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| Bayeux Tapestry with Halley's Comet *Heraldic Times.org |
I will stop here.
Concluding the lecture in which he claimed to have proved the Taniyama-Weil Conjecture for a class of examples, including those necessary to prove Fermat's Last Theorem. (1993)
~Andrew Wiles
The 101st day of the year; 101 is the sum of five consecutive primes, but even more exciting, 101 = 5! - 4! + 3! - 2! + 1! (What would be the next number created in a sequence like this?)
There are six ways you can pick two of the four smallest primes, 2, 3, 5, and 7. Form all six pairs, multiply each pair, and add all the products....boom, 101
101 is the largest known prime of the form 10n + 1.
There are 101 digits in the product of the 39 successive primes produced by the formula n2 + n + 41, where n = 1 to 39. This formula was used by Charles Babbage to demonstrate the capabilities of his Difference Engine (1819-1822). *Prime Curios
and The last five digits of 101101 are 10101.
1 + 6 + 8 = 15 = 2 + 4 + 9, and the sets remain equal if you square them before adding, 1^2 + 6^2 + 8^2 = 2^2 + 4^2 + 9^2 = 101
Folks in Kentucky know that Wild Turkey bourbon's most common production is its 101 proof. Brewed just down the road in Lawrenceburgh, Ky . Jump on the Bourbon Tour and stop by, and tell 'em Pat B sent ya'.
Wonowon, British Columbia i so named because it is at Mile Marker 101 on Highway 97, the Alaska Highway.
More Math facts on 101, and more... here
EVENTS
1594, the twenty-two-year-old Kepler arrived in southern Austria to take up his duties as teacher and as provincial mathematician. In the first year he had few pupils in mathematical astronomy and in the second year none, so he was asked to teach Vergil and rhetoric as well as arithmetic. But the young Kepler made his mark in another way; soon after coming to Graz, he issued a calendar and prognostication for 1595, which contained predictions of bitter cold, peasant uprisings, and invasions by the Turks. All were fulfilled, to the great enhancement of his local reputation. Five more calendars followed in annual succession, and later in Prague he issued prognostications for 1602 to 1606. These ephemeral items are now extremely rare, some surviving in unique copies; and all the copies of nearly half the editions are totally lost. *encyclopedia.comIn 1751, Ebenezer Kinnersley advertised in the Pennsylvania Gazette that he was to give a lecture on "The Newly Discovered Electrical Fire." His lectures were the first of the kind in America or Europe. The announcement read: "Notice is hereby given to the Curious, that Wednesday next, Mr. Kinnersley proposes to begin a course of experiments on the newly discovered Electrical Fire, containing not only the most curious of those that have been made and published in Europe, but a considerable number of new ones lately made in this city, to be accompanied with methodical Lectures on the nature and properties of that wonderful element." Thus, Kinnersley was one of the earliest popularizers of science. *TIS
1816 Gauss writes to Gerling from Goettingen. Gerling had written to Gauss in March about Legendre’s theory of parallels in the book elemens de geom. Gauss responded that Legendre’s argument does not carry the weight of proof for him, and then comments on what happens if Euclidean geometry is not correct.
It is easy to show that if Euclid’s geometry is not the true one then there are no similar figures: the angles in an equilateral triangle depend on the size of the edges, in which I do not find anything absurd. Then the angle is a function of the side, and the side a function of the angle, naturally such a function in which a linear constant appears. It seems somewhat paradoxical that a linear constant can be a priori possible; but I don’t find anything contradictory in this. It would be even desirable that Euclid’s geometry is not true, for then we would have a general measure a priori, for example, one could assume as the unit of space the side of the equilateral triangle whose angle = 59o 59’ 59’’.99999….*Stan Burris, Notes on Euclidean Geometry
Lambert wrote his Theorie der Parallellinien in an attempt to prove, by contradiction, the parallel postulate. He deduced remarkable consequences including this one, from the negation of that postulate. These consequences make his memoir one of the closest (probably the closest) text to hyperbolic geometry, among those that preceded the writings of Lobachevsky, Bolyai and Gauss. His conclusions include (6) below, and preceded Gauss' by about 50 years:
"(1) The angle sum in an arbitrary triangle is less than 180◦.
