The shoelace formula is an algorithm for finding the area of a polygon in the plane when the coordinates (x,y) are known. For example if the coordinates of a quadrilateral are given as (1,1); (3, -1); (4,4); and (0,3) then the area can be calculated by putting these in two columns (or rows as shown below) and multiplying along diagonals as shown (notice that the first coordinate pair are repeated at the end for ease of computation).
The diagonal products to each side are summed, then the absolute value of the difference of the two sums is multiplied by 1/2 to give the area. In this case the right products total to 23, the left to 2, for a difference of 21, so the area is one-half of that, or 10.5 square units. The points have to be taken in order around the polygon in either clockwise or counter-clockwise order using each number once as the first pair. It is the criss-cross appearance of the diagonals that draws the "shoestring" name to the approach.
The shoelace formula is just a simple diagrammatic extension of an earlier determinant method sometimes (perhaps seldom?) called the Surveyor's formula (not to be confused with the Ptolemaic Egyptian method of the same name for finding areas of quadrilaterals), which does the same computation with a sequence of determinants, like this: Note that This gives ½(-4+16+12-3) which is again the 10.5 sq units we had before. The calculation of each determinant constitute one product from each side of the shoelace algorithm and calculates their difference. (the sum of the differences is the same as the difference of the sums).
Additional illustrations and worked examples can be found at this file by Charles L. Hamberg and Ronald Vavrinek, from the Illinois Mathematics and Science Academy. It also includes a program you can use on your ti-84 or other programmable calculator.
The Shoelace formula was invented in 1769 by Albrecht Meister, but it is widely attributed to Gauss who made significant discoveries about polygons at the age of 18 in the 1790s. It may now be seen as an application of Green’s Theorem (1828).
While we are talking about shoelaces, they also showed up in an interesting book by Australian Mathematician Burkard Polster. In "The Shoelace Book", Polster examines various approaches to methods of lacing a pair of shoes, and "mathematizes" lacings formally enough to enumerate the possible lacing paths.. For a shoe with six eyelets on each side there turns out to be 43,200 different paths for a shoelace to pass through every eyelet, even with the added condition that each eyelet must contribute to the essential purpose of pulling the two halves of the shoe together..... go ahead, take a minute and check...I'll wait... dum de dumm..de dumm (all done?) OK.. If that was more difficult than you might have expected, you can find a good link that gives a glimpse of the work at Google Books where he describes lacings by such names as Crisscross, zigzag, bowtie, devil, angel, and star... I'm thinking of switching to the bowtie lacing myself, not just because it is efficient, but I like the look.
And in case you think this is all trivial math, take a look at this page from the early pages of the book:
Information is the resolution of uncertainty. ~Claude Shannon
The 55th day of the year; 55 is the largest triangular number that appears in the Fibonacci Sequence. (Is there a largest square number?)
55 is also the largest year day that is a triangular number that is the sum of five triangular numbers. 55 = 3+6+10+15+21.
55 is also a Kaprekar Number: 55² = 3025 and 30 + 25 = 55 (Thanks to Jim Wilder) There are three two-digit numbers that have this property.
And speaking of 52, Everyone knows that 32 + 42 = 52, but did you know that 332 + 442 = 552 But after that, there could be no more.... right? I mean, that's just too improbable, so why is he stil l going on like this? You don't think......Nah.
55 is the only year day that is both a non-trivial base ten palindrome and also a palindrome in base four.
EVENTS
1582 Pope Gregory XIII promulgated his calendar reform in the papal bull Inter gravissimus (Of the gravest concern). It took effect (in Italy and some other Catholic countries) October 5, 1582 (Julian Thursday, 4 October 1582, being followed by Gregorian Friday, 15 October 1582) Aloisious Lilus whose calendar work had been called the primary author of the reform died in 1576, but his suggestions for reform were taken almost in total. One exception was his plan to adjust the calendar by one day for ten consecutive years instead of the ten days at once.
