Saturday, 1 April 2017

OnThis Day in Math - April 1

first newspaper weather map - The Times, London, England

We used to think that if we knew one, we knew two, because one and one are two. We are finding that we must learn a great deal more about `and'.
~Arthur Eddington

The 91st day of the year; 10n + 91 and 10n + 93 are twin primes for n = 1, 2, 3 and 4. (For n less than ten, one of these expressions is prime for some other values of n, which?)

91 and it's reversal 19 are related to Ramanujan's Taxi-cab number, 1729 = 19x91, a palindrome product.  Note that the sum of the digits of 1729 are 19.

91 is : The sum of thirteen consecutive integers = 1 + 2 + 3 + ... + 11 + 12 + 13

The sum of one of each US coin less than a Silver Dollar is 91 cents.

       and of six consecutive squares= 12 + 22 + 32 + 42 + 52 + 62
       two consecutive cubes = 33 + 43 and the difference of two consecutive cubes = 63 - 53

1700 It was the English, it seems, who are responsible for all the mischief you will have to put up with on "April Fools Day". English pranksters begin popularizing the annual tradition of April Fool's Day by playing practical jokes on one another. * Tweet from @Historymag

1764 Annular eclipse visible in Ukkel, Belgium, on April's fool day. * Tweet from @PatrickPoitevin

1801 Gauss records in his diary that he extended his "purely analytical formula" for Easter to the Passover date. [Dunningham, p. 69] *VFR

1803 John Dalton makes the first entry in his first meteorological notebook. Dalton came to his views on atomism through his interest in meteorology. The volumes contain daily meteorological observations, vol. 1 covering from 1 Apr 1803 to 20 Mar 1816.

1824 Instrument maker Peter Barlow is paid 500 Pounds from the Board of Longitude for his "Iron Plate to improve ships compasses." Barlow had studied the "local attraction" or influence on the compass by iron on-board the ship and achieved a way of using an iron plate to minimize the deviation. *Derek Howse, Britain's Board of Longitude, The Finances.

In 1875, Sir Francis Galton published the first newspaper weather map - in The Times, London, England - now a standard feature in newspapers worldwide. He was the first to identify the anticyclone (as opposed to the cyclone), and introduced the use of charts showing areas of similar air pressure, as used on the modern weather map. Galton also devised several novel and ingenious mechanical instruments for recording information about the weather, while working at the Kew Observatory. He was also active as an explorer, anthropologist, statistician and criminologist. Galton was the first to place the study of fingerprints for identification on a scientific basis and so lay the groundwork for their use in criminal cases. *TIS

1876 The New-England Journal of Education (vol. 3, p. 161), in its weekly mathematics column, published a proof of the Pythagorean theorem by General James A. Garfield, Member of Congress from Ohio, and later President of the United States. They refer to the theorem as the pons asinorum, though today that term is reserved for Euclid I.5 which states that the base angles of an isosceles triangle are equal.
Garfield was a professor of mathematics (and languages) at Hiram College in Ohio for several years before being elected to the Ohio Senate in 1859. For more notes about his proof, and some othere tidbits on mathematical Presidents see this blog.

1939 To commemorate the New York World's Fair the U.S. issued a postage stamp picturing a trylon and perisphere. This was the 1st stamp in the world to picture geometric objects. Can you identify these shapes? They are not in my dictionaries. [Scott #853] *VFR (To answer Professor Rickey, they were photographed at the fair (above). The names were for the structures, not a particular geometric shape-The word Perisphere was coined using the Greek prefix peri-, meaning all around, about, or enclosing, surrounding. The word Trylon was coined from the phrase "triangular pylon". )

1948 Physicists Hans Bethe and George Gamow become acquainted with a bright young physicist with such an unusual name that they decided to write a joint paper, which was submitted to The Physical Review on this date. Its only unusual feature was its by-line, "by Alpher, Bethe, and Gamow." [Eves, Revisited, 268] *VFR  The article, about the possibility that the elements Carbon and Nitrogen were formed during the big  bang, which were needed for the creation of heavier elements in the centers of stars under the current theories.  The article is frequently called the "alphabet article."

