for a leaflet which compared Stalinism to German Nazism and Italian Fascism. The remainder of the story I learned from Lautaro Vergara@VergaraLautaro on Twitter as presented below, although there is a one day difference in his date of the arrest: On 28 April 1938, Landau was arrested. Piotr Kapitsa reacted immediately by sending a letter to Joseph Stalin, but no reaction followed. On 6 April 1939, Kapitsa wrote a letter to Molotov, in which he interceded with him to pay NKVD’s (secret service) attention to “accelerate the Landau’s case.” The reaction was very rapid: in a few days Kapitsa was invited to NKVD, where he was received by a large group of Lavrentiy Beria deputies led by the Head of the NKVD Investigation Unit Kobulov. There were five large volumes of “The Case of Landau” lying on a table. Kobulov suggested that Kapitsa should look through these materials. Kapitsa instantly realized that a discussion would follow the reading of these volumes, without any guarantee of success. Then he made a counter move and asked Kobulov and everyone else present a question “Here you claim that Landau has been a German spy, which is a crime. But every crime has to have a motive. Explain it: what kind of motives could Jew Landau have to become a German spy?” At this point a silent scene followed in the spirit of Gogol’s “Government Inspector.” Kapitsa’s question nonplussed the generals, up to this moment they had not thought about motives of crimes and did not even quite grasp the meaning of this word Kobulov immediately suggested to interrupt the conversation, and in two days he himself asked Kapitsa for a letter to Beria with an appeal to “release from custody the arrested Professor of Physics Lev D. Landau, on a personal guarantee.” In two days, on 28 April 1939, exactly one year after he was arrested, Landau was released. Apparently the puzzled generals could not find an answer to Kapitsa’s question about “motives.” This story was told by Isaak M.Khalatnikov, a close collaborator of Landau, in "From the Atomic Bomb to the Landau Institute"



1961 Patent issued for multilayer circuit boards. Hazeltyne, a US firm, patented hole technology and its use in multi-layer printed circuit board assemblies. The result was that component density increased, and the newly close-spaced electrical paths changed the design of printed circuit board assemblies dramatically.



1962 The Netherlands issued a stamp showing Christiaan Huygens’ Pendulum
Clock as pictured by van Ceulen. [Scott #B365] *VFR











1994 U.S. Companies Get Aid From Government   The Clinton administration unveils a multimillion-dollar program to aid U.S. companies that make flat-panel display screens as part of an effort to help the industry stay afloat in light of Japanese domination of 95 percent of the industry. The funding comes partly from the Defense Department, for use of flat screens on military equipment. The flat-panel display market had previously been limited to laptop computers. *CHM
Japanese Assembly Plant 



2002 The last successful reception of telemetry was received from Pioneer 10 on April 27, 2002; subsequent signals were barely strong enough to detect, and provided no usable data. Pioneer 10 was launched in 1972 . Pioneer 10 crossed the orbit of Saturn in 1976 and the orbit of Uranus in 1979.
On June 13, 1983, Pioneer 10 crossed the orbit of Neptune, the outermost planet at the time, and so became the first man-made object to leave the proximity of the major planets of the solar system. The final, very weak signal from Pioneer 10 was received on January 23, 2003 when it was 12 billion kilometers (80 AU) from Earth. *Wik
Wave Goodby




BIRTHS

1791 Samuel Finley Breese Morse (27 Apr 1791; 2 Apr 1872 at age 81) was an American artist and inventor who is famous for developing the Morse Code (1838) and independently perfecting an electric telegraph (1832-35). He spent the first part of his life as a portrait artist, and did not turn to science until 1832, when he was past his 40th birthday. He was returning to America from a tour of Europe, when he met Charles T. Jackson on the boat, who inspired him about newly discovered electromagnets. From that point, Morse worked to develop apparatus for electrical communications. Backed by Congress, he erected a line spanning 40 miles between Baltimore, Maryland and Washington D.C. which had its first trial on 23 May 1843. It was ready for public use on 1 Apr 1845. *TIS



1837 Paul Albert Gordan,(27 April 1837 – 21 December 1912) king of the invariant theorists, (died: 1912). He found simpler proofs that π and e are transcendental. Emmy Noether, the first woman to get a doctorate in Germany, was his student. *VFR
He was known as "the king of invariant theory". His most famous result is that the ring of invariants of binary forms of fixed degree is finitely generated. Clebsch–Gordan coefficients are named after him and 

