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| Double False Position from Gemma Frisius Arithmeticae Practicae Methodus Facilis (1540) *MAA Mathematical Treasures |
"I endeavor to keep their attention fixed on the main objects of all science, the freedom & happiness of man, so that coming to bear a share in the councils and government of their country, they will keep ever in view the sole objects of all legitimate government."
A plaque with this quotation, with the first phrase omitted, is in the stairwell of the pedestal of the Statue of Liberty.
~Thomas Jefferson, in a Letter to Tadeusz Kosciuszko, 26 February 1810
The 103rd day of the year; there are 103 geometrical forms of magic knight's tour of the chessboard.
103 is the reverse of 301. The same is true of their squares: 1032 = 10609 and 3012 = 90601. *Jim Wilder
The smallest prime whose reciprocal contains a period that is exactly 1/3 of the maximum length. (The period of the reciprocal of a prime p is always a divisor of p-1, so for 103 the period is 102/3 = 34. )
Using a standard dartboard, 103 is the smallest possible prime that cannot be scored with two darts.
Most mathematicians know the story of 1729, the taxicab number which Ramanujan recognized as a cube that was one more than the sum of two cubes, or the smallest number that could be expressed as the sum of two cubes in two different ways. But not many know that 103 is part of the second such pair \(64^3 + 94^3 = 103^3 + 1^3 \)
*************** Lots of additional math facts for days 91-120 at https://mathdaypballew.blogspot.com/
*************** Lots of additional math facts for days 91-120 at https://mathdaypballew.blogspot.com/
EVENTS
1560 On this day in 1560, Cardan's son Giambatista was executed after being found guilty of poisoning his wife. This was a blow from which Cardan never recovered.
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In 1620, the word "microscope" was coined as a suggested term in a letter written by Johannes Faber of Bamberg, Germany, to Federigo Cesi, Duke of Aquasparata and founder of Italy's Accademia dei Lincei (Academy of the Lynx). This Academy, possibly the world's first scientific society took its name after the animal for its exceptional vision. *TIS (Galileo had called it the occhiolino 'little eye').
1668 Lord Brouncker, President of the Royal Society, publishes "the fist mathematical result to be published in a mathematical journal" in the Philosophical transactions of the Royal Society. His demonstration of the method of quadrature of the rectangular hyperbola, y= x-1 extended the work of Wallis in Arithmetica infinitorium. Brouncker had been working with Wallis on extending the work of Torricelli's Opera geometrica hoping to apply the methods to the long-sought quadrature of the circle.
The rectangular hyperbola had eluded Fermat, and only been partially solved by de Saint Vincent by 1625. It was a fellow Jesuit of Saint Vincent, Alphonse Antonio de Sarasa he may have been the first to recognize that certain areas under the hyperbola are related to each other in the same was as logarithms. *Jacqueline Stedall, Mathematics Emerging, 2008.
1672 After presenting his paper on the composition of light as a, “heterogeneous mixture of differently refrangible rays” on 19 Feb, several critics emerged, most notably Robert Hooke. Newton responded to the critiques with a letter to the Royal Society, "Some Experiments propos'd in relation to Mr. Newtons Theory of light, printed in Numb. 80; together with the Observations made thereupon by the Author of that Theory; communicated in a Letter of his from Cambridge, April 13. 1672." Newton had performed a series of experiments to validate his theory, and here described the results. See the letter here.
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| Halley's Comet, March 8, 1986 |
1791 Legendre is named one of the French Academy’s three commissioners for the astronomical operations and triangulations necessary for determining the standard meter. The others were Mechain and Cassini IV. [DSB 8, 136]*VFR
1869, the first U.S. patent for an air brake was issued to George Westinghouse of Schnectady, N.Y., entitled “Improvement in steam-power-brake devices” (No. 88,929). It was used on an experimental train carrying officials of the Panhandle Railroad. Although it demonstrated its value, it was not entirely successful because it took longer for the air to reach the last cars of the train, so each car stopped at a different time. This was corrected with his “triple air brake” patent issued 5 Mar 1872 (No. 124,405). Fifteen years later, he invented an automatic brake.
BIRTHS
953 Abu Bekr ibn Muhammad ibn al-Husayn Al-Karaji (13 April 953 in Baghdad (now in Iraq) - died about 1029) Al-Karaji was an Islamic mathematician who wrote about the work of earlier mathematicians and who can be regarded as the first person to free algebra from geometrical operations and replace them with the type of operations which are at the core of algebra today. *SAUAl-Karaji gave the first formulation of the binomial coefficients and the first description of Pascal's triangle. He is also credited with the discovery of the binomial theorem.
