This result is too beautiful to be false;
it is more important to have beauty in one's equations
than to have them fit experiment.
it is more important to have beauty in one's equations
than to have them fit experiment.
Paul A M Dirac
The 220th Day of the Year
220 is the smallest amicable number, paired with 284. Amicable numbers are two different numbers so related that the sum of the proper divisors of each is equal to the other. Amicable numbers were known to the Pythagoreans, who credited them with many mystical properties. (what is the next pair?)
If you add the sum of all the divisors of the first 16 numbers, you get 220.
220 is the the largest difference between two consecutive primes less than 100,000,000.
220 is the tenth tetrahedral number, the sum of the first ten triangular numbers, 1 + 3 + 6 + ... + 55 *Wikipedia
220 is a pseudo-perfect number, the sum of a subset of its proper divisors. 220 = 110 + 55 + 44 + 11. Almost all abundant numbers (the sum of its proper divisors is greater than the number) are pseudoperfect, but Not quite all. Can you find the smallest of these 'weird" abundant numbers that are not pseudoperfect.
220 is the smallest amicable number, paired with 284. Amicable numbers are two different numbers so related that the sum of the proper divisors of each is equal to the other. Amicable numbers were known to the Pythagoreans, who credited them with many mystical properties. (what is the next pair?)
If you add the sum of all the divisors of the first 16 numbers, you get 220.
220 is the the largest difference between two consecutive primes less than 100,000,000.
220 is the tenth tetrahedral number, the sum of the first ten triangular numbers, 1 + 3 + 6 + ... + 55 *Wikipedia
220 is a pseudo-perfect number, the sum of a subset of its proper divisors. 220 = 110 + 55 + 44 + 11. Almost all abundant numbers (the sum of its proper divisors is greater than the number) are pseudoperfect, but Not quite all. Can you find the smallest of these 'weird" abundant numbers that are not pseudoperfect.
220 is a tetrahedral number, the sum of the first ten triangular numbers. 220= 1 + 3 + 6 + ...+ 55
Finding a number whose reciprocal is equal to the sum of two other reciprocals is an important idea in many areas of math and science. 220 turns out to be the largest of a triple of that type, 1/220 + 1/180 = 1/99
Because 220/4 = 55, 220 = 56^2 - 54^2, If all the diagonals of a regular dodecagon are drawn, they divide the dodecagon into 220 regions.
220 is the sum of four consecutive primes. 47 + 53 + 59 + 61.
Interesting that if you multiply the first 220 composite numbers, it is a composite number that falls between a pair of twin primes. *Prime Curios
Every number less than 220 can be formed by the sum of divisors of 220 .
220 is the largest gap between consecutive primes less than 10^8.
And Derek Orr Points out that the aliquot(proper divisors) sequence for 220 does not end in 1. This was known to the ancients who described such numbers as amicable numbers. 220 and 228 are each the aliquote sum of the other. There are a few other numbers which have repeating sequences of three or more in a loop. The aliquot sequence of perfect numbers is fixed by their definition. There are other non-perfect numbers whose sequence eventually lands on a perfect number and then repeats that number infinitly (are until you stop calculating). and there are a few other numbers which have repeating sequences of three or more in a loop.
You can make a 5x5 magic square with consecutive numbers from 32 to 44, following the order of the standard 5x5 magic square.... or simply add 31 to each one in the primitive square.
220 is the sum of four consecutive primes. 47 + 53 + 59 + 61.
Interesting that if you multiply the first 220 composite numbers, it is a composite number that falls between a pair of twin primes. *Prime Curios
Every number less than 220 can be formed by the sum of divisors of 220 .
220 is the largest gap between consecutive primes less than 10^8.
And Derek Orr Points out that the aliquot(proper divisors) sequence for 220 does not end in 1. This was known to the ancients who described such numbers as amicable numbers. 220 and 228 are each the aliquote sum of the other. There are a few other numbers which have repeating sequences of three or more in a loop. The aliquot sequence of perfect numbers is fixed by their definition. There are other non-perfect numbers whose sequence eventually lands on a perfect number and then repeats that number infinitly (are until you stop calculating). and there are a few other numbers which have repeating sequences of three or more in a loop.
