**The whole form of mathematical thinking was created by Euler. It is only with the greatest of difficulty that one is able to follow the writings of any author preceding Euler, because it was not yet known how to let the formulas speak for themselves. This art Euler was the first to teach.**

Ferdinand Rudio

The 215th day of the year; There are 215 sequences of four (not necessarily distinct) integers, counting permutations of order as distinct, such that the sum of their reciprocals is 1. Obviously, one of them is 1/4+1/4+1/4+1/4=1. How many can you find?

How many solutions with four distinct integers, not counting permutations?

215

_{[10]}= 555

_{[6]}

Lagrange's theorem tells us that each positive integer can be written as a sum of four squares, but Lagrange allowed the use of zeros, such as 1

^{2}+ 1

^{2}+ 1

^{2}+ 0

^{2}=3. Allowing only positive integers, there are 57 year days that are not expressible in less than four squares. 215 is the 34th of these year days that is NOT expressible with less than four positive squares. 215 = 1

^{2}+ 3

^{2}+ 6

^{2}+ 13

^{2}.

More Math Facts for every Year Day here

**1133**The last total solar eclipse at Jerusalem took place on August 2, 1133 . The next total solar eclipses will be on August 8, 2241. *NSEC

**1641**Frenicle de Bessy proposes a problem to Fermat, Use the fact that 221 = 10

^{2}+ 11

^{2}= 5

^{2}+ 14

^{2}to find the factors of this number. Almost a century later, Euler made extensive use of the method. *Oystein Ore, Number Theory and Its History.

**1733**Benjamin Franklin suggest writers could improve their literary style if they learned a little Geometry in The Pennsylvania Gazette, August 2, 1733. "If a Writer would persuade, he should proceed gradually from Things already allow’d, to those from which Assent is yet with-held, and make their Connection manifest. .... Perhaps a Habit of using good Method, cannot be better acquired, than by learning a little Geometry or Algebra. " *Natl. Archives

**1790**The first US National Census began on this day.On March 1, the US Congress had instructed to begin on the first Monday in August.

the marshals of the several judicial districts of the United States were required to*The history and growth of the United States census

cause the number of the inhabitants within their respective districts

to be taken, omitting Indians not taxed, and distinguishing free persons,

including those bound to service for a term of year, from all

others. This separation in itself was sufficient to meet all the constitutional

requirements of the enumeration, but the aet also required

the marshals to distinguish the sex and color of free persons and free

males of 16 years and upward from those under that age;

**In 1870**, Tower Subway, the first tube railway in the world, was opened under the River Thames in London, England. Engineer James Henry Greathead used a tunnelling shield he modified from Barlow's design to bore the 6-ft diameter tunnel near the Tower of London. It opened with steam operated lifts and a 12-seat carriage shuttled from end to end by wire rope powered by a steam engine. It was not successful due to low use and frequent breakdowns, and the railway closed within three months (Nov 1870). The tunnel was converted to a foot tunnel with stairs. It was closed in 1894 when the opening of the nearby Tower Bridge made it redundant. The tunnel now holds water mains and fibre optic cables.*TIS

**1876**The dead man's hand is a two-pair poker hand, namely "aces and eights". This card combination gets its name from a legend that it was the five-card-draw hand held by Wild Bill Hickok, when he was murdered on August 2, 1876, in Saloon No. 10 at Deadwood, South Dakota. "Wild Bill" Hickok was shot and killed by a drunken stranger at a poker table in Nuttall & Mann's Saloon No. 10 in Deadwood on August 2, 1876. Hickok had come to the Black Hills to explore the gold fields there, leaving his wife in Cincinnati. High School students should be able to find the probability of getting “the Dead Man’s hand” in a five card hand delt from a standard 52 card deck. *PB

**In 1880**, Greenwich Mean Time (GMT) was adopted officially by Parliament. Greenwich had been the national centre for time since 1675. GMT was originally set-up to aid naval navigation, but was not was used on land until transportation improved. In the 1840 's with the introduction of the railways there was a need in Britain for a national time system to replace the local time adopted by major towns and cities. (

*Thony Christie wrote to tell me that Edmund Halley had used Greenwich as 0 degree on a map in 1738*)