A famous quote attributed to Gordan about David Hilbert's proof of Hilbert's basis theorem, a result which vastly generalized his result on invariants, is "This is not mathematics; this is theology." The proof in question was the (non-constructive) existence of a finite basis for invariants. It is not clear if Gordan really said this since the earliest reference to it is 25 years after the events and after his death. Nor is it clear whether the quote was intended as criticism, or praise, or a subtle joke. Gordan himself encouraged Hilbert and used Hilbert's results and methods, and the widespread story that he opposed Hilbert's work on invariant theory is a myth (though he did correctly point out in a referee's report that some of the reasoning in Hilbert's paper was incomplete).




1843 Felix Muller He compiled the earliest mathematical calendar (that I know of)*VFR.His advisors were Weierstrass and Kummer.
In 1868 he entered Schellbach's mathematical-pedagogical seminar and in 1869 became an assistant teacher at the Friedrich-Wilhelm-Gymnasium and at a secondary school in Berlin and in 1870 a full teacher. Finally, in 1882 he became a senior teacher and in 1887 a professor at the Luisengymnasium in Berlin. He retired in 1897 and then lived as a private citizen in Oberloschwitz and on the Weißen Hirsch near Dresden . Around 1900 he lived briefly in Berlin-Steglitz .

In 1869, together with Carl Ohrtmann, he founded the Yearbook on the Advances in Mathematics based on the model of advances in physics , of which he was a member of the editorial board until 1906.

As a historian of mathematics, he was primarily concerned with the history of mathematical terminology and bibliographical work.


1875 (6th duke) (Louis-César-Victor-) Maurice de Broglie (27 Apr 1875; died 14 Jul 1960 at age 85.) a French physicist who made many contributions to the study of X rays. While in the navy (1895-1908), he first distinguished himself by installing the first French shipboard wireless. From 1912, his chief interest was X-ray spectroscopy. His “method of the rotating crystal” was an application of Bragg's “focussing effect” to eliminate spurious spectral lines. De Broglie discovered the third L absorption edge (1916), which led to the exploration of “corpuscular spectra.” During 1921-22, he worked with his brother Louis to refine Bohr's specification of the substructure of the various atomic shells. He also did pioneer work in nuclear physics and cosmic radiation.*TIS





1913 Philip Hauge Abelson (April 27, 1913 – August 1, 2004) was an American physicist, scientific editor and science writer. He proposed the gas diffusion process for separating uranium-235 from uranium-238 which was essential to the development of the atomic bomb. In collaboration with the U.S. physicist Edwin M. McMillan, he discovered a new element, later named neptunium, produced by irradiating uranium with neutrons. At the end WW II, his report on the feasibility of building a nuclear-powered submarine gave birth to the U.S. program in that field. In 1946, Abelson returned to the Carnegie Institution and pioneered in utilizing radioactive isotopes. As director of the Geophysics Laboratory of the Carnegie Institution (1953-71), he found amino acids in fossils, and fatty acids in rocks more than 1,000,000,000 years old. *TIS 





1920 Mark Alexandrovich Krasnosel'skii (April 27, 1920, Starokostiantyniv – February 13, 1997, Moscow) was a Soviet, Russian and Ukrainian mathematician renowned for his work on nonlinear functional analysis and its applications. *Wik


1932 Gian-Carlo Rota Rota (April 27, 1932 – April 18, 1999) worked on functional analysis for his doctorate and, up to about 1960, he wrote a series of papers on operator theory. Two papers in 1959-60, although still in the area of operator theory, looked at ergodic theory which is an area which requires considerable combinatorial skills. These papers seem to have led Rota away from operator theory and into the area of combinatorics. His first major work on combinatorics, which was to change the direction of the whole subject, was On the Foundations of Combinatorial Theory which Rota published in 1964.
Rota received the Steele Prize from the American Mathematical Society in 1988. The Prize citation singles out the 1964 paper On the Foundations of Combinatorial Theory as:-... the single paper most responsible for the revolution that incorporated combinatorics into the mainstream of modern mathematics. *SAU








