If you open a mathematics paper at random,
on the pair of pages before you, you will find a mistake.
~Joseph Doob
The 159th day of the year; 159 = 3 x 53, and upon concatenating these factors in order we have a peak palindrome, 353, which is itself a prime.*Prime Curios
159 is the sum of 3 consecutive prime numbers: 47 + 53 + 59 and can be written as the difference of two squares in two different ways.
Deshouillers (1973) showed that all integers are the sum of at most 159 prime numbers. I'm waiting for someone to tell me the number that takes 159 prime numbers to form???
48 x 159 = 5346, uses all nine non-zero digits
159 is the fifth Woodall number, a number of the form n*2
n -1. The
numbers were first studied by Allan J. C. Cunningham
and H. J. Woodall
in 1917, inspired by James Cullen
's earlier study of the similarly-defined Cullen numbers (n*2
n +1. )
EVENTS
1612 Paolo Gualdo wrote from Padua to say that Sagredo had sent him Galileo's letter on sunspots, which he had shown to many of his friends. *Stillman Drake, Galileo at Work
1637 The printing of Descartes’ Discours de la Methode, with its important appendix “La G´eom´etrie,” was completed. *VFR In 1637, the book Discourse on Method of Rightly Conducting the Reason, and Seeking Truth in the Sciences, was published by René Descartes, regarded as a major work in science and mathematics. He expresses his disappointment with traditional philosophy and with the limitations of theology; only logic, geometry and algebra hold his respect, because of the utter certainty which they can offer. Ushering in the "scientific revolution" of Galileo and Newton, Descartes' ideas swept aside ancient and medieval traditions of philosophical methods and investigation. *TIS
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| *Wik |
1724 Euler received his master’s degree in philosophy at age 17, giving a lecture comparing the philosophical ideas of Descartes and Newton. His bachelor’s speech, in the summer of 1722, was “On temperance.” *VFR Graduation with the same degree on that day was Johann II (Jean) Bernouli, only 14. *Ronald S. Calinger; Leonhard Euler: Mathematical Genius in the Enlightenment%20Jean%20.jpg)
1887 Herman Hollerith receives a patent for his punch card calculator. * The Geek Manual (I wonder what age is the lower threshold for recognition of the term "punch card" as a computer term.)
1911 The Aero Club of America issued its first pilot licenses to five established aviators. Presented alphabetically, Glenn Curtiss received license #1. Orville and Wilbur Wright held licenses #4 and #5 behind U.S. Army pilot Frank Lahm (#2) and French aviator Louis Paulhan (#3). Subsequent pilots had to pass a flight test to earn a license.Thirty-six-year-old Harriet Quimby became the first female licensed pilot in the U.S. on August 1, 1911, when she earned license #37 from the Aero Club of America. She became a prize-winning pilot at air meets and was the first woman to fly across the English Channel in April 1912. Like many aviators of her generation, Quimby’s life was cut short when she died in a plane crash near Boston on July 1, 1912.
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| *Linda Hall Org |
In 1918, Nova Aquila, the brightest nova since Kepler's nova of 1604, was discovered in the constellation of Aquila the eagle, a 1st magnitude star 6 degrees north of the Scutum star cloud. For the months that it shone, it was the brightest star in the sky, briefly half a million times brighter than the sun, but seen from 1200 light years (70,000 trillion miles) away. Between 1899 and 1936 there were 20 fairly bright novae, and five of those were in this same small area of the sky, the constellation Aquila. Seven years later Nova Aquila had faded to a bluish star apparently much smaller and denser than our sun. (Aquila belonged to Zeus, and was the eagle that carried the mortal Ganymede to the heavens to serve as Zeus' cup bearer.)TIS
1918 The total solar eclipse of June 8, 1918 crossed the United States from Washington State to Florida. This path is roughly similar to the August 21, 2017 total solar eclipse and was the last time totality crossed the nation from the Pacific to the Atlantic. *greatamericaneclipse.com
1921 Edith Clarke submits patent for the Clark Calculator. The calculator was a simple graphical device that solved equations involving electric current, voltage and impedance in power transmission lines. The device could solve line equations involving hyperbolic functions ten times faster than previous methods. She filed a patent for the calculator in 1921 and it was granted in 1925. Ms. Clarke is generally thought of as the first female electrical engineer in the U. S.