1616 Inquisition qualifiers deny teaching of Heliocentric view . On February 19, 1616, the Inquisition had asked a commission of theologians, known as qualifiers, about the propositions of the heliocentric view of the universe. On February 24 the Qualifiers delivered their unanimous report: the idea that the Sun is stationary is "foolish and absurd in philosophy, and formally heretical since it explicitly contradicts in many places the sense of Holy Scripture..."; while the Earth's movement "receives the same judgement in philosophy and ... in regard to theological truth it is at least erroneous in faith."At a meeting of the cardinals of the Inquisition on the following day, Pope Paul V instructed Bellarmine to deliver this result to Galileo, and to order him to abandon the Copernican opinions; should Galileo resist the decree, stronger action would be taken. On February 26, Galileo was called to Bellarmine's residence, and accepted the orders. *Wik
1755 William Hogarth’s satirical print, “An Election Entertainment,” was published. It contains a Tory sign bearing the inscription “Give us our eleven days.” This refers to the fact that eleven dates were removed from the calendar when England converted to the Gregorian calendar on September 14, 1752. *VFR
1772 Lagrange, in a letter to d’Alembert, called higher mathematics “decadent.” *Grabiner, Origins of Cauchy’s Rigorous Calculus, pp. 25, 185
1818 The word Tangram emerged in American vocabulary about this time. According to various dictionaries, the word may be derived from a Chinese word tang, or it may be derived from the obsolete English word trangam, meaning a trinket or a gimcrack. Merriam-Webster says the word is of unknown origin.
Trangam is found in a 1658 dictionary.
On June 1, 1809, the American Citizen reported, “Vast numbers of those ‘tangrams and gimcracks’ are piled up in the office, of every shape and size, making it a great toy shop. [Joel S. Berson]
A classified advertisement in the Franklin Gazette of Feb. 24, 1818, offers “Chinese Tangrams,” which were probably puzzles [Bill Mullins].
According to Wikipedia and another web page, the word tangram was coined by Dr. Thomas Hill in 1848 for his book Geometrical Puzzles for the Young. [Perhaps this is the first use of the word with its modern meaning.] The web page says the device{???}was invented between 1796 and 1802 in China by Yang-cho-chu-shih, who published the book Ch'i ch'iao t'u (Pictures using seven clever pieces). * Jeff Miller
1842 Sylvester resigned his position at the University of Virginia (after only four months), after a dispute with a student who was reading a newspaper in class. Persistent rumors that he killed the student are unfounded. *VFR
1880 The first commercial order of an Edison Lighting system was installed on the newly launched Steamship Columbia. The dynamo and lights were installed by Edison Engineers and first lighting was on May 2, 1880. The event was featured in the May issue of Scientific American. John Roach and Sons had built the ship in their Chester, Pennsylvania ship works and launched it on Feb 24, 1880. *The History of the American Bureau of Shipping.
1881 Cambridge University in England allowed women to officially take university examinations and to have their names posted along with those of the male students. Previously some women were given special permission to take the Tripos Exam. One of these was Charlotte Agnes Scott, who did quite well on the exam. 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 wavings of hats.” [Women of Mathematics. A Biobibliographic Sourcebook (1987), edited by Louise S. Grinstein and Paul J. Campbell, 194-195] *VFR
Moving to the United States in 1885, she became one of eight founding faculty and Associate Professor of Mathematics at Bryn Mawr College, and Professor from 1888 to 1917. She was the first mathematician at Bryn Mawr College and the first department head.[3] During this period she directed the PhD theses of some pioneering women mathematicians. Of the nine other women to earn doctorates in mathematics in the nineteenth century, three studied with Scott. Scott and Grace Andrews were the only two women listed in the first edition of American Men of Science, which appeared in 1906. *Wik
1896 Henri Becquerel read a report to the French Academy of Sciences of his investigation of the phosphorescent rays of some “double sulfate of uranium and potassium” crystals. He reported that he placed the crystals on the outside of a photographic plate wrapped in sheets of very thick black paper and exposed the whole to the sun for several hours. When he developed the photographic plate, he saw a black silhouette of the substance exposed on the negative. When he placed a coin or metal screen between the uranium crystals and the wrapped plate, he saw images of those objects on the negative. He did not yet know yet that the sun is not necessary to initiate the rays, nor did he yet realize that he had accidentally discovered radioactivity. He would learn more from a further accidental discovery on 26 Feb 1896.*TIS
1920 As part of the National Education Association’s annual meeting, 127 mathematics teachers from 20 states met in Cleveland, Ohio, for the “purpose of organizing a National Council of Mathematics Teachers.” *VFR
1931, the Fields Medal was established to recognize outstanding contributions to mathematics. It was conceived since there was no Nobel Prize for mathematicians. Although John Charles Fields probably thought of the medal at some earlier time, the first recorded mention of it was made on 24 Feb 1931 in minutes of a committee meeting. He was chairman of the Committee of the International Congress which had been set up by the University of Toronto to organize the 1924 Congress in Toronto. After the event, Fields proposed that income of $2,500 remaining from that convention would be designated for two medals to be awarded at future International Mathematical Congresses. In 1936, the first awards were made in Oslo. The medal was first awarded to Finnish mathematician Lars Ahlfors and American mathematician Jesse Douglas,*TIS
On this day in 1987, a supernova in the outskirts of the Tarantula Nebula in the Large Magellanic Cloud occurred visible to the naked eye. It was the closest observed supernova since Kepler's Supernova in 1604, which occurred in the Milky Way itself.