GMT was adopted by the U.S. at noon on 18 Nov 1883 when the telegraph lines transmitted time signals to all major cities. Prior to that there were over 300 local times in the USA. GMT was adopted worldwide on 1 Nov 1884 when the met International Meridian Conference in Washington, DC, USA and 24 time zones created.*TIS "The first printed chart or map known to have used Greenwich as its Prime Meridian was published in 1738. The Bradley Meridian not only defined the Zero of longitude for the first Ordnance Survey map published in 1801, but also remains the Zero Meridian used by the Ordnance Survey today." (

*This is about six meters west of the line agreed to in 1884 which is defined by the Airy Meridian now visited regularly by thousands (pb)*) *The Greenwich Meridian

**1906 R. D. Carmichael**proved that there are no triple perfect odd numbers that are the product of three distinct prime factors in the American Mathematical Monthly. A triple perfect, or \( P_3 \) , number is a number whose divisors (including the number itself, add up to three times the number. Robert Record recognized that 120 was such a number since the sum of its aliquot parts (divisors less than itself) sum to 240. The investigation of multiply perfect numbers was most active at first among French mathematicians and they used the terms "sous-double" for the triple perfect . *L E Dickson, History of the Theory of Numbers.

**1932**Carl D. Anderson discovered the positron in 1932, for which he won the Nobel Prize for Physics in 1936. Anderson did not coin the term

*positron*, but allowed it at the suggestion of the Physical Review journal editor to which he submitted his discovery paper in late 1932 The positron was the first evidence of antimatter and was discovered when Anderson allowed cosmic rays to pass through a cloud chamber and a lead plate. A magnet surrounded this apparatus, causing particles to bend in different directions based on their electric charge. The ion trail left by each positron appeared on the photographic plate with a curvature matching the mass-to-charge ratio of an electron, but in a direction that proved its charge was positive.

Anderson wrote in retrospect that the positron could have been discovered earlier based on Chung-Yao Chao 's work, if only it had been followed up. *Wik

**1939**Albert Einstein “wrote” President F. D. Roosevelt that “Some recent work by E. Fermi and L. Szilard ... leads me to expect that the element uranium may be turned into a new and important source of energy in the immediate future. ... This new phenomenon would also lead to the construction of bombs, and it is conceivable—though much less certain—that extremely powerful bombs of a new type may be constructed.”

The letter, drafted by Fermi, Szilard, and Wigner and seems not to have actually been signed by Einstein until August 10, and was then given to Alexander Sachs, a confident of Roosevelt, who did not deliver it to him until October 30. Roosevelt quickly started the Manhattan Project. Einstein later regretted signing this letter. *(VFR & Brody & Brody); (the letter can be read at Letters of Note) They recognized the process could generate a lot of energy leading to power and possibly weapons. There was also concern the Nazi government of Germany was already searching for an atomic weapon. This letter would accomplish little more than the creation of a "Uranium Committee" with a budget of $6,000 to buy uranium and graphite for experiments.

Sir Fred Soddy's book, The Interpretation of Radium, inspired H G Wells to write The World Set Free in 1914, and he dedicated the novel to Soddy's book. Twenty years later, Wells' book set Leo Szilard to thinking about the possibility of Chain reactions, and how they might be used to create a bomb, leading to his getting a British patent on the idea in 1936. A few years later Szilard encouraged his friend, Albert Einstein , to write a letter to President Roosevelt about the potential for an atomic bomb. The prize-winning science-fiction writer, Frederik Pohl , talks about Szilard's epiphany in Chasing Science (pg 25),

".. we know the exact spot where Leo Szilard got the idea that led to the atomic bomb. There isn't even a plaque to mark it, but it happened in 1938, while he was waiting for a traffic light to change on London's Southampton Row. Szilard had been remembering H. G. Well's old science-fiction novel about atomic power, The World Set Free and had been reading about the nuclear-fission experiment of Otto Hahn and Lise Meitner, and the light bulb went on over his head."

**1971**At the end of the last EVA of the Apollo 15 mission, Commander David Scott took a few minutes to conduct a classical science experiment in front of the TV camera that had been set up just outside the LM Falcon at the Hadley Rille landing site. recreating the experiment that Galileo may have done in Pisa, he dropped a hammer and a falcon feather from approximately 1.5 Meters, and you may judge the result for your self from the video.