You can make a 5x5 magic square with consecutive numbers from 32 to 44, following the order of the standard 5x5 magic square.... or simply add 31 to each one in the primitive square.
1576 Laying of the cornerstone of Tycho Brahe’s observatory on the island of Hveen. *VFR
1667. John Evelyn records a visit to Secretary of Royal Society held in Tower of London; "Visited Mr. Oldenburg, a close prisoner in the Tower, being suspected of writing intelligence. I had an order from Lord Arlington, Secretary of State, which caused me to be admitted. This gentleman was secretary to our Society, and I am confident will prove an innocent person." *Diary of John Evelyn
It seems to have been some rash political comment in Oldenburg's own letters during the Dutch war in 1667 which led to his imprisonment for two months in the Tower of London. But he was soon rehabilitated, and resumed his tireless work for the Royal Society, continuing to manage its voluminous correspondence until his death in 1677.
1786 Standards for the decimal system of money established (in the USA). *VFR The first really popular English language arithmetic by an American born author was in 1788 when Nicholas Pike published A New and Complete System of Arithmetic, which he said was "Composed for the use of the citizens of the United States". Well, patriotism probably won't hurt sells in a new country. Pikes book carried endorsements from several noted persons, including the governor of Massachusetts, James Bowdoin, and Yale President Ezra Stiles. The book even included a copy of the Act of Congress of 1786 which created the U. S. Federal Money System with denominations of mills (1/1000 of a dollar), cents, dimes, dollars, and Eagles (ten dollars). With all this emphasis on the new USA, it seems strange that none of the problems in the book involved the new American money, but instead were based on the English system. [The 2nd edition, in 1797, includes in the (very long) title; "adapted to the Federal Currency by Nathaniel Lord, A.M.;Boston]"
1802 We have William Herschel's Diary to thank for the exact date, unfortunately, he only paraphrased the words that passed between Napoleon and Laplace, so we have to sort out the various reports of those who were not present. My favorite version is told by Thomas Levenson in his "The Hunt for Vulcan..." It goes like this:
Napoleon took a moment during the brief peace of 1802 to engage in a bit of intellectual banter. He entertained a few savants - Sir William Herschel himself, the distinguished physicist Count Rumford, his minister of the interior - a chemist by profession - Jean Antoine Chaptal, and Laplace. After engaging politenesses with Herschel, the First Consul next turned to Laplace, who had just published the third volume of Celestial Mecahanics. Released from matters of state, Napoleon delighted in putting awkward questions to his guests, and so he told his mathematical friend that he had read Newton, and saw that his great book had mentioned God often. But "I have perused yours, but failed to find his name even once." Why is that, he asked?
In the grand tradition of this story, Laplace is reported to have replied, "I have no need of that hypothesis."
the letter from Herschel
In 1854, metal bullet cartridges were patented by Smith & Wesson.*TIS Prior to this, cartridges were formed from paper. In 1776 a schoolmaster in Vienna named Felkel completed a factor table to 408,000 that was intended to be part of a larger work to reach several million. The tables were published at the expense of the Austrian government in the hope that subscriptions would pay for the cost. When the subscriptions failed to meet expectations, the printed volumes were supposedly used for cartridge paper. *Oystein Ore.. Number Theorey and Its History, pg 54
1876 Thomas Alva Edison, of Menlo Park, New Jersey, obtained patent #180,857 for a “method of preparing autographic stencils for printing,” the first mimeograph machine. *VFR Only those of us who have been in the classroom a loooong time will remember these handy machines (and their intoxicating aroma). (addendum; Charles Wells has advised me "The solvent in mimeo ink was castor oil.")