In his book "Extraction of hidden waters" he has mentioned that earth is spherical in shape but considers it the center of the universe long before Galileo Galilei, Johannes Kepler or Isaac Newton, but long after Aristotle and Ptolemy. He expounded the basic principles of hydrology and this book reveals his profound knowledge of this science and has been described as the oldest extant text in this field.
Diagrams from Al-Karaji's work on "hidden waters" *Wik
1728 Paolo Frisi (13 Apr 1728; 22 Nov 1784 at age 56) Italian mathematician, astronomer, and physicist who is best known for his work in hydraulics (he designed a canal between Milan and Pavia). He was, however, the first to introduce the lightning conductor into Italy. His most significant contributions to science, however, were in the compilation, interpretation, and dissemination of the work of other scientists, such as Galileo Galilei and Sir Isaac Newton. His work on astronomy was based on Newton's theory of gravitation, studying the motion of the earth (De moto diurno terrae). He also studied the physical causes for the shape and the size of the earth using the theory of gravity (Disquisitio mathematica, 1751) and tackled the difficult problem of the motion of the moon. *TIS
1743 Thomas Jefferson, American President and Mathematical enthusiast, was born.
"Thomas Jefferson had four main accomplishments in mathematics. First, he took mathematics from the ranks of a secondary subject and raised it to such a prominence in the curriculum of the University of Virginia that it was not seen at any other college in the United States at the time. Through Jefferson’s influence, men like J.J. Sylvester, in 1841 (though unsuccessful), were recruited to build up the mathematics courses at the University of Virginia....David Eugene Smith sums it best in the following passage:
It is apparent that Jefferson was not a mathematician but that he was a man who appreciated the beauties, the grandeur, the values, the classics, and the uses of mathematics and did much to give to the science a recognized standing as a university subject. "
From an online article by Ajaz Siddiqui, See the short article here.
1802 George Palmer Williams (Woodstock, Vermont, April 13, 1802-Ann Arbor, September 4, 1881) He graduated Bachelor of Arts from the University of Vermont in 1825, and then studied about two years in the Theological Seminary at Andover, Massachusetts. He did not complete the course, but took up teaching, which proved to be his life work.
He was Principal of the Preparatory School at Kenyon College, Ohio, from 1827 to 1831. In 1831 he was elected to the chair of Ancient Languages in the Western University of Pennsylvania, but after two years he returned to Kenyon College, where he remained until called, in 1837, to the branch of the incipient University of Michigan at Pontiac.
In 1841, when the College proper was opened at Ann Arbor, he was made Professor of Natural Philosophy. In 1854 he was transferred to the chair of Mathematics and in 1863 to the chair of Physics. From 1875 to 1881 he was Emeritus Professor of Physics.
He received the degree of Doctor of Laws from Kenyon College in 1849. The University Senate in a memorandum relative to his death declared that: "Dr. Williams welcomed the first student that came to Ann Arbor for instruction; as President of the Faculty he gave diplomas to the first class that graduated, and from the day of his appointment to the hour of his death his official connection with the University was never broken."
In 1846 he was ordained to the ministry of the Protestant Episcopal Church; but he did no regular parish work, except for a short time in Ann Arbor. He was first and last a teacher, beloved by his colleagues and pupils and universally respected and honored.
Some years before his death the alumni raised a considerable fund, the proceeds of which were to be paid to him during his lifetime and after his death were to be used for maintaining a professorship named in honor of his memory. *Hinsdale and Demmon, History of the University of Michigan 221
George Palmer Williams, aka, “Punky” to his students.
1813 Duncan Farquharson Gregory (13 April 1813 in Edinburgh, Scotland - 23 Feb 1844 in Edinburgh, Scotland) Scottish mathematician who was one of the first to investigate modern ideas of abstract algebra.In this work Gregory built on the foundations of Peacock but went far further towards modern algebra. Gregory, in his turn, had a major influence on Boole and it was through his influence that Boole set out on his innovative research. *SAU
Gregory was initially recognized for his essay The Foundations of Algebra presented to the Royal Society of Edinburgh in 1838.
