Saturday 2 March 2024

On This Day in Math - March 2


Conway gate at CMS, Cambridge UK

Mathematics education is much more complicated than you expected, even though you expected it to be more complicated than you expected.
~Edward Griffith Begle

The 61st Day of the Year:The 61st Fibonacci number (2,504,730,781,961) is the smallest Fibonacci number which contains all the digits from 0 to 9 *Tanya Khovanova, Number Gossip (are there others that contain only the first 2, 3 .. 9 digits? ie 21 has 1,2 but 121393 has 1,2,3 but also a 9. Is there any that contain ONLY 1,2,3 or 1,2,3,4 etc?) 

 In 1657, Fermat challenged the mathematicians of Europe and England, "We await these solutions, which, if England or Belgic or Celtic Gaul do not produce, then Narbonese Gaul (Fermat's region) will." Among the challenges was this 500-year-old example from Bhaskara II: x^2 - 61y^2 = 1 (x, y > 0). *Prime Curios 

 Among all the primes less than 10^9, the final two digits most common is 61. 

Sixty-one has no repeat letters, and if you spell out any larger prime in English, you will never find another with no repeated letters.


1427, al-Kashi completed The Key to Arithmetic. The work was a major text intended to be used in teaching students in Samarkand, and in particular tried to give the necessary mathematics for those studying astronomy, surveying, architecture, accounting and trading. His best work was done while in Samarkand. He produced his Treatise on the Circumference in July 1424, a work in which he calculated 2π to nine sexagesimal places and translated this into sixteen decimal places. This was an achievement far beyond anything which had been obtained before, either by the ancient Greeks or by the Chinese (who achieved six decimal places in the 5th century). It would be almost 200 years before van Ceulen surpassed Al-Kashi's accuracy with 20 decimal places.
There is little doubt that al-Kashi was the leading astronomer and mathematician at Samarkand and he was called the second Ptolemy by an historian writing later in the same century.*MacTutor  

1713 The Graham/Tompion “proto-orreries” used to demonstrate the annual motion of the Earth around the Sun, the diurnal rotation of the Earth on its axis, and the revolution of the Moon around the Earth is demonstrated in the Spalding Gentlemen’s Society minutes:

Monday, March 2nd, 1713. Mr. Johnston gave the Soc. an Acct. of Mr. Tompion’s Curious Machine for explaining the Motion of the Sun, Moon & Earth according to the Copernic system. *Liba Taub, History of Science Society Newsletter

1784 Jean-Pierre Blanchard, a French balloonist, was born July 4, 1753. The Golden Age of Ballooning began on  Nov. 21, 1783, when  Pilâtre de Rozier and François d'Arlandes soared aloft in a hot-air balloon made by the Montgolfier brothers.  They launched from the  Château de la Muette just outside Paris and floated for some 5 miles.  Just over a week later, Jacques-Alexandre Charles and Nicolas Robert ascended to 3000 feet from the Tuileries in Paris, this time in a hydrogen balloon.  Blanchard was caught up immediately in balloon frenzy, designed his own hydrogen balloon, complete with "oars" to swim through the air and an always-open parachute to slow descent should the gas bag spring a leak, and headed for the skies .  He made his first ascent in a hydrogen balloon on Mar. 2, 1784, lifting off from the Champ de Mars. If there is a surviving contemporary image of that ascent, I have not seen it.

The difference between Blanchard and the Montgolfier brothers and Jacques Charles is that Blanchard was in it for the money.  He was the first barnstorming balloonist who charged admission for his ascents and seems to have given the public (who showed up by the thousands) their money's worth, especially on the first ascent, when a military student demanded to come along and attacked Blanchard and the balloon with a sword when he was refused. The somewhat bloodied Blanchard proceeded with the flight anyway, which I am sure delighted the crowd.

Seeking larger paydays, Blanchard travelled with his balloon to England in August of 1784 and began to organize public ascents there.  He made one ascent from Chelsea, for which (so it is recorded) 400,000 people showed up.  He made the ascent with an English physician, who was added to the gondola to increase local interest. An engraving recorded the event, which took place on Oct. 16, 1784.  Blanchard then ascended with another physician, John Jeffries (an ex-American, actually), on Nov. 30, 1784, and this time they wafted all the way from London to Kent. 

This set the stage for Blanchard's goal all along, to balloon across the English Channel.  Pilâtre de Rozier had the same idea; he was sitting on the other side of the channel with his hydrogen balloon, waiting for favorable winds to take him westward to Dover.  Blanchard won the battle of the winds.  He and Jeffries took off from Dover on Jan. 7, 1785.   They almost ended up in the sea, as their bag of hydrogen was providing insufficient lift, and they threw nearly everything overboard, including most of their clothes, to maintain altitude.  But the balloon for some reason recovered its buoyancy, and they made it to Calais and beyond, landing at Guines, to the great excitement of the local populace.