Supernova 1987A remnant near the center
In 1968, Nature carried the announcement of the discovery of a pulsar (a pulsating radio source). The first pulsar was discovered by a graduate student, Jocelyn Bell, on 28 Nov 1967, then working under the direction of Prof. Anthony Hewish. The star emitted radio pulses with clock-like precision. It was observed at the Mullard Radio Astronomy Observatory, Cambridge University, England. A special radio telescope, was used with 2,048 antennae arrayed across 4.4 acres. Pulsars prompted studies in quantum-degenerate fluids, relativistic gravity and interstellar magnetic fields. *TIS [Before the nature of the signal was determined, the researchers, Bell and her Ph.D supervisor Antony Hewish, somewhat seriously considered the possibility of extraterrestrial life, "We did not really believe that we had picked up signals from another civilization, but obviously the idea had crossed our minds and we had no proof that it was an entirely natural radio emission. It is an interesting problem - if one thinks one may have detected life elsewhere in the universe how does one announce the results responsibly? Who does one tell first?" The observation was given the half-humorous designation Little green men 1, until researchers Thomas Gold and Fred Hoyle correctly identified these signals as rapidly rotating neutron stars with strong magnetic fields.] Read the details in her own words here.
The existence of neutron stars was first proposed by Walter Baade and Fritz Zwicky in 1934, when they argued that a small, dense star consisting primarily of neutrons would result from a supernova.
80 periods of the pulsar CP 1919 stacked together, graphic originated by Howard D. Craft, Jr, 1970,
*Linda Hall Org
Jocelyn Bell and the radio telescope built by herself and other graduate students, used to discover the first pulsar, CP 1919, 1967 (Cambridge University Press via bigear.org)
*Linda Hall Org
2009 Comet Lulin, a non-periodic comet, makes its closest approach to Earth, peaking in brightness between magnitude +4 and magnitude +6. The comet was first photographed by astronomer Lin Chi-Sheng (林啟生) with a 0.41-metre (16 in) telescope at the Lulin Observatory in Nantou, Taiwan on July 11, 2007. However, it was the 19-year-old Ye Quanzhi (葉泉志) from Sun Yat-sen University in China, who identified the new object from three of the photographs taken by Lin. *Wik
Comet Lulin as seen on January 31st (top) and February 4th of 2009.
BIRTHS
1663 Thomas Newcomen (24 Feb 1663 (Newcomen was baptised OTD unfortunately there is no mention of his birth date in the baptism record); 5 Aug 1729 at age 66) English engineer and inventor of the the world's first successful atmospheric steam engine. His invention of c.1711 came into use by 1725 to pump water out of coal mines or raise water to power water-wheels. On each stroke, steam filled a cylinder closed by a piston, then a spray of water chilled and condensed the steam in the cylinder creating a vacuum, then atmospheric pressure pushed the piston down. A crossbeam transferred the motion of the piston to operating the pump. This was wasteful of fuel needed to reheat the cylinder for the next stroke. Despite being slow and inefficient, Newcomen's engine was relied on for the first 60 years of the new steam age it began, perhaps the single most important invention of the Industrial Revolution. *TIS
Animation of a schematic Newcomen engine.