Gregory never married. He was the youngest son of eleven children. His older brother William, like his father, was a chemist and physician. His great-great-grandfather James Gregory, the mathematician, designed the Gregorian telescope. James's nephew, David Gregory, was appointed a professor of mathematics at the University of Edinburgh in 1683.
Gregory's circumstances did not allow him to accept the Mathematical Chair at the University of Toronto offered in 1841. Illness overtook him the next year. Incapacitated, he left Cambridge in the spring of 1843, and died in Edinburgh the following February, at 30 years of age.*Wik
1869 Ada Isabel Maddison (April 12, 1869 - October 22, 1950) born in Cumberland, England. She attended Girton College, Cambridge, in the same class with Grace Chisholm Young and they attended lectures of Cayley. Then she went to Bryn Mawr, where she earned her Ph.D. in 1895. She continued there until retirement, involved mostly in administrative work. *WM
best known for her work on differential equations.
In 1892 Maddison passed the Cambridge Mathematical Tripos Exam earning a First Class degree, equal to the twenty-seventh Wrangler, but she was not allowed to receive a degree, as, at this time, women could not formally receive a degree at Cambridge. Instead, she was awarded the degree of Bachelor of Science with Honors from the University of London in 1893. Her fellow student Grace Chisholm also earned a First Class degree in the same Mathematical Tripos examinations.
Maddison was awarded the Mary E. Garrett Fellowship for study abroad. She used the award to study at the University of Göttingen in the academic year 1893-1894,where she attended lectures by Felix Klein and David Hilbert. *Wik
1879 Francesco Severi (13 April 1879 – 8 December 1961) was an Italian mathematicianborn in Arezzo, Italy. He is famous for his contributions to algebraic geometry and the theory of functions of several complex variables. He became the effective leader of the Italian school of algebraic geometry. Together with Federigo Enriques, he won the Bordin prize from the French Academy of Sciences.
He contributed in a major way to birational geometry, the theory of algebraic surfaces, in particular of the curves lying on them, the theory of moduli spaces and the theory of functions of several complex variables. He wrote prolifically, and some of his work has subsequently been shown to be not rigorous according to the then new standards set in particular by Oscar Zariski and David Mumford. At the personal level, according to Roth (1963) he was easily offended, and he was involved in a number of controversies. He died in Rome of cancer.*Wik
1889 Herbert Osborne Yardley (April 13, 1889 – August 7, 1958) American cryptographer who organized and directed the U.S. government's first formal code-breaking efforts during and after World War I. He began his career as a code clerk in the State Department. During WW I, he served as a cryptologic officer with the American Expeditionary Forces in France during WWI.
He founded and led the cryptographic organization the Black Chamber. Under Yardley, the cryptanalysts of The American Black Chamber broke Japanese diplomatic codes and were able to furnish American negotiators with significant information during the Washington Naval Conference of 1921–1922. Recipient of the Distinguished Service Medal. He wrote The American Black Chamber (1931) about his experiences there. He later helped the Nationalists in China (1938–1940) to break Japanese codes. Following his work in China, Yardley worked briefly for the Canadian government, helping it set up a cryptological section (Examination Unit) of the National Research Council of Canada from June to December 1941. Yardley was reportedly let go due to pressure either from the Secretary of War Henry L. Stimson or from the British.
In the 1920s, when he was chief of MI-8, the first U.S. peacetime cryptanalytic organization, he and a team of cryptanalysts exploited nearly two dozen foreign diplomatic cipher systems. MI-8 was disbanded in 1929 when the State Department withdrew funding. Jobless, Yardley caused a sensation in 1931 by publishing his memoirs of MI-8, The American Black Chamber, which caused new security laws to be enacted.*TIS
1821 Baldassarre Boncompagni, (10 May 1821 – 13 April 1894), noted historian of mathematics. He set up his own publishing house and published his own journal dealing with the history of mathematics from 1868 to 1887. He was responsible for making known the importance of Leonardo Fibonacci to the history of mathematics. *VFR Boncompagni edited Bullettino di bibliografia e di storia delle scienze matematiche e fisiche ("The bulletin of bibliography and history of mathematical and physical sciences") (1868-1887), the first Italian periodical entirely dedicated to the history of mathematics. He edited every article that appeared in the journal. He also prepared and published the first modern edition of Fibonacci's Liber Abaci.*Wik
1973 Sir Robert Alexander Watson-Watt (13 Apr 1892, 5 Dec 1973) Scottish physicist who is credited with the development of radar location of aircraft, in England. He studied at St Andrews University, taught at Dundee University, and in 1917 worked in the Meteorological Office, designing devices to locate thunderstorms, and investigating the ionosphere (a term he invented in 1926). He became head of the radio section of the National Physical Laboratory (1935), where he began work on locating aircraft. His work led to the development of radar (RAdio Detection And Ranging) which played a vital role in the defence of Britain against German air raids in 1940. He was knighted in 1942. *TIS
1935 Robert Watson-Watt submitted the idea for Radar to the Air Ministry in a secret memo, "Detection and location of aircraft by radio methods" . The method would be tested on Feb 26 in a field just off the present day A5 in Northamptonshire near the village of Upper Stowe. Watson-Watt received a patent on his device on April 2.