1900 Hilbert delivers his address to the International Congress of Mathematicians. Hilbert's problems form a list of twenty-three problems in mathematics published by German mathematician David Hilbert in 1900. The problems were all unsolved at the time, and several of them were very influential for 20th century mathematics. Hilbert presented only ten of the problems (1, 2, 6, 7, 8, 13, 16, 19, 21 and 22) at the Paris conference of the Second International Congress of Mathematicians, speaking on 8 August in the Sorbonne.
"Who of us would not be glad to lift the veil behind which the future is hidden..."
He had provided an extract of the speech (most unusual at that time) in French(?English?) before hand for those who were not fluent in French.
1931 George Birkhoff publishes “A Set of Postulates for Plane Geometry Based on Scale and Protractor" in Annals of Mathematics. The system has undefined elements of point and line, and undefined relations of distance and angle. (pb)
in 1932, G. D. Birkhoff created a set of four postulates of Euclidean geometry sometimes referred to as Birkhoff's axioms. These postulates are all based on basic geometry that can be confirmed experimentally with a scale and protractor. Since the postulates build upon the real numbers, the approach is similar to a model-based introduction to Euclidean geometry. Other often-used axiomizations of plane geometry are Hilbert's axioms and Tarski's axioms. Birkhoff's axiom system was utilized in the secondary-school text Basic Geometry (first edition, 1940) *Wik
1975 The term global warming was probably first used in its modern sense on 8 August 1975 in a science paper by Wally Broecker in the journal Science called "Are we on the brink of a pronounced global warming?". Broecker's choice of words was new and represented a significant recognition that the climate was warming; previously the phrasing used by scientists was "inadvertent climate modification," because while it was recognized humans could change the climate, no one was sure which direction it was going. The National Academy of Sciences first used global warming in a 1979 paper called the Charney Report, which said: "if carbon dioxide continues to increase, [we find] no reason to doubt that climate changes will result and no reason to believe that these changes will be negligible." The report made a distinction between referring to surface temperature changes as global warming, while referring to other changes caused by increased CO2 as climate change.
Global warming became more widely popular after 23 June, 1988 when NASA climate scientist James Hansen used the term in a testimony to Congress. He said: "global warming has reached a level such that we can ascribe with a high degree of confidence a cause and effect relationship between the greenhouse effect and the observed warming." His testimony was widely reported and afterward global warming was commonly used by the press and in public discourse. *Wik
1977 Derek T. Whiteside received the Sarton Medal, the highest honor that the History of Science Society can bestow, for his editorship of The Mathematical Papers of Isaac Newton. In delivering the award Richard S. Westfall said “Before Tom began, Newton’s mathematics was largely a land of myth and fable.” In his 25 years work on the papers, Whiteside has changed all that. *VFR
An account of Newton’s discovery of universal gravitation in John Conduitt’s hand. Conduitt was Newton’s assistant at the Royal Mint and married his niece Catherine Barton.
In 2007, Barbara Morgan became the first educator to safely reach space was launched on the U.S. Space Shuttle Endeavour to the International Space Station. In 1986, she was the alternate for the first teacher selected for a space mission, Christa McAuliffe (who died with six astronauts in the explosion of the Challenger space shuttle 73-sec after its launch). When the Endeavour reached orbit, Mission Control announced: “For Barbara Morgan and her crewmates, class is in session.” During the flight, Morgan spoke with students in Idaho, where she had taught elementary classes. She had astronaut training in Houston (1998) Since its previous flight in 2002, the Endeavour had a massive overhaul.*TiS