– Steam is shown pink and water is blue.
– Valves move from open (green) to closed (red)
1709 Jacques de Vaucanson (24 Feb 1709; 21 Nov 1782 at age 73) French inventor of automata - robot devices of later significance for modern industry. In 1737-38, he produced a transverse flute player, a pipe and tabor player, and a mechanical duck, which was especially noteworthy, not only imitating the motions of a live duck, but also the motions of drinking, eating, and "digesting." He made improvements in the mechanization of silk weaving, but his most important invention was ignored for several decades - that of automating the loom by means of perforated cards that guided hooks connected to the warp yarns. (Later reconstructed and improved by J.-M. Jacquard, it became one of the most important inventions of the Industrial Revolution.) He also invented many machine tools of permanent importance. *TIS
1804 Heinrich Friedrich Emil Lenz (24 Feb 1804, 10 Feb 1865 at age 61) was the Russian physicist who framed Lenz's Law to describe the direction of flow of electric current generated by a wire moving through a magnetic field. Lenz worked on electrical conduction and electromagnetism. In 1833 he reported investigations into the way electrical resistance changes with temperature, showing that an increase in temperature increases the resistance (for a metal). He is best-known for Lenz's law, which he discovered in 1834 while investigating magnetic induction. It states that the current induced by a change flows so as to oppose the effect producing the change. Lenz's law is a consequence of the, more general, law of conservation of energy. *TIS
1808 John Wise, (February 24, 1808 – September 28, 1879) was an American balloonist. Wise, who came from Lancaster, Penn., made his first ascent in 1835, and he added well over 400 subsequent flights during a 40-year career, if one can call ballooning a career. One of his early ascents (1838) was notable for his discovery, made under extreme circumstances at 13,000 feet, that an exploded balloon will collapse to form a parachute and allow for a safe if rather rapid descent. This conversion from balloon to parachute was only possible because the early balloons were surrounded with an enclosing network of rope, to keep the balloon from expanding at altitude, but which in this case served to confine and retain the punctured balloon, which air pressure formed into an umbrella shape .
Wise also made a trip from St. Louis to New York in 1859, which he self-proclaimed the most amazing balloon voyage of all time (this in his book, Through the Air: a Narrative of Forty Years’ Experience as an Aeronaut, 1873, which we have in our collections). He did make a drawing of Niagara Falls from the air that is rather impressive. During this trip, his balloon almost landed in Lake Ontario, which made for an even more dramatic pictorial record .
Wise's other claim to fame is that he made the nation's first airmail delivery for the US Postal Service. This was on Aug. 17, 1859, when he took off from Lafayette, Ind., with some 120 letters and a few flyers, headed for either New York or Philadelphia (fourth image). His balloon was called The Jupiter, and the feat was commemorated, on the centennial of the flight, with a postage stamp, the 7¢ Jupiter of 1959.
Purdue University traces the origin of its School of Aeronautics to the ascent of the Jupiter, even though the University wasn't even founded until 10 years later (and the School of Aeronautics not until 1945). What is often lost in all this hoopla is that the Jupiter made it approximately 2% of the way to New York, coming down in a field just 25 miles east of Lafayette. Wise hardly mentions his role as postal carrier in his book, commenting only that when he realized that the journey east was about to end, he dropped the letters to the ground via a handmade parachute. No wonder only one letter survived; it is in the Smithsonian Institution.