In strange turn of technology Karma, Watson-Watt reportedly was pulled over for speeding in Canada many years later by a radar gun-toting policeman. His remark was, "Had I known what you were going to do with it I would never have invented it!"*Wik
Chain Home radar installation at Poling, Sussex, photograph, 1945. The transmitting antennas were slung between the tall towers at left; the receiving antenna towers are at right
1905 Bruno Rossi (13 Apr 1905, 21 Nov 1993) Italian pioneer in the study of cosmic radiation. In the 1930s, his experimental investigations of cosmic rays and their interactions with matter laid the foundation for high energy particle physics. Cosmic rays are atomic particles that enter earth's atmosphere from outer space at speeds approaching that of light, bombarding atmospheric atoms to produce mesons as well as secondary particles possessing some of the original energy. He was one of the first to use rockets to study cosmic rays above the Earth's atmosphere. Finding X-rays from space he became the grandfather of high energy astrophysics, being largely responsible for starting X-ray astronomy, as well as the study of interplanetary plasma. *TISForced to emigrate in October 1938 due to the Italian racial laws, Rossi moved to Denmark, where he worked with Niels Bohr. He then moved to Britain, where he worked with Patrick Blackett at the University of Manchester. Finally he went to the United States, where he worked with Enrico Fermi at the University of Chicago, and later at Cornell University. Rossi stayed in the United States, and became an American Citizen.
Rossi's Cosmic Ray Telescope
At the Rome conference on nuclear physics in 1931, Rossi met Robert Millikan and Arthur Compton.
1909 Stanislaw M. Ulam (13 Apr 1909; 13 May 1984 at age 75) Polish-American mathematician, nuclear physicist and computer scientist who played a major role in the development of the hydrogen bomb at Los Alamos. He solved the problem of how to initiate fusion in the hydrogen bomb by suggesting that compression was essential to explosion and that shock waves from a fission bomb could produce the compression needed. He further suggested that careful design could focus mechanical shock waves in such a way that they would promote rapid burning of the fusion fuel. Ulam, with J.C. Everett, also proposed the "Orion" plan for nuclear propulsion of space vehicles. While Ulam was at Los Alamos, he developed "Monte-Carlo method" which searched for solutions to mathematical problems using a statistical sampling method with random numbers. *TIS He is buried in Santa Fe National Cemetery in Santa Fe, New Mexico, USA
In 1935, John von Neumann, whom Ulam had met in Warsaw, invited him to come to the Institute for Advanced Study in Princeton, New Jersey, for a few months. From 1936 to 1939, he spent summers in Poland and academic years at Harvard University in Cambridge, Massachusetts, where he worked to establish important results regarding ergodic theory. On 20 August 1939, he sailed for the United States for the last time with his 17-year-old brother Adam Ulam. He became an assistant professor at the University of Wisconsin–Madison in 1940, and a United States citizen in 1941.
During his years at Los Alamos, Ulam was a visiting professor at Harvard from 1951 to 1952, MIT from 1956 to 1957, the University of California, San Diego, in 1963, and the University of Colorado at Boulder from 1961 to 1962 and 1965 to 1967. In 1967, the last of these positions became permanent, when Ulam was appointed Professor and Chairman of the Department of Mathematics at the University of Colorado. He kept a residence in Santa Fe, which made it convenient to spend summers at Los Alamos as a consultant. He was an elected member of the American Academy of Arts and Sciences, the United States National Academy of Sciences, and the American Philosophical Society.
Mathematicians know Ulam for Ulam's prime spiral, which shows that when the positive integers are arrayed along the Ulam spiral, prime numbers, represented by dots, tend to collect along diagonal lines.