**2012**A blue moon month, there was another in July of 2015, and the next will be in January, 2018 and then again in March of the same year. *telegraph.co.uk

**1754 Pierre-Charles L'Enfant**(August 9, 1754 - June 14, 1825 (aged 70))French-born and educated as an architect, L'Enfant came to the U.S. as a French engineer who assisted the American Continental Army in its fight against the British during the American Revolution. Appointed by President Washington in 1791 to design the new federal city, L'Enfant designed the basic plan for Washington, D.C., based on many European cityscapes. L'Enfant was dismissed from his job in 1792 following professional disagreements and personality clashes with the three commissioners appointed by President Washington to oversee the project.*TIS

**1820 John Tyndall FRS**(2 August 1820 – 4 December 1893) was a prominent 19th century physicist. His initial scientific fame arose in the 1850s from his study of diamagnetism. Later he studied thermal radiation, and produced a number of discoveries about processes in the atmosphere. He was the first to prove the "Greenhouse Theory" of the Earth's atmosphere. Tyndall published seventeen books, which brought state-of-the-art 19th century experimental physics to a wider audience. From 1853 to 1887 he was professor of physics at the Royal Institution of Great Britain in London. *Wik

**1835 Elisha Gray**(August 2, 1835 – January 21, 1901) was a U.S. scientist and innovator who would have been known to us as the inventor of the telephone if Alexander Graham bell hadn't got to the patent office before him earlier that day, resulting in a famous legal battle. He subsequently joined Western Electric where he designed the telegraph printer, the answer-back call-box of the A.D.T. System, and the needle annunciator, among other inventions. He also goes down in history as the accidental creator of the first electronic musical instrument using his discovery of the basic single note oscillator and design of a simple loudspeaker device.*TIS

*It is interesting that Bell died on the date of Gray's birth.*

**1856 Ferdinand Rudio**(2 Aug 1856 in Wiesbaden, Germany - 21 June 1929 in Zürich, Switzerland)worked on group theory, algebra and geometry. He is best remembered for his work in the history of mathematics, in particular he wrote a major article on squaring the circle and he also wrote biographies of mathematicians.

One of his most important contributions to mathematics was editing the collected works of Euler. Rudio proposed the project in 1883 since this was the centenary of Euler's death. He continued to advocate the importance of this project and at the International Congress of Mathematicians at Zurich in 1897 he suggested it would be a suitable memorial for the year 1907 which was the bicentennial of Euler's birth. The project was not approved until 1909, twenty six years after Rudio first proposed it.

Rudio was appointed general editor for the project. He edited two volumes himself and collaborated in the editing of three more. In fact he supervised the production of over 30 volumes in his role as general editor. *SAU

**1887 Oskar Johann Viktor Anderson**(2 August 1887, Minsk, Belarus – 12 February 1960, Munich, Germany) was a German-Russian mathematician. He was most famously known for his work on mathematical statistics.Anderson was born from a German family in Minsk (now in Belarus), but soon moved to Kazan (Russia), on the edge of Siberia. His father, Nikolai Anderson, was professor in Finno-Ugric languages at the University of Kazan. His older brothers were the folklorist Walter Anderson and the astrophysicist Wilhelm Anderson. Oskar Anderson graduated from Kazan Gymnasium with a gold medal in 1906. After studying mathematics for one year at University of Kazan, he moved to St. Petersburg to study economics at the Polytechnic Institute. From 1907 to 1915, he was Aleksandr Chuprov's assistant. In 1912 he started lecturing at a commercial school in St. Petersburg. In 1918 he took on a professorship in Kiev but he was forced to flee Russia in 1920 due to the Russian Revolution, first taking a post in Budapest (Hungary) before becoming a professor at the University of Economics at Varna (Bulgaria) in 1924. In 1935 he was appointed director of the Statistical Institute for Economic Research at the University of Sofia and in 1942 he took up a full professorship of statistics at the University of Kiel, where he was joined by his brother Walter Anderson after the end of the second world war. In 1947 he took a position at the University of Munich, teaching there until 1956, when he retired.*Wik