1923 Art historian Joan Evans speaks on “Jewels of the Renaissance”, and becomes the first woman to give a Discourse at the Ri. *Royal Institution web page,
She was a British historian of French and English mediaeval art, especially Early Modern and medieval jewelry. Her notable collection was bequeathed to the Victoria and Albert Museum in London *Wik
1948 Carl Savit, a graduate student at Caltech, appeared in court to demand $1000 from Mottant Company of Chicago for solving the three classical construction problems. This offer was made in an advertisement that neglected to require that compass and straightedge be used. It is not known if he collected. [Mathematics Magazine 61 (1988), p 158].*VFR There are are many beautiful approaches to trisecting a general angle using other tools as I wrote in "
Trisecting the General Angle, A Plethora of Pretty Approaches"
1979 The Source, the first computer public information service, goes on line.
2004 The second most recent (most recent was in 2012)
transit of Venus when observed from Earth took place on June 8, 2004. The event received significant attention, since it was the first Venus transit to take place after the invention of broadcast media. No human alive at the time had witnessed a previous Venus transit, since the previous Venus transit took place on December 6, 1882. The next transit of Venus occurred on June 5–June 6 in 2012,. If you missed these two, the next transits of Venus will be in December 2117 and December 2125.*Wik
BIRTHS
1625 Jean Dominique Cassini (
June 8, 1625, Perinaldo - September 14, 1712, Paris)Italian-born French astronomer who in 1675 discovered Cassini's division, the dark gap subdividing Saturn's rings into two parts. He stated that Saturn's ring, believed by Huygens to be a single body, was actually composed of small particles. Cassini also discovered four of Saturn's moons: Iapetus (Sep 1671), Rhea (1672) and on 21 Mar 1684,* Tethys and Dione. He compiled new tables (1662) on the annual motion of the Sun. He observed shadows of four Galilean satellites on Jupiter (1664), and measured its rotation period by studying the bands and spots on its surface. He determined the period of rotation of Mars (1666), and attempted the same for Venus. His son Jacques was also an astronomer.*TIS
The pinhole-projected image of the Sun on the floor at Florence Cathedral. Jean Cassini measured a similar image over a year at San Petronio Basilica to try to prove the Earth orbited the Sun.
1724 John Smeaton (8 June 1724 – 28 October 1792) English civil engineer, who coined the term "civil engineering" (to distinguish from military engineers). He built the third Eddystone Lighthouse, Plymouth, Devon, using dovetailed blocks of portland stone (1756-59). He discovered the best mortar for underwater construction to be limestone with a high proportion of clay. Smeaton also constructed the Forth and Clyde Canal in Scotland between the Atlantic and the North Sea; built bridges in towns including Perth, Banff, and Coldstream, Scotland; and completed Ramsgate harbour, Kent. He introduced cast-iron shafts and gearing into wind and water mills, designed large atmospheric pumping engines for mines, and improved the safety of the diving bell.)*TIS
1725 Caspar Wessel(June 8, 1745, Vestby – March 25, 1818, Copenhagen) was a Norwegian mathematician who invented a geometric way of representing complex numbers which pre-dated Argand. *SAU
His fundamental paper, Om directionens analytiske betegning, was published in 1799 by the Royal Danish Academy of Sciences and Letters. Since it was in Danish, it passed almost unnoticed, and the same results were later independently found by Argand and Gauss.
One of the more prominent ideas presented in "On the Analytical Representation of Direction" was that of vectors. Even though this wasn't Wessel's main intention with the publication, he felt that a geometrical concept of numbers, with length and direction, was needed. Wessel's approach on addition was: "Two straight lines are added if we unite them in such a way that the second line begins where the first one ends and then pass a straight line from the first to the last point of the united lines. This line is the sum of the united lines". This is the same idea as used today when summing vectors. Wessel's priority to the idea of a complex number as a point in the complex plane is today universally recognized. His paper was re-issued in French translation in 1899, and in English in 1999 as On the analytic representation of direction (ed. J. Lützen et al.).*Wik
1858 Charlotte Agnas Scott (8 June 1858 – 10 November 1931, Cambridge) born in Lincoln, England. She attended Girton, the first (1869) college in England for women. In 1880 she took the tripos exam at Cambridge, but because she was a woman, her name could not be announced at the award ceremony. “The man read out the names and when he came to ‘eighth,’ before he could say the name, all the undergraduates called out ‘Scott of Girton,’ and cheered tremendously, shouting her name over and over again with tremendous cheers and waving of hats.” [Women of Mathematics. A Biobibliographic Sourcebook (1987), edited by Louise S. Grinstein and Paul J. Campbell] *VFR
1860 Alicia Boole Stott (June 8, 1860, Cork, Ireland – December 17, 1940, England) was the third daughter of George Boole. (Read more about Boole's descendents in my blog, "
Those Amazing Boole Girls." ) George Boole died when Alicia was only four years old and she was was brought up partly in England by her grandmother,(
Mary Everest Boole was a mathematician educator who was an early advocate of teaching children math through playful activities. It is almost certain she would have exposed her daughters to such activities {pb}) partly in Cork by her great-uncle. When she was twelve years old she went to London where she joined her mother and sisters.