DEATHS
1728 Samuel Molyneux (18 Jul 1689, 13 Apr 1728 at age 38)British astronomer (Royal Observatory at Kew) and politician. Together with assistant James Bradley, he made measurements of abberation - the diversion of light from stars. They made observations of the star  Draconis with a vertical telescope. Starting in 1725 they had the proof of the movement of the earth giving support to the Copernican model of the earth revolving around the sun. The star oscillated with an excursion of 39 arcsecs between its lowest declination in May and its the highest point of its oscillation in September. He was unfortunate to fall ill in 1728 and into the care of the Anatomist to the Royal Family, Dr Nathaniel St Andre, whose qualifications were as a dancing master. Molyneux died shortly thereafter. *TISMolyneux married Lady Elizabeth Capel, daughter of Algernon Capell, 2nd Earl of Essex, on 5 April 1717. In 1728, he suffered a fit while in the House of Commons. He was treated by court anatomist Nathaniel St André, but the treatment did not prove successful, and Molyneux died in Kew in April. On the night of the death, St André eloped with Molyneux's wife, Elizabeth, the two marrying in 1730. Samuel Madden, a relative of Molyneux's, claimed that St André had poisoned the MP. Although St André won an action for defamation, he found himself unable to secure regular work.*Wik
1890 Andrew Hart (14 March 1811 , 13 Apr 1890) was an Irish mathematician and Vice-Provost of Trinity College Dublin who wrote on geometry.
Hart obtained much reputation as a mathematician, and published useful treatises on hydrostatics and mechanics. Between 1849 and 1861 he contributed valuable papers to the Cambridge and Dublin Mathematical Journal, to the 'Proceedings of the Irish Academy,' and to the Quarterly Journal of Mathematics, chiefly on the subject of geodesic lines and on curves.
Hart's most important contribution was contained in his paper Extension of Terquem's theorem respecting the circle which bisects three sides of a triangle (1861). Hart wrote this paper after carrying out an investigation suggested by William Rowan Hamilton in a letter to Hart. In addition, Hart corresponded with George Salmon on the same topic. This paper contains the result which became known as Hart's Theorem, which is a generalization of Feuerbach's Theorem. Hart's Theorem states:
Taking any three of the eight circles which touch three others, a circle can be described to touch these three, and to touch a fourth circle of the eight touching circles.
1906 Walter Frank Raphael Weldon DSc FRS (Highgate, London, 15 March 1860 – Oxford, 13 April 1906) generally called Raphael Weldon, was an English evolutionary biologist and a founder of biometry. He was the joint founding editor of Biometrika, with Francis Galton and Karl Pearson.*Wik Pearson said of him, "He was by nature a poet, and these give the best to science, for they give ideas." *SAU
He moved to St John's College, Cambridge in 1878. There Weldon studied with the developmental morphologist Francis Balfour who influenced him greatly; Weldon gave up his plans for a career in medicine. In 1881 he gained a first-class honors degree in the Natural Science Tripos; in the autumn he left for the Naples Zoological Station to begin the first of his studies on marine biological organisms.
Upon returning to Cambridge in 1882, he was appointed university lecturer in Invertebrate Morphology. Weldon's work was centered on the development of a fuller understanding of marine biological phenomena and selective death rates of these organisms.
His interests were changing from morphology to problems in variation and organic correlation. He began using the statistical techniques that Francis Galton had developed for he had come to the view that "the problem of animal evolution is essentially a statistical problem." Weldon began working with his University College colleague, the mathematician Karl Pearson.
Weldon was one of the first scientists to provide evidence of stabilizing and directional selection in natural populations.
In 1894, Weldon rolled a set of 12 dice 26,306 times. He collected the data in part, 'to judge whether the differences between a series of group frequencies and a theoretical law, taken as a whole, were or were not more than might be attributed to the chance fluctuations of random sampling.' Weldon's dice data were used by Karl Pearson in his pioneering paper on the chi-squared statistic. *Wik
Bust in the Oxford University Museum
1925 Elwood Haynes (born 14 Oct 1857, 13 Apr 1925).
American inventor who built one of the first successful gasoline-powered automobiles. In 1886, when natural gas was found in his hometown of Portland, Indiana, Haynes organized a company to supply it to the town. He devised a method to dehydrate the gas prior to its being pumped through the lines. Also in 1886, he invented a small vapor thermostat used on natural gas. In 1893, he purchased a gasoline engine and designed a "horseless carriage." When Haynes was searching for an alloy that would make a durable spark plug electrode, he invented stellite alloy, which invention is still contributing to society today. Harder than steel and resistant to corrosion, this metal now plays an important part in fabrication of aeronautical materials suitable for exploration of outer space.
