Harrison H1 |

But mathematics is the sister, as well as the servant, of the arts and is touched by the same madness and genius.

~Marston Morse

The 84th day of the year, with nine points equally placed around a circle there are 84 different triangles using three of these points as vertices.

*Are any of them right triangles?*

84 is the only number that is spelled with ten letters that are all different.

Litttle is known of the life of Diophantus, but this problem, supposedly on his tomb, will reveal his age.

**If you get stuck, I posted the answer at the bottom of the blog.

Keith numbers are much rarer than the primes, with only 84 Keith numbers with digits.

Here is a Numberphile video explaining Keith numbers.

A hepteract is a seven-dimensional hypercube with 84 penteract 5-faces.

**EVENTS**

**1789**Throughout his life, Jefferson was avid to keep up with the mathematical world, and to spread knowledge about it to others. How deeply he explored mathematics depended obviously on what else was happening in his life at the time, but he was always keen to pass on what he had learned to his correspondents. Staying in Paris in 1789 he was eager to pass on information about the latest work by Lagrange In a letter to Harvard President Joseph Willard on March 24, 1789 he writes, "A very remarkeable work is the 'Mechanique Analytique' of La Grange in 4to. He is allowed to be the greatest mathematician now living, and his personal worth is equal to his science. The object of his work is to reduce all the principles of Mechanics to the single one of the Equilibrium, and to give a simple formula applicable to them all. The subject is treated in the Algebraic method, without diagrams to assist the conception. My present occupation not permitting me to read any thing which requires a long and undisturbed attention, I am not able to give you the character of this work from my own examination. It has been received with great approbation in Europe." *John Fauval, Lecture at Univ of Va.

Good book about Jefferson's Scientific interests and contributons:

**1899**Ren´e Louis Baire defended his doctoral thesis on the theory of functions of a real variable. He was inﬂuential in introducing transﬁnite set theory into analysis. *VFR

**1930**Planet X was officially named Pluto on March 24, 1930: On the nights of Jan 23 and 30th of January, 1930, Tombaugh found a planet in the images that he thought was the Planet X. "The discovery made front page news around the world. The Lowell Observatory, who had the right to name the new object, received over 1000 suggestions, from "Atlas" to "Zymal". Tombaugh urged Slipher to suggest a name for the new object quickly before someone else did. Name suggestions poured in from all over the world. Constance Lowell proposed Zeus, then Lowell, and finally her own first name. These suggestions were disregarded.

The name "Pluto" was proposed by Venetia Burney (later Venetia Phair), an eleven-year-old schoolgirl in Oxford, England. Venetia was interested in classical mythology as well as astronomy, and considered the name, one of the alternate names of Hades, the Greek god of the Underworld, appropriate for such a presumably dark and cold world. She suggested it in a conversation with her grandfather Falconer Madan, a former librarian of Oxford University's Bodleian Library. Madan passed the name to Professor Herbert Hall Turner, who then cabled it to colleagues in America. *Wik

**1959**TI Demonstrates Integrated Circuit Invented by Jack Kilby:

Texas Instruments demonstrates the first integrated circuit. Its inventor, Jack Kilby (b. Nov 8, 1923), created the device to prove that resistors and capacitors could exist on the same piece of semiconductor material. His circuit consisted of a sliver of germanium with five components linked by wires. It was Fairchild's Robert Noyce, however, who filed for a patent within months of Kilby and who made the IC a commercially-viable technology. Both men are credited as co-inventors of the IC.*CHM

**1693 John Harrison**(24 Mar 1693; 24 Mar 1776 at age 83)

English horologist who invented the first practical marine chronometer, which enabled navigators to compute accurately their longitude at sea. He was prompted to begin this work after a huge reward was offered by the British government for new navigational tools to avoid further disasters at sea. John Harrison took on the scientific and academic establishment of his time and won the longitude prize through extraordinary mechanical insight, talent and determination. *TIS [The Dictionary of Scientific Biographies shows an uncertainty in the date of birth as 24 Mar(?) 1693.] See deaths below for notes on a popular biography.

**1809 Joseph Liouville**(24 Mar 1809, 8 Sep 1882) French mathematician who discovered transcendental numbers (those which are not the roots of algebraic equations having rational coefficients), and that there are infinitely many of them. He also did work in real and complex analysis, number theory, and differential geometry. His name is remembered in the Sturm-Liouville theory of differential equations that generalizes Joseph Fourier's ideas, and are important in mathematical physics. He studied celestial mechanics. Liouville founded in 1836, and edited for nearly four decades, the Journal de Mathématique which remains a leading French mathematical publication. He edited and published (1843) the manuscripts left behind upon the untimely death of Evariste Galois 22 years earlier.*TIS Liouville was one of Lord Kelvin's mathematical heroes, and he once stopped a lecture in Glascow to ask his students, "Do you know what a mathematician is?" He then wrote on the blackboard the equation

and, pointing to the board stated, A mathematician is one to whom that is as obvious as twice two are four is to you. Liouville was a mathematician." *Walter Gratzer, Eurekas and Euphorias, pg 21