1627 Joseph Moxon (8 August 1627 - February 1691 (Royal Society archives state his death date as 28 February; the Oxford Dictionary of National Biography states that he was buried on 15 February???{I hope one of them was wrong}), hydrographer to Charles II, was an English printer of mathematical books and maps, a maker of globes and mathematical instruments, and mathematical lexicographer. He produced the first English language dictionary devoted to mathematics, "Mathematicks made easie, or a mathematical dictionary, explaining the terms of art and difficult phrases used in arithmetick, geometry, astronomy, astrology, and other mathematical sciences". In November 1678, he became the first tradesman to be elected as a Fellow of the Royal Society. *Wik Thony Christie has written that he was one of the first English Printers to print tables of Logarithms.1802 Germain Henri Hess (August 8, 1802 – November 30, 1850)Swiss-born Russian chemist whose studies of heat in chemical reactions formed the foundation of thermochemistry. He formulated an empirical law, Hess's law of constant heat summation (1840), which states that the heat evolved or absorbed in a chemical process is the same whether the process takes place in one or in several steps. It is explained by thermodynamic theory, which holds that enthalpy is a state function. Chemists have made great use of the law of Hess in establishing the heats of formation of compounds which are not easily formed from their constituent elements. His early investigations concerned minerals and the natural gas found near Baku, and he also discovered the oxidation of sugars to yield saccharic acid.*TIS
1901 Ernest Orlando Lawrence (August 8, 1901 – August 27, 1958) American physicist who was awarded the 1939 Nobel Prize for Physics for his invention of the cyclotron, the first device for the production of high energy particles. His first device, built in 1930 used a 10-cm magnet. He accelerated particles within a cyclinder at high vacuum between the poles of an electromagnetic to confine the beam to a spiral path while a high A.C. voltage increased the particle energy. Larger models built later created 8 x 104 eV beams. By colliding particles with atomic nuclei, he produced new elements and artificial radioactivity. By 1940, he had created plutonium and neptunium. He extended the use of atomic radiation into the fields of biology and medicine. Element 103 was named Lawrencium as a tribute to him.*TIS
The first cyclotron was 4 ½ inches across, so it is sometimes referred to as the 4” cyclotron, sometimes as the 5”, but it is all the same instrument. In the images above we see Lawrence holding the 4” cyclotron
 |
| *Linda Hall Org |
1902 Paul Adrien Maurice Dirac, OM, FRS (8 August 1902 – 20 October 1984) English theoretical physicist known for his work in quantum mechanics and for his theory of the spinning electron. In 1933 he shared the Nobel Prize for Physics with the Austrian physicist Erwin Schrödinger. *TIS One of my favorite Dirac anecdotes (of which there are many)
Dirac was watching Anya Kapitza knitting while he was talking physics with Peter Kapitza. A couple of hours after he left, Dirac rushed back, very excited. "You know, Anya," he said, "watching the way you were making this sweater I got interested in the topological aspect of the problem. I found that there is another way of doing it and that there are only two possible ways. One is the one you were using; another is like that. . . . " And he demonstrated the other way, using his long fingers. His newly discovered "other way," Anya informed him, is well known to women and is none other than "purling."
Douglas W Boone commented that, "Many discoveries are re-discoveries. But Dirac's naivety (supposing that purling was an innovation) is charming."
"On the other hand, he confirmed that knitting and purling are a closed set: he proved that another stitch will not be found."
Dirac is buried in Tallahassee, Florida, but a memorial plaque has been installed in Westminster Abbey, sporting the Dirac equation . The move to install the plaque drew some understandable protest from the Dean of the Abbey, since Dirac was an atheist. But he is far from being the only non-believer to be honored within its walls; Charles Darwin is actually buried there, not too far away.
1910 Johanna Weber (8 August 1910 – 24 October 2014) was a German-born British mathematician and aerodynamicist. She is best known for her contributions to the development of the Handley Page Victor bomber and the Concorde.
In 1939, Weber joined the Aerodynamics Research Institute (Aerodynamische Versuchsanstalt Göttingen) in Göttingen. She was part of a small theoretical team, and her initial training in aerodynamics consisted of wind tunnel corrections. Here she met and began her lifelong collaboration with Dietrich Küchemann.
Scientists at Institute had by then worked out a consistent theory of flow around an aircraft. This was, however, an approximation, using singularities to represent the vortices that generated lift, and Weber was given the task of improving it. She realised that some of her work overlapped with Küchemann's research on jet engine intakes. They teamed up, with Weber doing the theoretical development and wind tunnel testing, and Küchemann setting the direction of their research based on his consultation with manufacturers. Over the period of the Second World War, they created a substantial body of work.