1941 Annie Jump Cannon (11 Dec 1863; 13 Apr 1941) American, deaf astronomer who specialized in the classification of stellar spectra. In 1896 she was hired at the Harvard College Observatory, remaining there for her entire career. The Harvard spectral classification system had been first developed by Edward C. Pickering, Director of the Observatory, around the turn of the century using objective prism spectra taken on improved photographic plates. In conjunction with Pickering Cannon was to further develop, refine, and implement the Harvard system. She reorganized the classification of stars in terms of surface temperature in spectral classes O, B, A, F, G, K, M, and cataloged over 225,000 stars for the monumental Henry Draper Catalog of stellar spectra, (1918-24).*TIS
2004 David Herbert Fowler (April 28, 1937 – April 13, 2004) was a historian of Greek mathematics who published work on pre-Eudoxian ratio theory (using the process he called anthyphaeresis). He disputed the standard story of Greek mathematical discovery, in which the discovery of the phenomenon of incommensurability came as a shock.
His thesis was that, not having the real numbers, nor division, the Greeks faced difficulties in defining rigorously the notion of ratio. They called ratio 'logos'. Euclid Book V is an exposition of Eudoxus's theory of proportion, which Eudoxus discovered about 350BC, and which has been described as the jewel in the crown of Greek mathematics. Eudoxus showed by a form of abstract algebra how to handle rigorously the case when two ratios are equal, without actually having to define them. His theory was so successful that, in effect, it killed off perfectly good earlier theories of ratio, and Fowler's aim had been to find the evidence for the rediscovery of these previous theories.
In particular Thaetetus (c 414-369BC) introduced a definition of ratio using a procedure called anthyphairesis, based on the Euclidean subtraction algorithm. Fowler developed his ideas in a series of papers, culminating in the book The Mathematics of Plato's Academy: A New Reconstruction, which was published in 1987. This book is based on a study of the primary sources and on their assimilation and transformation.*Wik
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2008 John Archibald Wheeler (9 Jul 1911, 13 Apr 2008 at age 96) was the first American physicist involved in the theoretical development of the atomic bomb. He also originated a novel approach to the unified field theory. Wheeler was awarded the 1997 Wolf Prize "for his seminal contributions to black hole physics, to quantum gravity, and to the theories of nuclear scattering and nuclear fission." After recognizing that any large collection of cold matter has no choice but to yield to the pull of gravity and undergo total collapse. Wheeler first coined the term "black hole" in 1967.*TIS
For most of his career, Wheeler was a professor of physics at Princeton University, which he joined in 1938, remaining until 1976. At Princeton he supervised 46 PhD students, more than any other physics professor. Wheeler's graduate students included Jacob Bekenstein, Hugh Everett, Richard Feynman, David Hill, Bei-Lok Hu, John R. Klauder, Charles Misner, Kip Thorne, William Unruh, Robert M. Wald, Katharine Way, and Arthur Wightman and others you may well have heard of.
2014 Emma Castelnuovo (12 December 1913 – 13 April 2014) was an Italian mathematician and teacher.
It is well known that in the first half of the twentieth century an important field of mathematical research - algebraic geometry - was flourishing in Italy. Emma's father Guido Castelnuovo and her uncle Federigo Enriques, the brother of her mother Elbina, were prominent researchers in this field, both full professors in university. They were also very committed to mathematical education.
In 2013, the year of her 100th birthday, the International Commission on Mathematical Instruction created an award named after Castelnuovo to recognize outstanding contributions to mathematics education.
In 1948 she published the first of many editions of the book Intuitive geometry, which demonstrated her personal approach to teaching mathematics. Her teaching texts have since been translated into several other languages and used in schools, especially in Spanish-speaking countries. In 1978 and 1980 she was sent by UNESCO to Niger to teach in a class that corresponded to the Italian eighth grade.
She served as president of the "International Commission for the Improvement of Mathematics Teaching."
She died in Rome on 13 April 2014 and was buried in the Verano cemetery with her father and mother..
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
*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
is the latitude, 
is the longitude, and 
is the central meridian.
was also transcendental. *TIS