(2) The area of triangles is proportional to angle defect, that is, the
difference between 180◦
and the angle sum.
(3) There exist two coplanar disjoint lines having a common perpendicular
and which diverge from each other on both sides of
the perpendicular.
(4) Given two lines coplanar d1 and d2 having a common perpendicular,
if we elevate in the same plane a perpendicular d3 to
d1 at a point which is far enough from the foot of the common
perpendicular, then d3 does not meet d2.
(5) Suppose we start from a given point in a plane the construction
of a regular polygon, putting side by side segments having the
same length and making at the junctions equal angles having a
certain value between 0 and 180◦
(see Figure 2 below). Then,
the set of vertices of these polygons is not necessarily on a circle.
Equivalently, the perpendicular bisectors of the segment do not
necessarily intersect.
(6) There exist canonical measures for length and area."
*HYPERBOLIC GEOMETRY IN THE WORK OF J. H. LAMBERT; ATHANASE PAPADOPOULOS AND GUILLAUME THERET
1936 Zuse patent filed for automatic execution of calculations. German computer pioneer Konrad Zuse files for a patent for the automatic execution of calculations, a process he invents while working on what would become the Z-1, Germany's first computer. In the patent application, Zuse offers the first discussion of programmable memory, using the term ""combination memory"" to describe breaking programs down into bit combinations for storage. This is the first device to calculate in binary with translation to decimal. Zuse goes on to build a series of computers. *CHM (Christopher Sears sent a comment last year to tell me that, "There was a character in Tron: Legacy named "Zuse". I thought is was "Zeus" during the movie, but I saw it was spelled differently in the credits . Now I know where the reference came from.")
1970 Apollo 13 lifted off, an on-board computer and large computers on Earth performed the critical guidance and navigation calculations necessary for a successful journey. In addition, crews carried a slide rule for more routine calculations. NASA chose a 5-inch, metal rule, model "N600-ES," manufactured by the Pickett Company for their use. It was a model that was popular among engineers, scientists and students at the time. No modifications were needed for use in space.
This rule used by the crew of Apollo 13, in April 1970 was transferred from NASA to the National Air and Space Museum in 1984. *airandspace.si.edu
1986, Halley's Comet made its closest approach to Earth this trip, 63 million kilometers (39 million mi), on its outbound journey. Many observers were disappointed because the famous comet was barely visible to the naked eye. Some years are simply better than others, as in 1066 when the comet was so bright that it terrified millions of Europeans. Comet Halley isn't officially scheduled to visit Earth again until 2061 when it returns on its 76-year orbit. This comet's closest known approach to the Earth was 3 million miles on 10 Apr 837 AD). Its perihelion (the closest point to the Sun) occurred earlier in the year, on 9 Feb 1986, when it was 88 million km (55 million mi) from the Sun, between the orbits of Mercury and Venus. *TIS
BIRTHS
1798 Macedonio Melloni (11 Apr 1798; 11 Aug 1854 at age 56) Italian physicist who was the firstst to extensively research infrared radiation. Sir William Frederick Herschel discovered infrared radiation in 1800, but research stalled until the invention of a thermopile in 1830. That instrument was a series of strips of two different metals that produced electric current when one end was heated. Melloni improved the thermopile and used it to detect infrared radiation. In 1846, from an observation point high on Mount Vesuvius, he measured the slight heating effect of moonlight. He showed also that rock salt, being transparent to infrared, made suitable lenses and prisms to demonstrate the reflection, refraction, polarization and interference of infrared in the same manner as visible light.*TIS1829 Alexander Buchan (11 Apr 1829; 13 May 1907 at age 78) British meteorologist, eminent in his field, who first noticed what became known as Buchan spells - departures from the normally expected temperature occurring during certain seasons. They are now believed by meteorologists to be more or less random. Buchan is credited with establishing the weather map as the basis of weather forecasting as a result of his tracing (1868) the path of a storm across North America and the Atlantic into northern Europe. *TIS
1862 William Wallace Campbell (11 Apr 1862 near Findlay in Hancock county, Ohio; 14 Jun 1938 at age 76) American astronomer known particularly for his spectrographic determinations of the radial velocities of stars--i.e., their motions toward the Earth or away from it. In addition, he discovered many spectroscopic binary stars, and in 1924 he published a catalog listing more than 1,000 of them.*TIS
1894 Paul Finsler (born 11 April 1894, in Heilbronn, Germany, died 29 April 1970 in Zurich, Switzerland) was a German and Swiss mathematician.