**1835 Josef Stefan**(24 Mar 1835, 7 Jan 1893) Austrian physicist who proposed a law of radiation (1879) stating that the amount of energy radiated per second from a black body is proportional to the fourth power of its absolute temperature. (A black body is a theoretical object that absorbs all radiation that falls on it.) This law is known as Stefan's law or the Stefan-Bolzmann law. He also studied electricity, the kinetic theory of gases and hydrodynamics.*TIS

**1848 Jules Tannery**(March 24, 1848 – December 11, 1910) was a French mathematician who notably studied under Charles Hermite and was the PhD advisor of Jacques Hadamard.

He discovered a surface of the fourth order of which all the geodesic lines are algebraic. He was not an inventor, however, but essentially a critic and methodologist. He once remarked, "Mathematicians are so used to their symbols and have so much fun playing with them, that it is sometimes necessary to take their toys away from them in order to oblige them to think."

He notably influenced Paul Painlevé, Jules Drach, and Émile Borel to take up science.

His efforts were mainly directed to the study of the mathematical foundations and of the philosophical ideas implied in mathematical thinking.*Wik

**1892 Harold Calvin Marston Morse**(24 March 1892 in Waterville, Maine, USA - 22 June 1977 in Princeton, New Jersey, USA) developed variational theory in the large with applications to equilibrium problems in mathematical physics, a theory which is now called Morse theory and forms a vital role in global analysis*SAU

**1893 Walter Baade**(24 Mar 1893; 25 Jun 1960 at age 67) German-American astronomer who, with Fritz Zwicky, proposed that supernovae could produce cosmic rays and neutron stars (1934), and Baade made extensive studies of the Crab Nebula and its central star. During WW II blackouts of the Los Angeles area Baade used the 100-inch Hooker telescope to resolve stars in the central region of the Andromeda Galaxy for the first time. This led to his definition of two stellar populations, to the realization that there were two kinds of Cepheid variable stars, and from there to a doubling of the assumed scale of the universe. Baade and Rudolph Minkowski identified and took spectrograms of optical counterparts of many of the first-discovered radio sources, including Cygnus A and Cassiopeia A. *TIS

**1941 Joseph H. Taylor Jr**. (24 Mar 1941, )American radio astronomer and physicist who, with Russell A. Hulse, was the corecipient of the 1993 Nobel Prize for Physics for their joint discovery of the first binary pulsar (1974). This unique phenomenon, two stars orbiting each other - one of them giving off regular radio-frequency "beeps" - has been important as a deep space proving ground for Einstein's general theory of relativity. Their research group at Princeton used the 1,000 foot radio telescope at Arecibo, Puerto Rico, the largest and most sensitive in the world for catching radio waves from space. *TIS

**1948 Alice Chang**(24 March 1948 in Ci-an, China)is a Chinese American mathematician specializing in aspects of mathematical analysis ranging from harmonic analysis and partial differential equations to differential geometry. She is a professor of mathematics and chair of the department at Princeton University.*Wik Her husband Paul Yang works on a.o. differential geometry -currently Princeton U. (HT to C L O @cldm_ish)

DEATHS

**1776 John Harrison**(24 Mar 1693; 24 Mar 1776 at age 83)

English horologist who invented the first practical marine chronometer, which enabled navigators to compute accurately their longitude at sea. He was prompted to begin this work after a huge reward was offered by the British government for new navigational tools to avoid further disasters at sea. John Harrison took on the scientific and academic establishment of his time and won the longitude prize through extraordinary mechanical insight, talent and determination. *TIS

Dava Sobel's book, below, is a fun read, but it is important to point out that historians of science often find it less than satisfactory. Here is one clip from Rebekah Higgitt, an excellent young science historian at the Univ of Kent and former Curator of History of Science and Technology at the National Maritime Museum and the Royal Observatory, Greenwich. "Sobel’s book is well-done but greatly simplified journalistic history, in which she unashamedly creates a story by identifying heroes and villains, and by making astronomy and timekeeping rival rather than complementary methods for finding longitude. It has annoyed professional historians of science because it plays to some of the ‘sins’ of our field, typified by the notion of the “lone genius”, and causes angst because our preferred version of history is always richer and more complex," In a personal note she wrote, [The book] "Unfairly & inaccurately creates a villain (Maskleyne) as a foil."