Wise was not mentioned on the Jupiter stamp, nor is there much else in the way of grateful commemoration for his ballooning feats. The only monument we could find is in his home town of Lancaster, and we are not sure a great deal of money or thought went into its design . *Linda Hall Org
1868 James Ireland Craig (24 Feb 1868 in Buckhaven, Fife, Scotland - 26 Jan 1952 in Cairo, Egypt) graduated from Edinburgh and Cambridge. He taught at Eton and Winchester and then went to work on the Nile Survey for the Egyptian government. He made some significant inventions in map projections. He was killed when a mob attacked the Turf Club in Cairo.*SAU
1878 Felix Bernstein born. In 1895 or 1896, while still a Gymnasium student, he volunteered to read the proofs of a paper of Georg Cantor on set theory. In the process of doing this the idea came to him one morning while shaving of how to prove what is now called the Cantor/Bernstein theorem: If each of two sets is equivalent to a subset of the other, then they are equivalent. *VFR He also worked on transfinite ordinal numbers.*SAU
1909 Max Black (24 February 1909, 27 August 1988) was a British-American philosopher and a leading influence in analytic philosophy in the first half of the twentieth century. He made contributions to the philosophy of language, the philosophy of mathematics and science, and the philosophy of art, also publishing studies of the work of philosophers such as Frege. His translation (with Peter Geach) of Frege's published philosophical writing is a classic text. *Wik
1920 K C Sreedharan Pillai (1920–1985) was an Indian statistician who was known for his works on multivariate analysis and probability distributions. Pillai was honoured by being elected a Fellow of the American Statistical Association and a Fellow of the Institute of Mathematical Statistics. He was an elected member of the International Statistical Institute. *Wik Perhaps his best known contribution is the widely used multivariate analysis of variance test which bears his name.*SAU
1946 Gregori Aleksandrovich Margulis (24 Feb 1946 - )Russian mathematician who was awarded the Fields Medal in 1978 for his contributions to the theory of Lie groups, though he was not allowed by the Soviet government to travel to Finland to receive the award. In 1990 Margulis immigrated to the United States. Margulis' work was largely involved in solving a number of problems in the theory of Lie groups. In particular, Margulis proved a long-standing conjecture by Atle Selberg concerning discrete subgroups of semisimple Lie groups. The techniques he used in his work were drawn from combinatorics, ergodic theory, dynamical systems, and differential geometry.*TIS The napkin folding problem is a problem in geometry and the mathematics of paper folding that explores whether folding a square or a rectangular napkin can increase its perimeter. The problem is known under several names, including the Margulis napkin problem, suggesting it is due to Grigory Margulis *Wik
1955 Steven Paul Jobs (24 Feb 1955; 5 Oct 2011 at age 56) U S inventor and entrepreneur who, in 1976, co-founded Apple Inc. with Steve Wozniak to manufacture personal computers. During his life he was issued or applied for 338 patents as either inventor or co-inventor of not only applications in computers, portable electronic devices and user interfaces, but also a number of others in a range of technologies. From the outset, he was active in all aspects of the Apple company, designing, developing and marketing. After the initial success of the Apple II series of personal computers, the Macintosh superseded it with a mouse-driven graphical interface. Jobs kept Apple at the forefront of innovative, functional, user-friendly designs with new products including the iPad tablet and iPhone. Jobs was also involved with computer graphics movies through his purchase (1986) of the company that became Pixar *TIS
*Wik
1967 Brian Paul Schmidt AC, FRS (February 24, 1967, ) is a Distinguished Professor, Australian Research Council Laureate Fellow and astrophysicist at The Australian National University Mount Stromlo Observatory and Research School of Astronomy and Astrophysics and is known for his research in using supernovae as cosmological probes. He currently holds an Australia Research Council Federation Fellowship and was elected to the Royal Society in 2012. Schmidt shared both the 2006 Shaw Prize in Astronomy and the 2011 Nobel Prize in Physics with Saul Perlmutter and Adam Riess for providing evidence that the expansion of the universe is accelerating. *Wik
DEATHS
1728 Charles René Reyneau (11 June 1656 in Brissac, Maine-et-Loire, France - 24 Feb 1728 in Paris, France) was a French mathematician who published an influential textbook on the newly invented calculus.*SAU (He) "undertook to reduce into one body, for the use of his scholars, the principal theories scattered here and there in Newton, Descartes, Leibnitz, Bernoulli, the Leipsic Acts, the Memoirs of the Paris Academy, and in other works; treasures which by being so widely dispersed, proved much less useful than they otherwise might have been. The fruit of this undertaking, was his “Analyse Demontree,” or Analysis Demonstrated, which he published in 1708. He gave it the name of “Analysis Demonstrated,” because he demonstrates in it several methods which had not been handled by the authors of them, with sufficient perspicuity and exactness. The book was so well approved, that it soon became a maxim, at least in France, that to follow him was the best, if not the only way, to make any extraordinary progress in the mathematics and he was considered as the first master, as the Euclid of the sublime geometry." (From the 1812 Chalmer's Biography, vol. 26, p. 151)