1960 First televisioin picture of earth from space. It was taken by TIROS 1.*NASA History Office ‏@NASAhistory

1975 Martin Gardner announced that in November 1974, William McGregor, a graph theorist of Wappingers Falls, N.Y., discovered a counterexample to the four-color conjecture. He produced a map containing 110 regions that requires five colors. This "Mathematical Games" column provoked over one thousand letters including a threatened lawsuit from Ivan Guffvanoff III at the University of Wisconsin who destroyed his disproof after reading of this counterexample in The New York Times. The mathematics students at the University of Warwick realized that the column was an April Fool's joke, for they published this poem in Manifold, a journal of mathematical humor:
Oh Mr. Gardner,
What have you done?
You've started up a rumour
You should never have begun!
A four-colour hoax can't
Be undone so quick . . .
Oh Mr. Gardner, what
A bloody silly trick!"
For more details see Time Travel and Other Mathematical Bewilderments by Martin Gardner,
1988, pp. 134, 135
[  The actual map he claimed required five colors can be seen at the Math Forum site.]
   Gardiner also presented another Aprils Fool Joke in that article by claiming that Ramanujan had conjectured, and it had been proved, that \( e^{\pi \sqrt{163}}\) was an integer.  The "almost integer" became known as Ramanujan's constant.

1976 The Jovian–Plutonian gravitational effect, a hoax phenomenon stated to cause a noticeable short-term reduction in gravity on Earth, was an invention for April Fools' Day by the English astronomer Patrick Moore broadcast on BBC Radio 2 on 1 April 1976.
Moore stated to radio listeners that an astronomical event would take place at 9:47 a.m. that day, a conjunction of Jupiter and Pluto, which was expected to have an effect observable everywhere. As Pluto passed behind Jupiter, it would briefly cause a powerful combination of the two planets' gravitation which would noticeably decrease gravity on Earth. If listeners were to jump into the air at that exact moment, they would find they felt a floating sensation.
Soon after 9:47 on that morning, the BBC began to receive hundreds of telephone calls from people reporting they had observed the decrease in gravity. One woman who called in even stated that she and eleven friends had been sitting and had been "wafted from their chairs and orbited gently around the room".
Interestingly, in 1980, Moore collaborated with Clyde Tombaugh, the man who had discovered Pluto in 1930, to publish a new book about the dwarf planet.*Wik (ht to David Dickinson @Astroguyz)

1997 The Great Comet of 1997, comet Hale–Bopp passed perihelion. It had been iscovered on July 23, 1995, independently by two observers, Alan Hale and Thomas Bopp, both in the United States. Hale–Bopp's orbital position was calculated as 7.2 astronomical units (AU) from the Sun, placing it between Jupiter and Saturn and by far the greatest distance from Earth at which a comet had been discovered by amateurs. It was discovered at such a great distance from the Sun that it raised expectations that the comet would brighten considerably by the time it passed close to Earth. Although predicting the brightness of comets with any degree of accuracy is very difficult, Hale–Bopp met or exceeded most predictions when it passed perihelion

