## Sunday, 2 April 2017

### On This Day in Math - April 2

 12th century copy of Gerber's De geometria. *Wik

The notion of a set is too vague for the continuum hypothesis to have a positive or negative answer.
~Paul Cohen

The 92nd day of the  year; 92 is the smallest composite number for which the reverse of its digits in hexadecimal, decimal, octal, and binary are all prime.  *Prime Curios (Is there a smaller Prime that could also be prime when reversed in all these bases?)

And... There are exactly 92 Johnson Solids: The Johnson solids are the convex polyhedra having regular faces and equal edge lengths (with the exception of the completely regular Platonic solids, the "semiregular" Archimedean solids, and the two infinite families of prisms and antiprisms). *Geometry Fact ‏@GeometryFact
and a related point, The snub dodecahedron has 92 faces (80 triangular, 12 pentagonal), the most an Archimedean solid can have.

92 is the number of different arrangements of 8 non-attacking Queens on an 8 by 8 chessboard (i.e. no two Queens should share the same row, column, or diagonal)

92= 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 the sum of eight consecutive integers

92 is a palindrome in bases 6 (2326), and 7 (1617)

## EVENTS

999   Gerbert was elected Pope Sylvester II. He introduced into the West the practice of making calculations by using marked discs (apices). This method, which has nearly all the advantages of positional arithmetic, was used in abacus calculations throughout the eleventh and twelfth centuries.  *VFR More about Pope Sylvester's Abacus.

1792   U.S. Mint established. It was Jefferson who suggested decimal coinage. *VFR

1827  lead pencils were first manufactured by Joseph Dixon, who built his factory in Salem, Mass. Dixon was responsible for the development of the graphite industry in the U.S. In 1859 he patented graphite crucibles. When he died, the Joseph Dixon Crucible Company was the largest manufacturer of graphite products in the world. The first* pencil factory in the U.S. however, was started earlier by William Monroe of Concord, Mass., in Jun 1812. His first 30 pencils were bought by Benjamin Adams, a hardware dealer in Boston, Mass. The first pencils made in Great Britain (1584) used graphite from Borrowdale, Cumberland. *TIS
The Pencil, A History of Design and Circumstance

1845 Fizeau and Foucault take the first successful photograph of the sun. *VFR
"Taking advantage of a relatively new technology, the daguerreotype, French physicists Louis Fizeau and Leon Foucault made the first successful photographs of the sun on April 2, 1845. The original image, taken with an exposure of 1/60th of a second, was about 4.7 inches (12 centimeters) in diameter and captured several sunspots, visible in this reproduction. "( I find it interesting that the first photo of the sun was over five years after the first photo of the moon.  Can you think why ?)

1933 Emmy Noether's right to teach at Gottingen was withdrawn because of her Jewish ancestry. The resulting infusion of scientists played a major role in transferring mathematical leadership from Germany to the United States. See AMM, 90(1983), 717. *VFR  Thony Christie  sent me a note assuring me that it was not her religion, but her politics. Seems she had Marxist leanings. Many others in her department were discharged at the same time. After the sweeping removal of "undesirables" Minister of Education Bernhard Rust supposedly had the following conversation with  David Hilbert.
Rust: “I hear you have some problems in the mathematics department at Göttingen Herr Professor”.
Hilbert: “No, there are no problems; there is no mathematics department in Göttingen”.

1935 Sir Robert Watson-Watt received a patent on a radio device for detecting and locating an aircraft. He had submitted the idea to the Air Ministry in secret memo, Detection and location of aircraft by radio methods on Feb 12 of the same year. The method was tested on Feb 26 in a field just off the present day A5 in Northamptonshire near the village of Upper Stowe. *Wik

1948 Kurt Godel became a United States citizen. Being the diligent individual that he was, he studied the constitution carefully beforehand and felt that he had found a contradiction. On the way to the ceremony Einstein and Oskar Morgenstern tried to keep his mind on other issues, but when the judge called them into his chambers (so that he could meet Einstein) he asked Godel if he had anything to say. It was only with considerable effort that his friends were able to change the subject when Godel brought up the contradiction. *VFR
Paul O'Malley directed me to a site where a more complete version of this anecdote is spelled out by writer Jeffrey Kegler. I've included here a link to a pdf document that has a draft recollection of the story from Morgenstern.

1953 the journal Nature published a paper with this date from Francis Crick and James Watson, titled Molecular Structure of Nucleic Acids: A Structure for Deoxyribose Nucleic Acid, in which they described a double helix structure for DNA. The diagram published with the caper was captioned, "The figure is purely diagrammatic. The two ribbons symbolize the phosphate-sugar chains, and the horizontal rods the pairs of bases holding the chains together. The vertical line marks the fibre axis." *TIS

BIRTHS

1618 – Francesco Maria Grimaldi (2 April 1618 – 28 December 1663) was an Italian Jesuit priest, mathematician and physicist who taught at the Jesuit college in Bologna.
Between 1640 and 1650, working with Riccioli, he investigated the free fall of objects, confirming that the distance of fall was proportional to the square of the time taken. In astronomy, he built and used instruments to measure geological features on the Moon, and drew an accurate map or selenograph which was published by Riccioli. He was the first to make accurate observations on the diffraction of light (although by some accounts Leonardo da Vinci had earlier noted it), and coined the word 'diffraction'. Later physicists used his work as evidence that light was a wave, and Isaac Newton used it to arrive at his more comprehensive theory of light.  *Wik
Thony Christie has a nice post about his influential work in the early investigation of refraction that is well worth reading.