In 1896, Henri Becquerel reported his discovery of the penetrating rays of a uranium compound to the French Academy of Sciences. The photographic plate, fogged by these rays, showing the outline of a metal cross lying between the compound and the plate, is the first recognition of the effects later known as radioactivity. *TIS
Image of Becquerel's photographic plate which has been fogged by exposure to radiation from a uranium salt. The shadow of a metal Maltese Cross placed between the plate and the uranium salt is clearly visible.


 In 1949, the first round the world nonstop airplane flight was completed in a U.S. Air Force B-50 Superfortress bomber, the Lucky Lady II with a crew of 14 headed by Captain James Gallagher. They landed back at Carswell Air Force base, Fort Worth, Texas, which they had left on 26 Feb 1949, about 94 hours earlier. The airplane was refueled several times in midflight on its 23,452 journey. Its average speed was 249-mph. This was at the time of the Berlin Airlift and the Cold War. The flight showed that the USAF was capable of projecting air power anywhere in the world. The first jets - three U.S. Air Force B-52 Stratofortress bombers - to fly nonstop around the world - took 45 hours (16-18 Jan 1957), completing 24,325 miles at an average speed of 525-mph. *TIS

In 1972, U.S. spacecraft Pioneer 10 was launched. It passed close by Jupiter and Neptune before leaving the solar system. It is now more than six billion miles from Earth. *TIS

1836 Julius Weingarten (2 March 1836 in Berlin – 16 June 1910 in Freiburg im Breisgau) was a German mathematician. He made some important contributions to the differential geometry of surfaces, such as the Weingarten equations.*Wik

1862 Robert Allardice studied at Edinburgh University and was then appointed assistant to Professor Chrystal there. He was a founder member of the EMS and became President in 1890. He left Edinburgh to become Professor at Stanford University in California. He worked in Geometry. *SAU

1862 Boris Borisovich Golitsyn (2 Mar 1862; 17 May 1916 at age 54) (Prince) Russian physicist known for his work on methods of earthquake observations and on the construction of seismographs. He invented the first effective electromagnetic seismograph in 1906. A seismometer of this type picks up earthquake waves with a pendulum that supports a coil of insulated wire between the poles of a magnet rigidly linked to the earth. The relative motion between the magnet and the coil caused by tremors in the earth generates corresponding electric currents in the coil. The currents can be amplified to operate a pen recorder. *TIS

Golitsyn seismograph at the National Museum of Nature and Science, Tokyo, Japan **Wik

1902 Edward Uhler Condon (March 2, 1902 – March 26, 1974) was a distinguished American nuclear physicist, a pioneer in quantum mechanics, and a participant in the development of radar and nuclear weapons during World War II as part of the Manhattan Project. The Franck–Condon principle and the Slater–Condon rules are named after him.
He was the director of the National Bureau of Standards (now NIST) from 1945 to 1951. In 1946, Condon was president of the American Physical Society, and in 1953 was president of the American Association for the Advancement of Science.
During the McCarthy period, when efforts were being made to root out communist sympathizers in the United States, Edward Condon was a target of the House Un-American Activities Committee on the grounds that he was a 'follower' of a 'new revolutionary movement', quantum mechanics; Condon defended himself with a famous commitment to physics and science. During the McCarthy period, when efforts were being made to root out communist sympathizers in the United States, Edward Condon was a target of the House Un-American Activities Committee on the grounds that he was a 'follower' of a 'new revolutionary movement', quantum mechanics; Condon defended himself with a famous commitment to physics and science.
Years later, Carl Sagan reported how Condon described one encounter with a loyalty review board. A board member stated his concern: "Dr. Condon, it says here that you have been at the forefront of a revolutionary movement in physics called...quantum mechanics. It strikes this hearing that if you could be at the forefront of one revolutionary could be at the forefront of another". Condon said he replied: "I believe in Archimedes' Principle, formulated in the third century B.C. I believe in Kepler's laws of planetary motion, discovered in the seventeenth century. I believe in Newton's laws...." and continued with a catalog of scientists from earlier centuries, including the Bernoulli, Fourier, Ampère, Boltzmann, and Maxwell] He once said privately: "I join every organization that seems to have noble goals. I don't ask whether it contains Communists".*Wik

(In 1955, when he was working for Corning Glass, he finally lost his security clearance and had to resign his position to prevent Corning from losing their government contracts. Richard Nixon, smarmy and disgraceful even then, took credit for getting Condon's clearance revoked. *Linda Hall Org)

Condon became widely known in 1968 as principal author of the Condon Report, an official review funded by the United States Air Force that concluded that unidentified flying objects (UFOs) have prosaic explanations. The lunar crater Condon is named for him. *Wik

1912 Clifford Hugh Dowker (2 March 1912 in Parkhill, Western Ontario, Canada- 14 Oct 1982 in London, England) was a topologist known for his work in point-set topology and also for his contributions in category theory, sheaf theory and knot theory. *SAU


