Tuesday 2 April 2024

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)

Unlike 91 (and lots of other numbers) 92 can not be written as the sum of three positive squares.

Because 92 is divisible by four, it is the difference of two squares, 24^2 - 22^2


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.  The previous page at this site shows the arabic letters in use at this time, 10th-11th centuries.


1792   U.S. Mint established. It was Jefferson who suggested decimal coinage. *VFR After the U.S. Constitution was ratified, Congress passed the "Mint Act" of April 2, 1792, which established the coinage system of the United States and the dollar as the principal unit of currency. By this Act the U.S., became the first country in the world to adopt the decimal system for currency.  United States money is expressed in dollars, dimes or tenths, cents or hundredths,1 and mills or thousandths. A dime is a tenth of a dollar, a cent is a hundredth of a dollar, and a mill is a thousandth of a dollar.  

 On May 8, 1792 an act was passed to make copper coins, "On the reverse of the copper coins, there express the denomination of the coin as one-cent or half-cent."  Half cents were made by the Philadelphia mint from 1793 - 1857. That same year they discontinued both the half cents and the large cents (cents back then were about the size of a quarter) and started minting pennies that are the same size as today's pennies.

The Nickname "Pennies" comes from the English unit of money worth 1/12 of a shilling.  The English pennies was a plural term for the singular unit of pence.

The first silver dollars, precisely 1,758 of them, were coined on October 15, 1794, and were immediately delivered to Mint Director David Rittenhouse for distribution to dignitaries as souvenirs. Thereafter, until 1804, they were struck in varying quantities.

1794 Liberty head cent, and 1794 "flowing hair dollar

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 ?)

1921 Einstein made it known that he would arrive in New York harbor on April 2, 1921 for his first trip to the United States. A crowd of thousands gathered in Battery Park to await his arrival, while reporters and dignitaries interested in his theory of relativity came aboard the ship to meet Dr Einstein. City officials, including Mayor John Francis Hylan, were eager to greet Dr. Einstein. Mayor Hylan bestowed the honorary award the 'freedom of the city' on Dr. Einstein and chemist Dr. Chaim Weizmann.

Albert Einstein arrived in New York on the SS Rotterdam IV;

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

The story is told that years later while traveling across Canada, he was caught speeding with a radar gun.  As the officer was writing up the ticket, Watson-Watt said, "If I knew you were going to use it for this, I would never have invented it."

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 source 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 paper 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

1980  Microsoft Corporation announces the Z80 SoftCard--their first and (for many years) only hardware product--a microprocessor on a printed circuit board that plugged into the Apple II personal computer. It retailed for $349.00. The SoftCard allowed programs running under the CP/M operating system (included with the card, as was Microsoft BASIC) to run on the 6502-based Apple II with only minor modifications. In particular, the word processor WordStar was so popular that people bought the SoftCard and a companion "80-column card" just to run it. At one time, SoftCard brought in about half of Microsoft's total revenue. It was discontinued in 1986.


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.

In the late 1640s, he produced a large and detailed map of the moon, based on his own observations. His fellow Jesuit and Bolognese, Giambattista Riccioli, then invented a naming system for the various craters and seas, and published Grimald's map with his own names in his Almagestum Novum (1651). The map is especially noteworthy because Riccioli’s lunar nomenclature – one of several then available – turned out to be the one we still use. So the Sea of Tranquility (Mare tranquilitatis), where Apollo 11 landed, first appeared with that name on the Grimaldi/Riccioli map. *Wik

1878 Edward Kasner (April 2, 1878 – January 7, 1955) was an American mathematician who was appointed Tutor on Mathematics in the Columbia University Mathematics Department. Kasner was the first Jewish person appointed to a faculty position in the sciences at Columbia University.[1] Subsequently, he became an adjunct professor in 1906, and a full professor in 1910, at the university. Differential geometry was his main field of study. In addition to introducing the term "googol", he is known also for the Kasner metric and the Kasner polygon.

In 1940, with James R. Newman, Kasner co-wrote a non-technical book surveying the field of mathematics, called Mathematics and the Imagination (ISBN 0-486-41703-4). It was in this book that the term "googol" was first popularized:

Words of wisdom are spoken by children at least as often as by scientists. The name "googol" was invented by a child (Dr. Kasner's nine-year-old nephew) who was asked to think up a name for a very big number, namely, 1 with a hundred zeros after it. He was very certain that this number was not infinite, and therefore equally certain that it had to have a name. At the same time that he suggested "googol" he gave a name for a still larger number: "Googolplex." A googolplex is much larger than a googol, but is still finite, as the inventor of the name was quick to point out. It was suggested that a googolplex should be 1, followed by writing zeros until you get tired. This is a description of what would happen if one actually tried to write a googolplex, but different people get tired at different times and it would never do to have Carnera a better mathematician than Dr. Einstein, simply because he had more endurance. The googolplex then, is a specific finite number, with so many zeros after the 1 that the number is a googol. A googolplex is much bigger than a googol. You will get some idea of the size of this very large but finite number from the fact that there would not be enough room to write it, if you went to the farthest star, touring all the nebulae and putting down zeros every inch of the way. *Wik  


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 (April 2, 1923, Grimsby, Lincolnshire, England, August 25, 2016  ) 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

During his time at Cambridge,[clarification needed] Spencer-Brown was a chess half-blue. He held two world records as a glider pilot, and was a sports correspondent to the Daily Express.[9] He also wrote some novels and poems, sometimes employing the pen name James Keys.

Spencer-Brown died on 25 August 2016. He was buried at the London Necropolis, Brookwood, Surrey.

1934  Paul Joseph Cohen (2 Apr 1934, March 23, 2007 )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


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 prominences.*TIS

1902 Thomas Gerald Room FRS FAA (10 November 1902 – 2 April 1986) was an Australian mathematician who is best known for Room squares. He was a Foundation Fellow of the Australian Academy of Science.He studied mathematics in St John's College, Cambridge, and was a wrangler in 1923. He continued at Cambridge as a graduate student, and was elected as a fellow in 1925, but instead took a position at the University of Liverpool. He returned to Cambridge in 1927, at which time he completed his PhD, with a thesis supervised by H. F. Baker.  Room remained at Cambridge until 1935, when he moved to the University of Sydney, where he accepted the position of Chair of the Mathematics Department, a position he held until his retirement in 1968.
During World War II he worked for the Australian government, helping to decrypt Japanese communications.

Room's PhD work concerned generalizations of the Schläfli double six, a configuration formed by the 27 lines on a cubic algebraic surface.
In 1938 he published the book The geometry of determinantal loci through the Cambridge University Press. Nearly 500 pages long, the book combines methods of synthetic geometry and algebraic geometry to study higher-dimensional generalizations of quartic surfaces and cubic surfaces. It describes many infinite families of algebraic varieties, and individual varieties in these families, following a unifying principle that nearly all loci arising in algebraic geometry can be expressed as the solution to an equation involving the determinant of an appropriate matrix.
Room invented Room squares in a brief note published in 1955.

A Room square, named after Thomas Gerald Room, is an n × n array filled with n + 1 different symbols in such a way that:

Each cell of the array is either empty or contains an unordered pair from the set of symbols
Each symbol occurs exactly once in each row and column of the array
Every unordered pair of symbols occurs in exactly one cell of the array.
An example, a Room square of order seven, if the set of symbols is integers from 0 to 7:
(It is known that a Room square (or squares) exist if and only if n is odd but not 3 or 5.)

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

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