1799 Georg Christoph Lichtenberg (1 Jul 1742, 24 Feb 1799 at age 56). German physicist and satirical writer, best known for his aphorisms and his ridicule of metaphysical and romantic excesses. At Göttingen University, Lichtenberg did research in a wide variety of fields, including geophysics, volcanology, meteorology, chemistry, astronomy, and mathematics. His most important were his investigations into physics. Notably, he constructed a huge electrophorus and, in the course of experimentations, discovered in 1777 the basic principle of modern xerographic copying; the images that he reproduced are still called "Lichtenberg figures." These are radial patterns formed when sharp, pointed conducting bodies at high voltage get near enough to insulators to discharge electrically, or seen on persons struck by lightning. *TIS
1810 Henry Cavendish (10 Oct 1731; 24 Feb 1810) English chemist and physicist who conducted experiments with diverse interests in his private laboratory. Most notably, he determined the mass and density of the Earth. He investigated the properties of hydrogen and carbon dioxide, including comparing their density to that of air. Cavendish also showed that water was a compound and measured the specific heat of various substances. His manuscripts (published 1879) revealed discoveries he made in electrostatics before Coulomb, Ohm and Faraday - including deducing the inverse square law of electrostatic attraction and repulsion. He also found specific inductive capacity. His family name is attached to the Cavendish Laboratory (founded 1871, funded by a later family member) at Cambridge University. *TIS Cavendish was supposedly so shy that for his only portrait the artist painted his coat from a hook in the hall, then painted Cavendish body from memory. *"Shock and Awe", BBC broadcast on the history of electricity
Cavendish's apparatus for making and collecting hydrogen
1812 Étienne-Louis Malus (23 Jun 1775, 24 Feb 1812 at age 36) He served in Napoleon's corps of engineers, fought in Egypt, and contracted the plague during Napoleon's aborted campaign in Palestine. Posted to Europe after 1801, he began research in optics. In 1808, he discovered that light rays may be polarized by reflection, while looking through a crystal of Iceland spar at the windows of a building reflecting the rays of the Sun. He noticed that on rotating the crystal the light was extinguished in certain positions. Applying corpuscular theory, he argued that light particles have sides or poles and coined the word "polarization." *TIS He studied geometric systems called ray systems, closely connected to Julius Plücker's line geometry. He conducted experiments to verify Christiaan Huygens' theories of light and rewrote the theory in analytical form. His discovery of the polarization of light by reflection was published in 1809 and his theory of double refraction of light in crystals, in 1810. Malus attempted to identify the relationship between the polarising angle of reflection that he had discovered, and the refractive index of the reflecting material. While he deduced the correct relation for water, he was unable to do so for glasses due to the low quality of materials available to him (most glasses at that time showing a variation in refractive index between the surface and the interior of the glass). It was not until 1815 that Sir David Brewster was able to experiment with higher quality glasses and correctly formulate what is known as Brewster's law. Malus is probably best remembered for Malus' law, giving the resultant intensity, when a polariser is placed in the path of an incident beam. His name is one of the 72 names inscribed on the Eiffel tower.*Wik
1844 Antoine-André-Louis Reynaud (12 Sept 1771, 24 Feb 1844) Reynaud published a number of extremely influential textbooks. He published a mathematics manual for surveyors as well as Traité d'algèbre, Trigonométrie rectiligne et sphérique, Théorèmes et problèmes de géométrie and Traité de statistique. His best known texts, however, were his editions of Bézout's Traité d'arithmétique which appeared in at least 26 versions containing much original work by Reynaud. It appears that Reynaud became interested in algorithms when he was working with de Prony. At this time de Prony was very much involved in trying to get his logarithmic and trigonometric tables published and it seems to have made Reynaud think about analysing algorithms. Certainly Reynaud, although his results in this area were rather trivial, must get the credit for being one of the first people to give an explicit analysis of an algorithm, an area of mathematics which is of major importance today. *SAU
1856 Nikolai Ivanovich Lobachevsky (December 1, 1792 – February 24, 1856 (N.S.); November 20, 1792 – February 12, 1856 (O.S.)) was a Russian mathematician and geometer, renowned primarily for his pioneering works on hyperbolic geometry, otherwise known as Lobachevskian geometry. William Kingdon Clifford called Lobachevsky the "Copernicus of Geometry" due to the revolutionary character of his work. *Wik A yahoo recording of the classic Tom Lehrer song about Lobachevsky is here with lyrics. Lehrer has stated there is no accusation of Lobachevsky plagiarizing anything, and his name was chosen for the rhythmic characteristics.