2005 Astronomy Picture of Day gives visual evidence of water on Mars.

Seth Ward (1 April, 1617 – 6 January 1689) was an English mathematician, astronomer, and bishop, born in Hertfordshire, and educated at Sidney Sussex College, Cambridge, where he graduated B.A. in 1636 and M.A. in 1640, becoming a Fellow in that year. In 1643 he was chosen university mathematical lecturer, but he was deprived of his fellowship next year for opposing the Solemn League and Covenant (with Isaac Barrow, John Barwick and Peter Gunning).
In the 1640s, he took instruction in mathematics from William Oughtred, and stayed with relations of Samuel Ward.
In 1649, he became Savilian professor of astronomy at Oxford University, and gained a high reputation by his theory of planetary motion. It was propounded in the works entitled In Ismaelis Bullialdi astro-nomiae philolaicae fundamenta inquisitio brevis (Oxford, 1653), against the cosmology of Ismael Boulliau, and Astronomia geometrica (London, 1656) on the system of Kepler.[4][5] About this time he was engaged in a philosophical controversy with Thomas Hobbes,[4] in fact a small part of the debate with John Webster launched by the Vindiciae academiarum he wrote with John Wilkins which also incorporated an attack on William Dell.
He was one of the original members of the Royal Society of London. In 1659, he was appointed President of Trinity College, Oxford, but not having the statutory qualifications he resigned in 1660.*Wik

1640 Georg Mohr (also Jorgen)(April 1, 1640 – January 26, 1697)
His only original contribution to geometry was the proof that any geometric construction which can be done with compass and straightedge can also be done with compasses alone, a result now known as the Mohr–Mascheroni theorem. He published his proof in the book Euclides Danicus, Amsterdam, 1672.
In Denmark the Georg Mohr Competition is a mathematics competition aimed at mathematics students interested in secondary education. The purpose of Georg Mohr contest is to stimulate interest in mathematics by challenging the brightest students with assignments in severity beyond that they encounter in their daily education. The contest also functions as a step in the selection of participants to the IMO, the International Mathematics Olympiad. *Wik

1644 Otto Mencke (22 March (OS) April 1, 1644 – 18 Jan (OS) 29 Jan 1707) was a 17th-century German philosopher and scientist. He obtained his doctorate at the University of Leipzig in 1666 with a thesis entitled: Ex Theologia naturali — De Absoluta Dei Simplicitate, Micropolitiam, id est Rempublicam In Microcosmo Conspicuam.
He is notable as being the founder of the very first scientific journal in Germany, established 1682, entitled: Acta Eruditorum. *Wik

1776 Sophie Germain (1 Apr 1776; died 27 Jun 1831 at age 55) French mathematician who is known for her work in number theory and contributions to the applied mathematics of acoustics and elasticity. Germain was self-taught from books, and from lecture notes supplied by male friends attending the Ecole Polytechnique which she, as a woman, was not permitted to attend. Using a male pseudonym, M. LeBlanc,{"In describing the honourable mission I charged him with, M. Pernety informed me that he made my name known to you. This leads me to confess that I am not as completely unknown to you as you might believe, but that fearing the ridicule attached to a female scientist, I have previously taken the name of M. LeBlanc in communicating to you those notes that, no doubt, do not deserve the indulgence with which you have responded." Letter to Gauss (1807)} She corresponded with Lagrange who recognized her skill, and subsequently sponsored her work. She accomplished a limited proof of Fermat's last theorem, for any prime under 100 where certain conditions were met. In 1816, she won a prize sponsored by Napoleon for a mathematical explanation of Chladni figures, the vibration of elastic plates. She died at age 55, from breast cancer.*TIS She worked in several areas of mathematics and science, including number theory. She proved Fermat's Last Theorem for exponents less than 100. In 1816 she won the Prix Bordin for her work on vibrations of elastic plates. Naturally, she was the first woman to win this prize. The competition question had be first set in 1811, and Germain was the only entry. In the reopened competitions of 1813 she was again the only entry, and she received an honorable mention. In the 1815 competition she was deemed worthy of the prize. *WM

1801 Henry Perigal, Jr. FRAS MRI (1 April 1801 – 6 June 1898) was a British stockbroker and amateur mathematician, known for his dissection-based proof of the Pythagorean theorem and for his unorthodox belief that the moon does not rotate.
In his booklet Geometric Dissections and Transpositions (London: Bell & Sons, 1891) Perigal provided a proof of the Pythagorean theorem based on the idea of dissecting two smaller squares into a larger square. The five-piece dissection that he found may be generated by overlaying a regular square tiling whose prototile is the larger square with a Pythagorean tiling generated by the
two smaller squares. Perigal had the same dissection printed on his business cards, and it also appears on his tombstone.