1840 (Heinrich) Wilhelm (Matthäus) Olbers(11 Oct 1758; 2 Mar 1840) was a German astronomer and physician, born in Arbergen, Germany. While practising medicine at Bremen, he calculated the orbit of the comet of 1779, discovered the minor planets (asteroids) Pallas (1802) and Vesta (1807), and discovered five comets (all but one already observed at Paris). He also invented a method for calculating the velocity of falling stars. He is also known for Olber's paradox which asks "why is the night sky dark if there are so many bright stars all around to light it?" *TIS

1885 Joseph Alfred Serret (30 Aug 1819 in Paris, France - 2 March 1885 in Versailles, France) He was a French mathematician best remembered for the Serret-Frenet formulas for a space-curve. In 1860 Serret succeeded Poinsot in the Académie des Sciences. In 1871 he retired to Versailles as his health began to deteriorate.
Serret also worked in number theory, calculus and mechanics. He edited the works of Lagrange which were published in 14 volumes between 1867 and 1892. He also edited the 5th edition of Monge in 1850.*SAU

In differential geometry, the Frenet–Serret formulas describe the kinematic properties of a particle moving along a differentiable curve in three-dimensional Euclidean space, or the geometric properties of the curve itself irrespective of any motion. More specifically, the formulas describe the derivatives of the so-called tangent, normal, and binormal unit vectors in terms of each other. 

1962 Charles-Jean Étienne Gustave Nicolas de la Vallée Poussin (14 August 1866 - 2 March 1962) was a Belgian mathematician. He is most well known for proving the Prime number theorem. This states that π(x), the number of primes ≤ x, tends to x/Lnx as x tends to infinity. (actually by this time the method of attack involved the use of Li(n), the logarithmic integral as described by Gauss).
The prime number theorem had been conjectured in the 18th century, but in 1896 two mathematicians independently proved the result, namely Hadamard (whose proof was much simpler) and Vallée Poussin. The first major contribution to proving the result was made by Chebyshev in 1848, then the proof was outlined by Riemann in 1851. The clue to two independent proofs being produced at the same time is that the necessary tools in complex analysis had not been developed until that time. In fact the solution of this major open problem was one of the major motivations for the development of complex analysis during the period from 1851 to 1896.
The king of Belgium ennobled him with the title of baron. *SAU

1978 Edward Griffith Begle (27 Nov 1914, 2 Mar 1978 at age 63) American mathematician, a topologist, who led development of "new math." When the Soviet Union launched the Sputnik satellite (1957), beating the U.S. into space, the effectiveness of science and mathematics education in American schools came under scrutiny. Begle's idea was to replace the traditional focus on mathematics as memorization and algorithmic computation. Instead, he designed a program to emphasise the fundamental importance of understanding the principles of mathematics. He directed (1958-72) the School Mathematics Study Group, funded by the National Science Foundation. SMSG produced teaching materials for all grade levels with this approach. Ultimately, initiating lasting reform through teachers was unsuccessful. *TIS Many people think the Math Wars were fought and won, or lost, somewhere in the mid to late Sixties, but those in the classroom know that the wars kept coming under new waves of attempted innovation by the NCTM and others.  My personal recollections of events in 2008 are here.

2008 Frederick Seitz (4 Jul 1911, 2 Mar 2008 at age 96) American physicist who made fundamental contributions to the theory of solids, nuclear physics, fluorescence, and crystals. As Eugene Wigner's first doctoral student, late in 1932, Seitz developed the cellular method of deriving solid-state wave functions. The widespread application of this Wigner-Seitz method to the understanding of metals is regarded as the catalyst for the formation of the field of solid-state physics in the U.S. His subsequent research focused on the theory and properties of crystals. He studied dislocations and imperfections in crystal structures, the effect of irradiation on crystals, and the process of diffusion (the movement of atoms or particles caused by random collision) in crystalline materials. *TIS 
He was an American physicist, tobacco industry lobbyist, climate change denier and former head of the United States National Academy of Sciences. (Cause of death might have been "Tottaly full of SH*T")

2009 Jacob Theodore "Jack" Schwartz (January 9, 1930 – March 2, 2009) was an American mathematician, computer scientist, and professor of computer science at the New York University Courant Institute of Mathematical Sciences. He was the designer of the SETL programming language and the NYU Ultracomputer. He founded the New York University Department of Computer Science, chairing it from 1964 to 1980.
His research interests included: the theory of linear operators, von Neumann algebras, quantum field theory, time-sharing, parallel computing, programming language design and implementation, robotics, set-theoretic approaches in computational logic, proof and program verification systems; multimedia authoring tools; experimental studies of visual perception; multimedia and other high-level software techniques for analysis and visualization of bioinformatic data.
He authored 18 books and more than 100 papers and technical reports.*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

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