Weber also began her research into supersonic transport. In 1955, she showed that a thin delta wing with a high angle of attack could generate sufficient lift to provide the take-off and landing capability, while simultaneously enabling efficient supersonic performance. Küchemann then advocated this wing configuration with the UK Government, resulting in the support for a Mach 2 airliner by the Supersonic Transport Advisory Committee (STAC) in 1956.
In 1961, a prototype aircraft, the Handley Page HP.115, was built to test the low speed performance of the slender delta wing.*Wik
1921 Edwin Henry Spanier (August 8, 1921 – October 11, 1996) was an American mathematician at the University of California at Berkeley, working in algebraic topology. He co-invented Spanier–Whitehead duality and Alexander–Spanier cohomology, and wrote what was for a long time the standard textbook on algebraic topology (Spanier 1981).
Spanier attended the University of Minnesota, graduating in 1941. During World War II, he served in the United States Army Signal Corps. He received his Ph.D. degree from the University of Michigan in 1947 for the thesis Cohomology Theory for General Spaces written under the direction of Norman Steenrod. After spending a year as a research fellow at the Institute for Advanced Study in Princeton, New Jersey, in 1948 he was appointed to the faculty of the University of Chicago, and then a professor at UC Berkeley in 1959. He had 17 doctoral students, including Morris Hirsch and Elon Lages Lima.
1952 Roman Juszkiewicz (born 8 August 1952, died 28 January 2012) is a Polish astrophysicist whose work is concerned with fundamental issues of cosmology.
Juszkiewicz's scientific interests include the theory of gravitational instability, origins of the large-scale structure, microwave background radiation and Big Bang nucleosynthesis. He wrote nearly one hundred research papers, mostly in the area of cosmology. Calculated results based on observed motions of pairs of galaxies, obtained in 2000 by Roman Juszkiewicz and the group led by him, aimed at estimating the amount of dark matter in the Universe, were confirmed by the recently published data from the South Pole's ACBAR detector. *Wik
1555 Oronce Fine (20 December 1494 - 8 August 1555) was a French mathematician who published a major work on mathematics and astronomy.*SAU Although primarily a popularizer, Fine was one of the most prolific authors of mathematical books of his age. He worked in a wide range of mathematical fields, including practical geometry, arithmetic, optics, gnomonics, astronomy, and instrumentalism.
He gave the value of pi to be (22 2/9)/7 in 1544. Later, he gave 47/15 and, in De rebus mathematicis (1556), he gave 3 11/78. *Wik
1979 Jacob Lionel Bakst Cooper (27 December 1915 – 8 August 1979) was a South African mathematician who worked in operator theory, transform theory, thermodynamics, functional analysis and differential equations.1979
Within operator theory, Cooper worked in the area of linear operators on real or complex Hilbert spaces. He studied the unbounded operators that arose from quantum theory, extending basic work of Frigyes Riesz and John von Neumann.
Within transform theory, he worked on the representation and uniqueness of integral transforms, on approximation, and on linear transformations that satisfy functional relations arising from representations of linear groups In this he collaborated closely with P.L. Butzer of RWTH Aachen. *Wik
1989 Taro Morishima (22 April 1903 in Wakayama, Japan - 8 Aug 1989 in Tokyo, Japan)...His passion was algebraic number theory and he had a particular love of Fermat's Last Theorem. His first paper on Fermat's Last Theorem was published in the Proceedings of the Imperial Academy of Japan in 1928. It was the first of 12 papers written in German with the title Über die Fermatsche Vermutung, with 10 of these papers being in the Proceedings of the Imperial Academy of Japan between the years 1928 and 1935. By 1935 he had published a total of 16 papers, the other 6 being: Über den Fermatschen Quotienten (1931); On recent results about Fermat's last Theorem (Japanese) (1932); Über die Einheiten und Idealklassen des Galoisschen Zahlkörpers und die Theorie der Kreiskörper der l-ten Einheitswurzein (1933); and Über die Theorie der Kreiskörper der l-ten Einheitswurzein (1935). He also published a monograph Fermat's Problem (1934) in Japanese. All his papers are full of good ideas but they are extremely difficult to read since Morishima did not present enough detail.