**1902 Mina Spiegel Rees**(2 August 1902 - 25 October 1997) was an American mathematician. She was the first female President of the American Association for the Advancement of Science (1971) and head of the mathematics department of the Office of Naval Research of the United States. She was valedictorian at Hunter College High School in New York City.[1] She graduated Summa cum Laude with a math major at Hunter College in 1923. She received a masters in mathematics from Columbia University in 1925. At that time she was told unofficially that "the Columbia mathematics department was not really interested in having women candidates for Ph.D's". She started teaching at Hunter College then took a sabbatical to study for the doctorate at the University of Chicago in 1929. She earned her doctorate in 1931 with a thesis on "Division algebras associated with an equation whose group has four generators," published in the American Journal of Mathematics, Vol 54 (Jan. 1932), 51-65. Her advisor was Leonard Dickson. *Wik

She became one of the earliest female computer pioneers. Before her death in 1997, Rees would leave her mark in the worlds of computers, mathematics, and education. Rees graduated with degrees in mathematics from Hunter College and Columbia University and ran the Office of Naval Research (ONR) after World War II, where she organized work on early computers such as the Harvard Mark I. Throughout her career, she made many important contributions to the use of computers in solving applied mathematical problems and was known for her strong administrative skills and influence. *CHM

**1971 Ruth Elke Lawrence-Naimark**(2 August 1971, Bristol, UK; ) is an Associate Professor of mathematics at the Einstein Institute of Mathematics, Hebrew University of Jerusalem, and a researcher in knot theory and algebraic topology. Lawrence's 1990 paper, Homological representations of the Hecke algebra, in Communications in Mathematical Physics, introduced, among other things, certain novel linear representations of the braid group — known as Lawrence–Krammer representation. In papers published in 2000 and 2001, Daan Krammer and Stephen Bigelow established the faithfulness of Lawrence's representation. This result goes by the phrase "braid groups are linear." Outside academia, she is best known for being a child prodigy in mathematics. She passed the GCSE in Math at age five, and in 1981 she passed the Oxford University interview entrance examination in mathematics, coming first out of all 530 candidates sitting the examination, and joining St Hugh's College in 1983 at the age of just twelve.*Wik

**1823 Lazare Nicolas Marguerite, Comte Carnot**(13 May 1753 – 2 August 1823) died. Carnot is best known as a geometer. In 1803 he published Géométrie de position in which sensed magnitudes were first systematically used in geometry.*Wik

**1922 Alexander Graham Bell**(March 3, 1847 – August 2, 1922) Scottish inventor of the telephone died in Beinn Bhreagh, Nova Scotia. Born in 1847, Bell's career was influenced by his grandfather (who published The Practical Elocutionist and Stammering and Other Impediments of Speech), his father (whose interest was the mechanics and methods of vocal communication) and his mother (who was deaf). As a teenager, Alexander was intrigued by the writings of German physicist Hermann Von Helmholtz, On The Sensations of Tone. At age 23 he moved to Canada. In 1871, Bell began giving instruction in Visible Speech at the Boston School for Deaf Mutes. This background set his course in developing the transmission of voice over wires. *TIS

**1962 John Smith**graduated from Glasgow University and then stayed on as a lecturer. He taught at Campbeltown Grammar School and Dollar Academy and then became an HM Schools Inspector. *SAU

**1976 László Kalmár**(March 27, 1905 – August 2, 1976) worked on mathematical logic and theoretical computer science. He was ackowledged as the leader of Hungarian mathematical logic. *SAU

**2016 Ahmed Hassan Zewail**(February 26, 1946 – August 2, 2016) was an Egyptian-American scientist, known as the "father of femtochemistry". He was awarded the 1999 Nobel Prize in Chemistry for his work on femtochemistry and became the first Egyptian and the first Arab to win a Nobel Prize in a scientific field. He was the Linus Pauling Chair Professor of Chemistry, Professor of Physics, and the director of the Physical Biology Center for Ultrafast Science and Technology at the California Institute of Technology.

Zewail died aged 70 on the evening of August 2, 2016, after a long battle with cancer. *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

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