1871 Julius Ludwig Weisbach (10 August 1806 in Mittelschmiedeberg (now Mildenau Municipality), Erzgebirge, 24 February 1871, Freiberg) was a German mathematician and engineer. He studied with Carl Friedrich Gauss in Göttingen and with Friedrich Mohs in Vienna. He wrote an influential book for mechanical engineering students, called Lehrbuch der Ingenieur- und Maschinenmechanik, which has been expanded and reprinted on numerous occasions between 1845 and 1863. *Wik He wrote fourteen books and 59 papers he wrote on mechanics, hydraulics, surveying, and mathematics. It is in hydraulics that his work was most influential, with his books on the topic continuing to be of importance well into the 20th century. *SAU
1923 Edward Williams Morley (29 Jan 1838; 24 Feb 1923) American chemist who is best known for his collaboration with the physicist A.A. Michelson in an attempt to measure the relative motion of the Earth through a hypothetical ether (1887). He also studied the variations of atmospheric oxygen content. He specialized in accurate quantitative measurements, such as those of the vapor tension of mercury, thermal expansion of gases, or the combining weights of hydrogen and oxygen. Morley assisted Michelson in the latter's persuit of measurements of the greatest possible accuracy to detect a difference in the speed of light through an omnipresent ether. Yet the ether could not be detected and the physicists had seriously to consider that the ether did not exist, even questioning much orthodox physical theory. *TIS
1933 Eugenio Bertini (8 Nov 1846 in Forli, Italy - 24 Feb 1933 in Pisa, Italy) was an Italian mathematician who worked in projective and algebraic geometry. His work in algebraic geometry extended Cremona's work. He studied geometrical properties invariant under Cremona transformations and used the theory to resolve the singularities of a curve. A paper by Kleiman studies what the authors calls the two fundamental theorems of Bertini. These two fundamental theorems are among the ones most used in algebraic geometry. The first theorem is a statement about singular points of members of a pencil of hypersurfaces in an algebraic variety. The second theorem is about the irreducibility of a general member of a linear system of hypersurfaces. *SAU
Memorial in childhood home of Gaylord, Mi
2001 Claude Shannon (30 April 1916 in Petoskey, Michigan, USA - 24 Feb 2001 in Medford, Massachusetts, USA) founded the subject of information theory and he proposed a linear schematic model of a communications system. His Master's thesis was on A Symbolic Analysis of Relay and Switching Circuits on the use of Boole's algebra to analyse and optimise relay switching circuits. *SAU While working with John von Neumann on early computer designs, (John) Tukey introduced the word "bit" as a contraction of "binary digit". The term "bit" was first used in an article by Claude Shannon in 1948. Among several statues to Shannon, one is erected in his hometown of Gaylord, Michigan. The statue is located in Shannon Park in the center of downtown Gaylord, which was Shannon's boyhood home. Shannon Park is the former site of the Shannon Building, built and owned by Claude Shannon's father. Dr. Claude E Shannon with an electronic mouse which has a 'super' memory and can learn its way round a maze without a mistake after only one 'training' run, on May 10, 1952.
1918 Katherine Coleman Goble Johnson (August 26, 1918 in White Sulphur Springs, W. Va {pop 800)- Feb 24, 1980) is an American physicist, space scientist, and mathematician who contributed to America's aeronautics and space programs with the early application of digital electronic computers at NASA. As the small town she was born in had no schools for blacks beyond the eighth grade, her father sent her and her siblings to Institute, West Virginia, for high school. She graduated from the historically black West Virginia State College and taught at black public schools before becoming one of three black students to integrate West Virginia graduate schools in 1939. Known for accuracy in computerized celestial navigation, she calculated the trajectory for Project Mercury and the 1969 Apollo 11 flight to the Moon. From 1953 through 1958, Johnson worked as a "computer" for NACA (later to become NASA), doing analysis for topics such as gust alleviation for aircraft. She calculated the trajectory for the space flight of Alan Shepard, the first American in space, in 1959. She also calculated the launch window for his 1961 Mercury mission. She plotted backup navigational charts for astronauts in case of electronic failures. In 1962, when NASA used computers for the first time to calculate John Glenn's orbit around Earth, officials called on her to verify the computer's numbers (other versions say it was Glenn himself who requested she check the data). On November 24, 2015, President Barack Obama her with the Presidential Medal of Freedom and cited as a pioneering example of African American women in STEM *Wik NASA announced her death at 101 on Feb 24, 2020.