Morishima's high research activity seems to have greatly lessened after 1935. Although difficulties relating to World War II and the difficult years in Japan following the war were partly responsible, nevertheless it does appear that he had already reduced his research activities. He did publish the book Higher Algebra in 1940 (in Japanese) but this and one further paper on Fermat's Last Theorem (in 1952) was all in published in the 30 years between 1935 and 1965.*SAU
Morishima's high research activity seems to have greatly lessened after 1935. Although difficulties relating to World War II and the difficult years in Japan following the war were partly responsible, nevertheless it does appear that he had already reduced his research activities. He did publish the book Higher Algebra in 1940 (in Japanese) but this and one further paper on Fermat's Last Theorem (in 1952) was all in published in the 30 years between 1935 and 1965.*SAU
1996 Sir Nevill F(rancis) Mott (30 September 1905 – 8 August 1996) English physicist who shared (with P.W. Anderson and J.H. Van Vleck of the U.S.) the 1977 Nobel Prize for Physics for his independent researches on the magnetic and electrical properties of amorphous semiconductors. Whereas the electric properties of crystals are described by the Band Theory - which compares the conductivity of metals, semiconductors, and insulators - a famous exception is provided by nickel oxide. According to band theory, nickel oxide ought to be a metallic conductor but in reality is an insulator. Mott refined the theory to include electron-electron interaction and explained so-called Mott transitions, by which some metals become insulators as the electron density decreases by separating the atoms from each other in some convenient way.*TIS
2009 Muriel Kennett Wales (9 Jun 1913 – 8 August 2009) was an Irish-Canadian mathematician, and is believed to have been the first Irish-born woman to earn a PhD in pure mathematics.
She was first educated at the University of British Columbia (BA 1934, MA 1937 with the thesis Determination of Bases for Certain Quartic Number Fields). In 1941 she was awarded the PhD from the University of Toronto for the dissertation Theory Of Algebraic Functions Based On The Use Of Cycles under Samuel Beatty (himself the first person to receive a PhD in mathematics in Canada, in 1915).
She spent most of the 1940s working in atomic energy, in Toronto and Montreal, but by 1949 had retired back to Vancouver where she worked in her step-father's shipping company.*Wik
2017 Cathleen Synge Morawetz (May 5, 1923; Toronto, Canada - August 8, 2017 ) is a mathematician. Morawetz's research was mainly in the study of the partial differential equations governing fluid flow, particularly those of mixed type occurring in transonic flow. She is Professor Emerita at the Courant Institute of Mathematical Sciences at the New York University, where she has also served as director from 1984 to 1988.
Morawetz's father, John Lighton Synge was an Irish mathematician, specializing in the geometry of general relativity and her mother also studied mathematics for a time. Her childhood was split between Ireland and Canada. Both her parents were supportive of her interest in mathematics and science, and it was a woman mathematician, Cecilia Krieger, who had been a family friend for many years who later encouraged Morawetz to pursue a PhD in mathematics. Morawetz says her father was influential in stimulating her interest in mathematics, but he wondered whether her studying mathematics would be wise (suggesting they might fight like the Bernoulli brothers)
In 1981, she became the first woman to deliver the Gibbs Lecture of The American Mathematical Society, and in 1982 presented an Invited Address at a meeting of the Society for Industrial and Applied Mathematics. She was named Outstanding Woman Scientist for 1993 by the Association for Women in Science. In 1995, she became the second woman elected to the office of president of the American Mathematical Society. In 1998 she was awarded the National Medal of Science; she was the first woman to receive the medal for work in mathematics. In 2004 she received the Leroy P. Steele Prize for Lifetime Achievement. In 2006 she won the George David Birkhoff Prize in Applied Mathematics. In 2012 she became a fellow of the American Mathematical Society.*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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