With no formal education she surprised everyone when, at the age of eighteen, she was introduced to a set of little wooden cubes by her brother-in-law Charles Howard Hinton. Alicia Boole experimented with the cubes and soon developed an amazing feel for four dimensional geometry. She introduced the word 'polytope' to describe a four dimensional convex solid.
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| *Wik |
MacHale, writes:-
She found that there were exactly six regular polytopes on four dimensions and that they are bounded by 5, 16 or 600 tetrahedra, 8 cubes, 24 octahedra or 120 dodecahedra. She then produced three-dimensional central cross-sections of all the six regular polytopes by purely Euclidean constructions and synthetic methods for the simple reason that she had never learned any analytic geometry. She made beautiful cardboard models of all these sections....
After taking up secretarial work near Liverpool in 1889 she met and married Walter Stott in 1890. Stott learned of Schoute's work on central sections of the regular polytopes in 1895 and Alicia Stott sent him photographs of her cardboard models. Schoute came to England and worked with Alicia Stott, persuading her to publish her results which she did in two papers published in Amsterdam in 1900 and 1910.
The University of Groningen honoured her by inviting her to attend the tercentenary celebrations of the university and awarding her an honorary doctorate in 1914.
In 1930 she was introduced to Coxeter and they worked together on various problems. Alicia Stott made two further important discoveries relating to constructions for polyhedra related to the golden section. *Wik
1867 Frank Lloyd Wright (June 8, 1867 – April 9, 1959) was born in Richland Center, Wisconsin. Widely regarded as America's most significant architect, Wright transformed twentieth-century
residential design; his influential Prairie School houses and plans for public buildings proved simultaneously innovative, aesthetically striking, and practical. A social visionary, Wright's commitment to a context-driven "organic architecture," which harmonized with both its occupants' needs and the surrounding landscape, underscored his creative genius across a long and productive career.*Library of Congress
1870 Peter Pinkerton (8 June 1870 in Kilmarnock, Scotland -22 November 1930 in Glasgow, Scotland) studied at Glasgow and Dublin. After teaching at various schools he became Rector of Glasgow High School. He became President of the EMS in 1908. *SAU
1896 Eleanor Pairman (June 8, 1896-September 14, 1973) graduated from Edinburgh. She went to London where she worked with Karl Pearson and then went to the USA where she gained a doctorate from Radcliffe College.*SAUShw was the third woman to receive a doctorate in math from Radcliffe College in Massachusetts. Later in life she developed novel methods to teach mathematics to blind students.
About 1950, Pairman started focusing on teaching mathematics to blind students, learning Braille and learning how to make diagrams using her sewing machine and other household items. Her daughter Margaret later wrote, “Geometry was a particular problem, because you really need diagrams. Braille is done on paper like thin cardstock. So she rounded up all kinds of household implements like pinking shears and pastry wheels and such and created diagrams that could be felt with the fingers, like the Braille symbols. Apparently nobody had ever done this before."
1905 Edward Hubert Linfoot (8 June 1905, Sheffield, England - 14 October 1982, Cambridge, England)
After attending King Edward VII School he won a scholarship to Balliol College at the University of Oxford.
During his time at Oxford he met the number theorist G. H. Hardy, and after graduating in 1926, Linfoot completed a D.Phil under the supervision of Hardy with a thesis entitled Applications of the Theory of Functions of a Complex Variable.
After brief stints at the University of Göttingen, Princeton University, and Balliol College, Linfoot took a job in 1932 as assistant lecturer, and later lecturer, at the University of Bristol. During the 1930s Linfoot's interests slowly made the transition from pure mathematics to the application of mathematics to the study of optics, but not before proving an important result in number theory with Hans Heilbronn, that there are at most ten imaginary quadratic number fields with class number 1 *WIK
1915 José Luis Massera (Genoa, Italy, June 8, 1915 – Montevideo, September 9, 2002) was a Uruguayan dissident and mathematician who researched the stability of differential equations.