Finsler's thesis work concerned differential geometry, and Finsler spaces were named after him by Élie Cartan in 1934. The Hadwiger–Finsler inequality, a relation between the side lengths and area of a triangle in the Euclidean plane, is named after Finsler and his co-author Hugo Hadwiger. Finsler is also known for his work on the foundations of mathematics, developing a non-well-founded set theory with which he hoped to resolve the contradictions implied by Russell's paradox. *Wik
1901 Donald Howard Menzel (11 Apr 1901 in Florence, Colorado; 14 Dec 1976 at age 75) was an American astronomer who was best known for his arguments against the existence of extraterrestrial UFO's. Menzel was one of the first practitioners of theoretical astrophysics in the United States and pioneered the application of quantum mechanics to astronomical spectroscopy. An authority on the sun's chromosphere, he discovered with J. C. Boyce (1933) that the sun's corona contains oxygen. With W. W. Salisbury he made (1941) the first of the calculations that led to radio contact with the moon in 1946. He supervised the assignment of names to newly discovered lunar features. *TIS
1904 Phillip Hall (11 April 1904, Hampstead, London, England – 30 December 1982, Cambridge,England) was the main impetus behind the British school of group theory and the growth of group theory to be one of the major mathematical topics of the 20th Century was largely due to him. *SAU
1914 Dorothy Lewis Bernstein (April 11, 1914 – February 5, 1988) was an American mathematician known for her work in applied mathematics, statistics, computer programming, and her research on the Laplace transform.
Dorothy Bernstein was born in Chicago, the daughter of Russian immigrants to the US. She was a member of the American Mathematical Society and the first woman elected president of the Mathematical Association of America. Due in great part to Bernstein's ability to get grants from the National Science Foundation, Goucher College (where she taught for decades) was the first women's university to use computers in mathematics instruction in the 1960s.*Wik
1921 Leo Moser (April 11, 1921, Vienna—February 9, 1970, Edmonton) was an Austrian-Canadian mathematician, best known for his polygon notation.
A native of Vienna, Leo Moser immigrated with his parents to Canada at the age of three. He received his Bachelor of Science degree from the University of Manitoba in 1943, and a Master of Science from the University of Toronto in 1945. After two years of teaching he went to the University of North Carolina to complete a Ph.D., supervised by Alfred Brauer. There, in 1950, he began suffering recurrent heart problems. He took a position at Texas Technical College for one year, and joined the faculty of the University of Alberta in 1951, where he remained until his death at the age of 48. *Wik In mathematics, Steinhaus–Moser notation is a means of expressing certain extremely large numbers. It is an extension of Steinhaus’s polygon notation.
a number n in a triangle means nn.
a number n in a square is equivalent with "the number n inside n triangles, which are all nested."