As well as being interested in mathematics, Perigal was an accomplished lathe worker, and made models of mathematical curves for Augustus De Morgan. He believed (falsely) that the moon does not rotate with respect to the fixed stars, and used his knowledge of curvilinear motion in an attempt to demonstrate this belief to others. *Wik

1874 Ernest William Barnes (1 April 1874 in Birmingham, England - 29 Nov 1953 in Sussex, England) English mathematician and theologian
In all, Barnes wrote 29 mathematical papers during the years 1897-1910. His early work was concerned with various aspects of the gamma function, including generalisations of this function given by the so-called Barnes G-function, which satisfies the equation


and to the double gamma function. Barnes next turned his attention to the theory of integral functions, where, in a series of papers, he investigated their asymptotic structure. He also considered second-order linear difference equations connected with the hypergeometric functions. In the last five of his papers dealing with the hypergeometric functions, Barnes made extensive use of the integrals studied by Mellin in which the integral involves gamma functions of the variable of integration. It was in these papers that he brought to the attention of British mathematicians the power and simplicity associated with these integrals, and which now bear the name Mellin-Barnes integrals. His last mathematical paper, published in 1910, was a short and elegant demonstration of a previously known result of Thomae concerning a transformation of a generalised hypergeometric function of unit argument into a more rapidly convergent function of the same kind. *SAU
He was educated at King Edward's School, Birmingham and Trinity College, Cambridge. He was Master of the Temple from 1915 to 1919. He was made Bishop of Birmingham in 1924. Barnes was perhaps the best known liberal bishop of his time, identified with the modernist or broad church movement. His episcopate was marked by continual controversy. His book The Rise of Christianity (1947) attacked many Christian claims, including the Virgin Birth and the bodily Resurrection of Christ.[9] This led to calls that he should resign as a bishop. This Barnes refused to do. Earlier he had written "Should Such a Faith Offend?" (1927) and "Scientific Theory and Religion" (1933), and he was a contributor to 18 other books. His "Gorilla sermons", in which he promoted a Darwinian integration into theology, were famous throughout the country. *Wik

1895 Alexander Craig Aitken (1 April 1895 in Dunedin, New Zealand - 3 Nov 1967 in Edinburgh, Scotland) He was asked to turn 4/47 into a decimal. After four seconds he answered, giving one digit every three-quarters of a second: `Point 08510638297872340425531914.' He stopped there|after 24 seconds, discussed the matter for a minute, and then started up again. `Yes, 191489. I can get that.' Five-second pause. `361702127659574468. Now that's the repeating point. It starts again at 085. So, if that's 46 places, I'm right.' " Exercise: Check this calculation on your hand calculator. Quoted from The Body by Anthony Smith, NY: Walker & amp; Co., 1968, p. 320. *VFR [Most hand calculators won't show all of the decimal places.. a nice property of repeating fractions can help uncover the rest.]

1898 – William James Sidis(April 1, 1898 – July 17, 1944) an American child prodigy with exceptional mathematical and linguistic abilities. He became famous first for his precocity, and later for his eccentricity and withdrawal from the public eye. He avoided mathematics entirely in later life, writing on other subjects under a number of pseudonyms. The difficulties Sidis encountered in dealing with the social structure of a collegiate setting may have shaped opinion against allowing such children to rapidly advance through higher education in his day.*Wik

1932 Norman Abramson (1 Apr 1932, )American computer scientist who created ALOHANET, the first modern data network, which formed the basis of the protocols essential in the Ethernet now in wide use. It opened in 1970, operating at 9600 bits per second, using radio to provide a wireless packet-switched data network between several Hawaii islands. Its innovations included the first packet radio sensors, the first packet radio repeaters, the first satellite packet network and the first radio access to the Internet. Abramson's U.S. patents include the first patent for CRC redundancy checks to provide data error control technique (No. 3,114,130), and the first patent issued for the design of burst errors in digital systems (No. 3,163,848).*TIS