Massera's lemma is named after him. He published over 40 papers during 1940–1970. A militant Communist, he was a political prisoner during 1975–1984. In the 1930s, Julio Rey Pastor gave regular weekend lectures on topology in Montevideo to a group that included Massera. Stimulated by contact with Argentine mathematics, the 1950s saw Uruguay develop a fine school in mathematics, of which Massera was very much a part.
Massera developed new notions of stability, and published several foundational papers and an influential textbook. His results in (Massera 1950) on periodic differential equations have been heavily cited and are referred to as Massera's theorem. His work in (Massera 1949) and (Massera 1956) on the converse to Lyapunov's criterion is also influential, and contain the well known Massera's lemma. His textbook (Massera & Schäffer 1966) is also heavily cited.
After military intervention in Uruguay in 1973, Massera was arrested on October 22, 1975 in Montevideo and was held in solitary confinement for nearly a year. During this time he was subjected to repeated torture resulting in injuries including a fractured pelvis. In October 1976 he was taken from solitary confinement, tried and convicted for "subversive association", and given a 24-year prison sentence. On June 22, 1979, as a consequence of a proposal put forward by Gaetano Fichera and unanimously approved by the whole Mathematics Faculty Council of the Sapienza University of Rome, he was awarded the laurea honoris causa while still being under conviction. He was released in 1984. *Wik
During his youth a revolution began in Uruguay he began looking up words in his fathers massive dictionary. Looking up "equation" he found dozens of different types of equations and began to explore, and finding other terms in thos definition expanded his search. On a trip with his father he found a huge bookstore in Paris and his father bought him a classical geometry book and a trigonometry which he "devoured in a short time."
1923 Gloria Olive (8 June 1923, New York City, USA - 17 April 2006, Dunedin, New Zealand)
Gloria Olive completed her school educations at Abraham Lincoln High School in Brooklyn, New York, graduating in 1940. She then entered Brooklyn College in New York where she studied mathematics, graduating with an B.A. in 1944. Perhaps the most famous of her lecturers was Jesse Douglas who had been awarded the Fields Medal at the International Congress of Mathematicians at Oslo in 1936. After graduating, Olive was appointed as a Graduate Assistant at the University of Wisconsin where she spent the two academic years 1944-46. In addition to teaching she studied for her Master's Degree during these two years and was awarded the degree in 1946.
From Wisconsin, Olive moved to the University of Arizona in 1946 where she was appointed as an instructor. After two years she was appointed to Idaho State University where again she spent two years teaching as an instructor. Her next appointment in Oregon State University in 1950 was as a Graduate Assistant and after this one-year post she left the academic world for a short time, taking a job as a cryptographer in the U.S. Department of Defense in Washington, D.C. After a year in Washington, Olive returned to an academic position being appointed to Anderson College in 1952.
Anderson Bible Training School had been founded in 1917 as an educational establishment to train leaders and workers for a life in the church. It rapidly developed a broader, more general, education program, and changed its name first to Anderson College and Theological Seminary, and then to Anderson College. At Anderson College, Olive built up the mathematics department and began to become interested in mathematical research, in particular studying generalised powers. C C MacDuffee, who had taught Olive at the University of Wisconsin, agreed to accept a visiting professorship at Oregon State University so that he could supervise her doctoral thesis. Sadly he died in 1961 and Olive was left without a thesis advisor. However she was awarded a Ph.D. for her thesis Generalized Powers in 1963.
Olive continued to at Anderson College until 1968 when she accepted a professorship at the University of Wisconsin-Superior. She stayed at the University of Wisconsin-Superior until 1972, the year after it joined the University of Wisconsin, and went to New Zealand where she was appointed as a senior lecturer at the University of Otago. She continued in this post until she retired in 1989. Mac Lane and Rayner wrote on her retirement
For all of her time with the Mathematics and Statistics Department of Otago University, Gloria has been the only female on the staff with tenure, and as such has been a shining example to both staff and students. She has fought hard for the issues she championed, and contributed to several worthwhile changes (such as the current internal assessment policy applauded by both staff and students). Her colleagues will miss her lively contributions to the debates in departmental meetings.