1888 Antonio Signorini (2 April 1888 – 23 February 1963) was an influential Italian mathematical physicist and civil engineer of the 20th century. He is known for his work in finite elasticity, thermoelasticity and for formulating the Signorini problem.
The Signorini problem is the first variational inequality problem, : it consists in finding the elastic equilibrium configuration of an anisotropic non-homogeneous elastic body, resting on a rigid frictionless surface and subject only to its mass forces. The name was coined by Gaetano Fichera to honour his teacher, Antonio Signorini: the original name coined by him is problem with ambiguous boundary conditions.   The problem was posed by Antonio Signorini during a course taught at the Istituto Nazionale di Alta Matematica in 1959. The problem was taken up, in particular, by one of his students,  Gaetano Fichera.
On the first days of January 1963, Fichera was able to give a complete proof of the existence and uniqueness of a solution for the problem with ambiguous boundary condition, which he called "Signorini problem" to honour his teacher. The preliminary note later published as Fichera 1963 was written up and submitted to Signorini exactly a week before his death: He was very satisfied to see a positive result.

1906 Shokichi Iyanaga (April 2, 1906 – June 1, 2006) was a Japanese mathematician. Iyanaga published many papers which arose through several courses such as algebraic topology, functional analysis, and geometry, which he taught. He became Professor at the University of Tokyo in 1942. It was during World War II. Towards the end of the war, many Japanese cities were bombarded and he had to find refuge in the countryside. He was busy in editing textbooks from primary and secondary schools and he continued to give courses and organise seminars.*Wik

1923 – George Spencer-Brown (born April 2, 1923, Grimsby, Lincolnshire, England,   ) is a polymath best known as the author of Laws of Form. He describes himself as a "mathematician, consulting engineer, psychologist, educational consultant and practitioner, consulting psychotherapist, author, and poet.",*Wik
In a 1976 letter to the Editor of Nature, Spencer-Brown claimed a proof of the four-color theorem, which is not computer-assisted. The preface of the 1979 edition of Laws of Form repeats that claim, and further states that the generally accepted computational proof by Appel, Haken, and Koch has 'failed' (page xii). Spencer-Brown's claimed proof of the four-color theorem has yet to find any defenders; Kauffman provides a detailed review of parts of that work. *VFR

1934  Paul Joseph Cohen (2 Apr 1934,  )American mathematician who received the Fields Medal (1966) for his fundamental work on the foundations of set theory. Cohen invented a technique called "forcing" to prove the independence in set theory of the axiom of choice and of the generalised continuum hypothesis. The continuum hypothesis problem was the first of Hilbert's famous 23 problems delivered to the Second International Congress of Mathematicians in Paris in 1900. Hilbert's famous speech The Problems of Mathematics challenged (then and now) mathematicians to solve these fundamental questions and Cohen has the distinction of solving Problem 1. He also worked on differential equations and harmonic analysis. *TIS

DEATHS

1952 Bernard(-Ferdinand) Lyot (27 Feb 1897; 2 Apr 1952 at age 55) French astronomer who invented the coronagraph (1930), an instrument which allows the observation of the solar corona when the Sun is not in eclipse. Earlier, using his expertise in optics, Lyot made a very sensitive polariscope to study polarization of light reflected from planets. Observing from the Pic du Midi Observatory, he determined that the lunar surface behaves like volcanic dust, that Mars has sandstorms, and other results on the atmospheres of the other planets. Modifications to his polarimeter created the coronagraph, with which he photographed the Sun's corona and its analyzed its spectrum. He found new spectral lines in the corona, and he made (1939) the first motion pictures of solar pro
minences.*TIS

1995 Hannes Olof Gösta Alfvén (30 May 1908, 2 Apr 1995 at age 86) was a Swedish astrophysicist who was one of the founders of the field of plasma physics (the study of ionized gases). He shared the 1970 Nobel Prize in Physics (with Frenchman Louis Néel). Alfvén was recognized “for fundamental work in magnetohydrodynamics with fruitful applications in different parts of plasma physics.” He conceived plasma cosmology as an alternative to the Big Bang theory of the origin of the universe. In the concept of plasma cosmology, the universe has no specific beginning nor has any forseeable end. Instead of a dominance by gravitational forces, the theory maintains that it is the electromagnetic forces of plasma throughout the universe that organizes the matter of the universe into its observed structure of stars. *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