a number n in a pentagon is equivalent with "the number n inside n squares, which are all nested."- *Wik
1953 Sir Andrew John Wiles, KBE, FRS (born 11 April 1953)[1] is a British mathematician and a Royal Society Research Professor at Oxford University, specializing in number theory. He is most famous for proving Fermat's Last Theorem in 1995 (and my proof was nearly complete, ;-{
DEATHS
1626 Marino Ghetaldi (2 Oct 1568 in Ragusa, Dalmatia (now Dubrovnik, Croatia)- 11 April 1626 in Ragusa, Dalmatia (now Dubrovnik, Croatia)) Marino Ghetaldi was a Croatian mathematician who published work with early applications of algebra to geometry.*SAU1734 Thomas Fantet de Lagny (7 Nov 1660 in Lyon, France - 11 April 1734 in Paris, France was a French mathematician who is well known for his contributions to computational mathematics, calculating π to 120 places. [V F Rickey has this as the 12th of April.... and shares], using Gregory’s series, Maupertius was called to de Lagny’s deathbed, and finding the poor man unconscious, asked him for the square of 12. Like an automaton, de Lagny rose in bed, gave the answer, and immediately passed away. [Eves, Circles, 238◦ and Allen Debus, World Who’s Who in Science] *VFR
1875 Samuel Heinrich Schwabe (25 Oct 1789, 11 Apr 1875 at age 85) Amateur German astronomer who discovered the 10-year sunspot activity cycle. Schwabe had been looking for possible intramercurial planets. From 11 Oct 1825, for 42 years, he observed the Sun virtually every day that the weather allowed. In doing so he accumulated volumes of sunspot drawings, the idea being to detect his hypothetical planet as it passed across the solar disk, without confusion with small sunspots. Schwabe did not discover any new planet. Instead, he published his results in 1842 that his 17 years of nearly continuous sunspot observations revealed a 10-year periodicity in the number of sunspots visible on the solar disk. Schwabe also made (1831) the first known detailed drawing of the Great Red Spot on Jupiter. *TIS
1907 Christian Gustav Adolph Mayer (February 15, 1839 – April 11, 1907) was a German mathematician. Mayer studied at Heidelberg, and submitted his habilitation thesis to the University of Heidelberg. He gained the permission to teach at universities in 1866. He taught mathematics at the University of Heidelberg for the rest of his life. He did research on differential equations, the calculus of variations and mechanics. His research on the integration of partial differential equations and a search to determine maxima and minima using variational methods brought him close to the investigations which Sophus Lie was carrying out around the same time.
Several letters were exchanged between Mayer and mathematician Felix Klein from 1871 to 1907. Those letters provide insights into the scientific and personal relations among Felix Klein, Mayer and Lie over the period.
Mayer's students included : Friedrich Engel, Felix Hausdorff and Gerhard Kowalewski. *Wik
1974 Abraham Robinson (born Robinsohn; October 6, 1918 – April 11, 1974) was a mathematician who is most widely known for development of non-standard analysis, a mathematically rigorous system whereby infinitesimal and infinite numbers were incorporated into mathematics. *Wik He is the creator of non-standard analysis.
1989 Emil Grosswald (December 15, 1912 – April 11, 1989) was a Romanian-American mathematician who worked primarily in number theory. His career is closely associated with that of his teacher, Hans Rademacher. Grosswald completed some works of his teacher Hans Rademacher, who died in 1969. Rademacher had prepared notes for an Earle Raymond Hedrick Lecture in Boulder, Colorado in 1963 on Dedekind sums, but fell ill, and Grosswald gave the lecture for him. After Rademacher's death, Grosswald edited and completed the notes and published them in the Carus Mathematical Monographs series as Dedekind Sums. He also edited for publication Rademacher's posthumous textbook Topics in Analytic Number Theory.*Wik
2020 John Horton Conway ceases to play the game of life.
John Horton Conway (born 26 December 1937, died April 11, 2020 ) was a prolific mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory. He has also contributed to many branches of recreational mathematics, notably the invention of the cellular automaton called the Game of Life.
Conway is currently Professor of Mathematics and John Von Neumann Professor in Applied and Computational Mathematics at Princeton University. He studied at Cambridge, where he started research under Harold Davenport. He received the Berwick Prize (1971),[1] was elected a Fellow of the Royal Society (1981), was the first recipient of the Pólya Prize (LMS) (1987), won the Nemmers Prize in Mathematics (1998) and received the Leroy P. Steele Prize for Mathematical Exposition (2000) of the American Mathematical Society. He has an Erdős number of one.*Wik
Conway was known for his sense of humor, and the last proof in his "On Numbers and Games" is this:
Theorem 100; This is the last Theorem in this book.
The Proof is Obvious.
Conway was exposed to the corona virus and took a fever around the 8th of April. He had suffered from ill health for an extended time, and in three days, on April 11, 2020 he died at his home in New Jersey.
I really enjoyed Siobhan Roberts biography of Conway. You may, too.
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
Solution to 101 coins
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