Much of Olive's research was on applications of generalised powers. She published papers such as Binomial functions and combinatorial mathematics (1979), A combinatorial approach to generalized powers (1980), Binomial functions with the Stirling property (1981), Some functions that count (1983), Taylor series revisited (1984), Catalan numbers revisited (1985), A special class of infinite matrices (1987), and The ballot problem revisited (1988). *SAU
1924 Samuel Karlin (June 8, 1924 - December 18, 2007) made fundamental contributions to game theory, analysis, mathematical statistics, total positivity, probability and stochastic processes, mathematical economics, inventory theory, population genetics, bioinformatics, and biomolecular sequence analysis, was born in Yonova, Poland, and immigrated to Chicago as a child. Karlin earned a doctorate in mathematics at age 22 from Princeton in 1947. He taught at Caltech from 1948 to 1956 before moving to Stanford as a Professor of Math and Stat. Overall, Karlin had over 70 PhD students, to whom he was an extraordinary teacher and advisor.(*David Bee)
2013 Gury Ivanovich Marchuk ( 8 June 1925 – 24 March 2013) was a Soviet and Russian scientist in the fields of computational mathematics, and physics of atmosphere. Academician (since 1968); the President of the USSR Academy of Sciences in 1986–1991. Among his notable prizes are the USSR State Prize (1979), Demidov Prize (2004), Lomonosov Gold Medal (2004).
Marchuk was born in Orenburg Oblast, Russia. A member of the Communist Party of the Soviet Union since 1947, Academician Marchuk was elected to the Central Committee of the Party as a candidate member in 1976 and as a full member in 1981. He was elected as deputy of the Supreme Soviet of the Union of Soviet Socialist Republics in 1979. He was appointed to succeed Vladimir Kirillin as chairman of the State Committee for Science and Technology (GKNT) in 1980.
Marchuk was a proponent of the Integrated Long-Term Programme (ILTP) of Cooperation in Science & Technology that was established in 1987 as a scientific cooperative venture between India and the Soviet Union. The programme allowed the scientists of the countries to collaboratively undertake research in areas as diverse as healthcare and lasers. Marchuk co-chaired the programme's Joint Council with Prof. C.N.R. Rao for 25 years and was made an honorary member of India's National Academy of Sciences. In 2002, the Government of India conferred the Padma Bhushan on him *Wik
1936 Kenneth Geddes "Ken" Wilson (June 8, 1936 – June 15, 2013) was an American physicist who was awarded the 1982 Nobel Prize for Physics for his development of a general procedure for constructing improved theories concerning the transformations of matter called continuous, or second-order, phase transitions. These take place at characteristic temperatures (or pressures), but unlike first-order transitions they occur throughout the entire volume of a material as soon as that temperature (called the critical point) is reached. One example of such a transition is the complete loss of ferromagnetic properties of certain metals when they are heated to their Curie points (about ºC for iron). Wilson's work provided a mathematical strategy for constructing theories that could apply to physical systems near the critical point. *TiS
1955 Tim Berners-Lee (8 June 1955- ), English computer scientist who invented the World Wide Web and director of the World Wide Web Consortium, which oversees its continued development. In 1984, he took up a fellowship at CERN, to work on distributed real-time systems for scientific data acquisition and system control. While there , in 1989, he proposed a global hypertext project, to be known as the World Wide Web, which permitted people to collaborate by sharing knowledge in a web of hypertext documents. On 6 Aug 1991, the first World Wide Web site was made available to the Internet at large, giving information on a browser and how to set up a Web server. He then expanded its reach, always nonprofit, to become an international mass medium. *TIS
DEATHS
1882 John Scott Russell (9 May 1808, Parkhead, Glasgow – 8 June 1882, Ventnor, Isle of Wight) British civil engineer best known for researches in ship design. He designed the first seagoing battleship built entirely of iron. He was the first to record an observation of a soliton, while conducting experiments to determine the most efficient design for canal boats. In Aug 1834, he observed what he called the "Wave of Translation," a solitary wave formed in the narrow channel of a canal which continues ahead after a canal boat stops. [
This is now recognised as a fundamental ingredient in the theory of 'solitons', applicable to a wide class of nonlinear partial differential equations.] He also made the first experimental observation of the "Doppler shift" of sound frequency as a train passes (1848). He designed (with Brunel) the Great Eastern and built it; he designed the Vienna Rotunda and helped to design Britain's first armored warship, the Warrior. *TIS