DEATHS

1936 Karl Pearson, (27 March 1857 in London, England - 27 April 1936 in Coldharbour, Surrey, England) English mathematician, one of the founders of modern statistics. Pearson's lectures as professor of geometry evolved into The Grammar of Science (1892), his most widely read book and a classic in the philosophy of science. Stimulated by the evolutionary writings of Francis Galton and a personal friendship with Walter F.R. Weldon, Pearson became immersed in the problem of applying statistics to biological problems of heredity and evolution. The methods he developed are essential to every serious application of statistics. From 1893 to 1912 he wrote a series of 18 papers entitled Mathematical Contributions to the Theory of Evolution, which contained much of his most valuable work, including the chi-square test of statistical significance. *TIS l There is a plaque in the church at Crambe in No. Yorkshire where he was born and many of his family are buried. 

1978 Guido Stampacchia (March 26, 1922 - April 27, 1978) was a 20th century mathematician. Stampacchia was active in research and teaching throughout his career. He made key contributions to a number of fields, including calculus of variation and differential equations. In 1967 Stampacchia was elected President of the Unione Matematica Italiana. It was about this time that his research efforts shifted toward the emerging field of variational inequalities, which he modeled after boundary value problems for partial differential equations.
Stampacchia accepted the position of Professor Mathematical Analysis at the University of Rome in 1968 and returned to Pisa in 1970. He suffered a serious heart attack in early 1978 and died of heart arrest on April 27 of that year *Wik




Gerard Kitchen O'Neill (February 6, 1927 – April 27, 1992) was an American physicist and space activist. As a faculty member of Princeton University, he invented a device called the particle storage ring for high-energy physics experiments. Later, he invented a magnetic launcher called the mass driver. In the 1970s, he developed a plan to build human settlements in outer space, including a space habitat design known as the O'Neill cylinder. He founded the Space Studies Institute, an organization devoted to funding research into space manufacturing and colonization.*Wik

As a leading advocate of space colonization, he wrote in his book The High Frontier (1978), that space colonies could be the ultimate solution to such terrestrial problems as pollution, overpopulation, and the energy shortage. He designed a 1-km long sealed cylindrical space station to be built primarily of processed lunar materials and using solar energy. It would be capable of sustaining a human colony indefinitely in space between the Earth and the Moon. *TIS





1999 Rolf William Landauer (4 Feb 1927; 27 Apr 1999) German-born American physicist known for his formulation of Landauer's principle concerning the energy used during a computer's operation. Whenever the machine is resetting for another computation, bits are flushed from the computer's memory, and in that electronic operation, a certain amount of energy is lost. Thus, when information is erased, there is an inevitable "thermodynamic cost of forgetting," which governs the development of more energy-efficient computers. While engineers dealt with practical limitations of compacting ever more circuitry onto tiny chips, Landauer considered the theoretical limit, that if technology improved indefinitely, how soon will it run into the insuperable barriers set by nature?*TIS



1999 Mark David Weiser (23 Jul 1952, 27 Apr 1999 at age 46) American computer scientist and visionary who was the chief technology officer at XEROX PARC, and is remembered for developed the pioneering idea for what he referred to as “ubiquitous computing.” He coined that term in 1988 to describe a future in which personal computers will be replaced with tiny computers embedded in everyday “smart” devices (everyday items such as coffeepots and copy machines) and their connection via a network. He said, “First were mainframes, each shared by lots of people. Now we are in the personal computing era, person and machine staring uneasily at each other across the desktop. Next comes ubiquitous computing, or the age of calm technology, when technology recedes into the background of our lives.” He died at age 46, only six weeks after being diagnosed as having gastric cancer. *TIS



2002 Ruth Marianna Handler (née Mosko; November 4, 1916 – April 27, 2002) was an American inventor who created the Barbie Doll (1959), a teenage doll with a tiny waist and slender hips, and Ken, a boy doll (1961), which she named after her children. She co-founded the Mattel company in 1942. The business originally sold picture frames, and later dollhouse furniture which shortly led to specializing in toys. With a blonde ponytail and a zebra-striped swimsuit, the first "Barbie Teen-Age Fashion Model" sold over 350,000 the first year. The company soon made $100m annually. After being diagnosed with breast cancer in 1970, resulting in a mastectomy, she founded Ruthton Corporation to manufacture and market a prosthetic breast for women with a similar need.  *TIS





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