1947 Alain Connes (1 Apr 1947, )French mathematician won the 1982 Fields Medal (awarded in 1983) for his work in operator theory. His most remarkable contributions are (1)general classification and a structure theorem for factors of type III, obtained in his thesis (1973); (2) classification of automorphisms of the hyperfinite factor, which served as a preparation for the next contribution; (3) classification of injective factors; and (4) application of the theory of C*-algebras to foliations and differential geometry in general. Connes' recent work has been on noncommutative geometry and he has studied applications to theoretical physics *TIS

1820 Rev. Isaac Milner FRS (11 January 1750 – 1 April 1820) was a mathematician, an inventor, the President of Queens' College, Cambridge and Lucasian Professor of Mathematics.
He began his education at a grammar school in Leeds in 1756, but this ended in 1760 with the death of his father. He was apprenticed as a weaver, reading the classics when time permitted, until his elder brother, Joseph Milner, provided him with an opportunity. Joseph was offered the mastership at Hull's grammar school and invited Isaac to become the institution's usher.
Through the patronage of his brother, Milner was subsequently freed from his duties in Hull and entered Queens' College, Cambridge, as a sizar in 1770. He graduated BA as senior wrangler in 1774, winning the Smith's first prize.
In 1776 Nevil Maskelyne hired him as a computer for the board of longitude, and two of his mathematical papers were presented to the Royal Society, of which he was elected fellow in 1780. In these papers Milner displayed three things: proficiency in mathematics, suspicion of French philosophy, and adherence to English Newtonian mechanics.
In 1782 the Jacksonian professorship of natural philosophy was established and the syndicate selected Milner as the inaugural professor, a position he retained until 1792.
Milner also developed an important process to fabricate nitrous acid, a key ingredient in the production of gunpowder. His paper describing this process was published in the Royal Society's Philosophical Transactions in 1789 alongside an article of Joseph Priestley's, and the two corresponded on the subject. In later years Milner transferred his elaborate collection of chemical apparatus into the president's lodge at Queens' and performed experiments with E. D. Clarke, William Whewell, and the Wollaston brothers; he also collaborated with Humphry Davy and Joseph Banks in an attempt to cure gout.
He was instrumental in the 1785 religious conversion of William Wilberforce and a great supporter of the abolitionists' campaign against the slave trade, steeling Wilberforce with his assurance before the 1789 Parliamentary debate: "If you carry this point in your whole life, that life will be better spent than in being prime minister of many years."

1863 Jakob Steiner (18 Mar 1796; 1 Apr 1863 at age 67) Swiss mathematician who was one of the greatest, contributors to projective geometry. He discovered the Steiner surface which has a double infinity of conic sections on it. The Steiner theorem states that the two pencils by which a conic is projected from two of its points are projectively related. He is also known for the Poncelet-Steiner theorem which shows that only one given circle and a straight edge are required for Euclidean constructions. His work included conic sections and surfaces, the theory of second-degree surfaces and centre-of-gravity problems. He developed the principle of symmetrization (1840-41). In 1848 he ws the first to define various polar curves with respect to a given curve, and introduced the “Steiner Curves.” *TIS