1883 Joel E. Hendricks, (March 10, 1818 - June 9, 1893) a noted mathematician, was born in Bucks County, Pennsylvania, March 10, 1818. He early developed a love of mathematics and began to teach school at nineteen years of age. He chanced to procure Moore's Navigation and Ostrander's Astronomy and, without instruction, soon became able to work in trigonometry and calculate solar and lunar eclipses. He took up algebra while teaching and soon became master of that science without instruction. He taught mathematics two years in Neville Academy, Ohio, and then occupied a position on a Government survey in Colorado in 1861. In 1864 he located in Des Moines, Iowa and pursued his mathematical studies. In 1874 he began the publication of the Analyst, a journal of pure and applied mathematics and soon won a reputation in Europe among eminent scholars as one of the most advanced mathematicians of the day. His Analyst was taken by the colleges and universities of Europe and found a place in the best foreign libraries. His name became famous among all mathematical experts of the world. Among his correspondents were Benjamin Silliman, John W. Draper and James D. Dana; while his journal was authority at Yale and Johns Hopkins Universities. For ten years, up to 1884, this world-famous Analyst was published at Des Moines by Dr. Joel E. Hendricks. Up to the time it was discontinued, no journal of mathematics had been published so long in America. It is one of the remarkable events of the Nineteenth Century that a self-educated man should, by his own genius and industry, without instruction, reach such an exalted place among the world's great scholars. Dr. Hendricks died in Des Moines on the 9th of June, 1893. *History of Iowa From the Earliest Times to the Beginning of the Twentieth Century/Volume 4 by Benjamin F. GueA more complete mathematical biography of Mr. Hendricks can be found in The American Mathematical Monthly, Vol 1, #3, 1894.
1920 Augusto Righi (27 August 1850 – 8 June 1920) was an Italian physicist and a pioneer in the study of electromagnetism. He was born and died in Bologna.
Righi was the first person to generate microwaves, and opened a whole new area of the electromagnetic spectrum to research and subsequent applications. His work L'ottica delle oscillazioni elettriche (1897), which summarised his results, is considered a classic of experimental electromagnetism. Marconi was his student. *Wik
1935 Alexander Wilhelm von Brill (20 September 1842 – 18 June 1935) was a German mathematician.
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| Cardboard 'Sliceforms' by John Sharp. |
Born in Darmstadt, Hesse, Brill was educated at the University of Giessen, where he earned his doctorate under supervision of Alfred Clebsch. He held a chair at the University of Tübingen, where Max Planck was among his students. In 1933, he joined the National Socialist Teachers League as one
of the first members from Tübingen.
The London Science Museum contains sliceform objects prepared by Brill and Felix Klein. *Wik
1988 Roger Conant Lyndon (December 18, 1917 – June 8, 1988) was an American mathematician, for many years a professor at the University of Michigan.[1] He is known for Lyndon words, the Curtis–Hedlund–Lyndon theorem, Craig–Lyndon interpolation and the Lyndon–Hochschild–Serre spectral sequence.
Lyndon's Ph.D. thesis concerned group cohomology; the Lyndon–Hochschild–Serre spectral sequence, coming out of that work, relates a group's cohomology to the cohomologies of its normal subgroups and their quotient groups.
A Lyndon word is a nonempty string of symbols that is smaller, lexicographically, than any of its cyclic rotations; Lyndon introduced these words in 1954 while studying the bases of free groups.
Lyndon was credited by Gustav A. Hedlund for his role in the discovery of the Curtis–Hedlund–Lyndon theorem, a mathematical characterization of cellular automata in terms of continuous equivariant functions on shift spaces.
The Craig–Lyndon interpolation theorem in formal logic states that every logical implication can be factored into the composition of two implications, such that each nonlogical symbol in the middle formula of the composition is also used in both of the other two formulas. A version of the theorem was proved by William Craig in 1957, and strengthened by Lyndon in 1959.
In addition to these results, Lyndon made important contributions to combinatorial group theory, the study of groups in terms of their presentations in terms of sequences of generating elements that combine to form the group identity. *Wik
1998 Maria Reiche (May 15, 1903, Dresden - June 8, 1998, Peru) German-born Peruvian mathematician and archaeologist who was the self-appointed keeper of the Nazca Lines, a series of desert ground drawings over
1,000 years old, near Nazcain in southern Peru. For 50 years the "Lady of the Lines" studied and protected these etchings of animals and geometric patterns in 60 km (35 mi) of desert. Protected by a lack of wind and rain, the figures are hundreds of feet long best seen from the air. She investigated the Nazca lines from a mathematical point of view. Death at age 95 interrupted her new mathematical calculations: the possibility that the lines predicted cyclical natural phenomena like El Nino, a weather system that for centuries has periodically caused disastrous flooding along the Peruvian coast.
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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