**1956 Christine Mary Hamill**(July 24, 1923 – March 24, 1956) was an English mathematician who specialized in group theory and finite geometry. After receiving her Ph.D. at the University of Cambridge in 1951, she was appointed to a lectureship in the University of Sheffield and later was appointed lecturer in the University College, Ibadan, Nigeria.*Wik

**1956 Sir Edmund Taylor Whittaker**(24 Oct 1873; March 24 1956) English mathematician who made pioneering contributions to the area of the special functions, which is of particular interest in mathematical physics. Whittaker is best known work is in analysis, in particular numerical analysis, but he also worked on celestial mechanics and the history of applied mathematics and physics. He wrote papers on algebraic functions and automorphic functions. His results in partial differential equations (described as most sensational by Watson) included a general solution of the Laplace equation in three dimensions in a particular form and the solution of the wave equation. On the applied side of mathematics he was interested in relativity theory and he also worked on electromagnetic theory. *TIS

**1962 Auguste Antoine Piccard**(28 January 1884 – 24 March 1962) was a Swiss physicist, inventor and explorer. Piccard and his twin brother Jean Felix were born in Basel, Switzerland. Showing an intense interest in science as a child, he attended the Swiss Federal Institute of Technology (ETH) in Zurich, and became a professor of physics in Brussels at the Free University of Brussels in 1922, the same year his son Jacques Piccard was born. He was a member of the Solvay Congress of 1922, 1924, 1927, 1930 and 1933.

In 1930, an interest in ballooning, and a curiosity about the upper atmosphere led him to design a spherical, pressurized aluminum gondola that would allow ascent to great altitude without requiring a pressure suit. Supported by the Belgian Fonds National de la Recherche Scientifique (FNRS) Piccard constructed his gondola.

An important motivation for his research in the upper atmosphere were measurements of cosmic radiation, which were supposed to give experimental evidence for the theories of Albert Einstein, whom Piccard knew from the Solvay conferences and who was a fellow alumnus of ETH.

On May 27, 1931, Auguste Piccard and Paul Kipfer took off from Augsburg, Germany, and reached a record altitude of 15,781 m (51,775 ft). (FAI Record File Number 10634) During this flight, Piccard was able to gather substantial data on the upper atmosphere, as well as measure cosmic rays. On 18 August 1932, launched from Dübendorf, Switzerland, Piccard and Max Cosyns made a second record-breaking ascent to 16,201 m (53,153 ft). (FAI Record File Number 6590) He ultimately made a total of twenty-seven balloon flights, setting a final record of 23,000 m (75,459 ft).

In the mid-1930s, Piccard's interests shifted when he realized that a modification of his high altitude balloon cockpit would allow descent into the deep ocean. By 1937, he had designed the bathyscaphe, a small steel gondola built to withstand great external pressure. Construction began, but was interrupted by the outbreak of World War II. Resuming work in 1945, he completed the bubble-shaped cockpit that maintained normal air pressure for a person inside the capsule even as the water pressure outside increased to over 46 MPa (6,700 psi). Above the heavy steel capsule, a large flotation tank was attached and filled with a low density liquid for buoyancy. Liquids are relatively incompressible and can provide buoyancy that does not change as the pressure increases. And so, the huge tank was filled with gasoline, not as a fuel, but as flotation. To make the now floating craft sink, tons of iron were attached to the float with a release mechanism to allow resurfacing. This craft was named FNRS-2 and made a number of unmanned dives in 1948 before being given to the French Navy in 1950. There, it was redesigned, and in 1954, it took a man safely down 4,176 m (13,701 ft).

Piccard was the inspiration for Professor Cuthbert Calculus in The Adventures of Tintin by Belgian cartoonist Hergé. Piccard held a teaching appointment in Brussels where Hergé spotted his unmistakable figure in the street.

Gene Roddenberry named Captain Jean-Luc Picard in Star Trek after one or both of the twin brothers Auguste and Jean Felix Piccard, and derived Jean-Luc Picard from their names. *Wik

**1995 (Noël) Joseph (Terence Montgomery) Needham**(9 Dec 1900, 24 Mar 1995 at age 94)was an English biochemist, embryologist, and historian of science who wrote and edited the landmark history Science and Civilization in China, a remarkable multivolume study of nearly every branch of Chinese medicine, science, and technology over some 25 centuries. As head of the British Scientific Mission in China (1942-46) he worked to assure adequate liaison between Chinese scientists and technologists and their colleagues in the West. As an historian of science and technology he wanted to break through the parochial, Europe-centred views of most of his colleagues by disclosing the achievements of traditional China and the contributions made by China leading up to the scientific revolution. *TIS

**1976 Francis Dominic Murnaghan**(4 Aug 1893 in Omagh, Co. Tyrone, Ireland- 24 March 1976 in Baltimore, Maryland, USA) was an Irish mathematician, former head of the mathematics department at Johns Hopkins University. His name is attached to developments in group theory and mathematics applied to continuum mechanics (Murnaghan and Birch–Murnaghan equations of state).*SAU

* Diophantus died at 84, why else would I have it on the 84th day of the year?

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