1872 Martin Ohm (6 May 1792 in Erlangen, Bavaria (now Germany)- 1 April 1872 in Berlin, Prussia, German Empire) was a German mathematician and a younger brother of physicist Georg Ohm. He earned his doctorate in 1811 at Friedrich-Alexander-University, Erlangen-Nuremberg where his advisor was Karl Christian von Langsdorf. Ohm was the first to fully develop the theory of the exponential ab when both a and b are complex numbers in 1823. He is also often credited with introducing the name "golden section" (goldener Schnitt).
Ohm's students included Friedrich August, Friedrich Bachmann, Paul Bachmann, Joseph Brutkowski, Heinrich Eduard Heine, Rudolf Lipschitz, Leo Pochhammer, Friedrich Prym, Wilhelm Wagner, Hermann Waldaestel, Wilhelm Wernicke, Elena Gerz, Valentien Gerz, and Johanna Gerz. *Wik
Martin Ohm made a distinction between writing for mathematicians and writing for students, a distinction that many of his contemporaries, including Hermann Grassmann, did not consider appropriate. His colleagues Steiner and Kummer also ridiculed him for not following Alexander von Humboldt's firm belief in the unity of teaching and research. It is quite difficult to assess the importance of Ohm's mathematical contributions. The first thing to say is that they certainly weren't as important as he himself thought. He had a very high opinion of himself as the following quotation indicates. Niels Abel wrote to Christopher Hansteen, the professor of astronomy at the University of Christiania, while he was on a visit to Berlin in 1826

There is at [August Crelle's] house some kind of meeting where music is mainly discussed, of which unfortunately I do not understand much. I enjoy it all the same since I always meet there some young mathematicians with whom I talk. At Crelle's house, there used to be a meeting of mathematicians, but he had to suspend it because of a certain Martin Ohm with whom nobody could get along due to his terrible arrogance.

1912 Pyotr Nikolayevich Lebedev (8 Mar 1866; 1 Apr 1912 at age 46) Russian physicist who, in experiments with William Crookes' radiometer, proved (1910) that light exerts a minute pressure on bodies (as predicted by James Clerk Maxwell's theory of electromagnetism), and furthermore that this effect is twice as great for reflecting surfaces than for absorbent surfaces. He had proposed that light pressure on small particles of cosmic dust could be greater than gravitational attraction, thus explaining why a comet's tail points away from the Sun (though it is now understood the solar wind has a greater influence). He built an extremely small vibrator source capable of generating 4-6 mm waves, which he used to demonstrate the first observation of douible refraction of electromagnetic waves in crystals of rhombic sulphur.*TIS

1921 Carl Johannes Thomae (11 December 1840, Laucha an der Unstrut – 1 April 1921, Jena) (sometimes called "Johannes Thomae", "Karl Johannes Thomae", or "Johannes Karl Thomae") was a German mathematician. Carl Johannes Thomae's research was concerned with function theory and with what German-speaking mathematicians often call "Epsilontik", the precise development of analysis, differential geometry, and topology using epsilon-neighborhoods in the style of Weierstrass. The Thomae function, the Thomae transformation formula (aka, Thomae's transformation and Thomae's theorem), the Thomae formula for hyperelliptic curves, and the Sears–Thomae transformation formula are named after him. He called himself Riemann's student, although he never attended a lecture by Riemann. *TIS

1968 Lev Davidovich Landau (22 Jan 1908; 1 Apr 1968) Soviet physicist who worked in such fields as low-temperature physics, atomic and nuclear physics, and solid-state, stellar-energy, and plasma physics. Several physics terms bear his name. He was awarded the 1962 Nobel Prize for Physics for his theory to explain the peculiar superfluid behaviour of liquid helium at very low temperature (2.18 K). Landau's further contributions are partly reflected in such terms as Landau diamagnetism and Landau levels in solid-state physics, Landau damping in plasma physics, the Landau energy spectrum in low-temperature physics, or Landau cuts in high-energy physics. *TIS

1971 Dame Kathleen Lonsdale (28 Jan 1903; 1 Apr 1971) British crystallographer (née Yardley) who developed several X-ray techniques for the study of crystal structure. Her experimental determination of the structure of the benzene ring by x-ray diffraction, which showed that all the ring C-C bonds were of the same length and all the internal C-C-C bond angles were 120 degrees, had an enormous impact on organic chemistry. She was the first woman to be elected (1945) to the Royal Society of London. *TIS

And for a final is an April Fools video about complex numbers.. enjoy

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 & Campbel
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