Johnson working at the Spacecraft Controls Branch of NASA in 1966.
*Wik
Credits : *CHM=Computer History Museum *FFF=Kane, Famous First Facts *NSEC= NASA Solar Eclipse Calendar *RMAT= The Renaissance Mathematicus, Thony Christie *SAU=St Andrews Univ. Math History *TIA = Today in Astronomy *TIS= Today in Science History *VFR = V Frederick Rickey, USMA *Wik = Wikipedia *WM = Women of Mathematics, Grinstein & Campbell
~Carl F. Gauss, His motto. He would limit his publications to work he regarded as complete and perfect.
Rubik's cube has 54 squares
The 54th day of the year; 54 is the smallest number that can be written as the sum of 3 squares in 3 ways.(Well, go on, find all three ways!) There are 54 ways to draw six circles through all the points on a 6x6 lattice. *gotmath.com
54 is the fourth Leyland number, after mathematician Paul Leyland. Leyland numbers are numbers of the form \(x^y + y^x \) where x,y are both integers greater than 1.
And the Sin(54o) is one-half the golden ratio.
EVENTS
Drawing by Athanasius Kircher, 1684
1668/9 Cheerleaders Rejoice, The Megaphone is born.. A Letter from Newton on this date is extended by John Collins. In it he mentions "Another useful Instrument lately invented here, is Sir Samuell Morelands loud speaking Trumpett, of which he hath written a Booke or history with the title of Tuba Stentorophonica value one shilling, by which persons may discourse at about a Mile and a halfes distance, if not more". A very similar type of instrument had been thought of by Athanasius Kircher. Two years earlier he described a device that could be used for both broadcasting on one end and “overhearing” on the other. The term ‘megaphone’ was seemingly coined by Thomas Edison 200 years later. *Wik The image at right shows "war tubas" to detect sound of enemy aircraft in the 1920' and 30's before radar. This one shows Emperor Showa inspecting mobile Japanese tubas, but they were common in many countries. *Chris Wild, The strange history of listening before radar.
1826 Lobachevsky first announced his principles of non-Euclidean geometry. This was done in a talk at his home University of Kazan. Unfortunately no record of the talk survives. *VFR The first published treatise on hyperbolic geometry is Lobachevsky’s Elements of geometry, printed in installments in the Kazan Messenger in the years 1829-1830. Before that article, Lobachevsky wrote a memoir on the same subject, which he presented on the 12th (Old Style; 23rd New Style) of February 1826 to the Physico-mathematical Section of Kazan University. The title of the memoir is Exposition succinte des principes de la g´eom´etrie avec une d´emonstration rigoureuse du th´eor`eme des parall`eles (A brief Exposition of the principles of geometry with a rigorous proof of the theorem on parallels). The manuscript of the memoir does not survive; it was “lost” by the referees. *HYPERBOLIC GEOMETRY IN THE WORK OF J. H. LAMBERT ; ATHANASE PAPADOPOULOS AND GUILLAUME THERET
1855 At 1:05 a.m., Johann Carl Friedrich Gauss, Professor of Mathematics and Director of the Observatory at G¨ottingen, ceased breathing. His pocket watch, which he had carried with him most of his life, ceased ticking at almost exactly the same time. [Eves, Adieu, 43◦]*VFR See Death
1886 Charles Martin Hall, assisted by his older sister Julia Brainerd Hall, invented an inexpensive method for producing aluminum from bauxite, which became the first metal to attain widespread use since the prehistoric discovery of iron. He was one of the founders of Alcoa.*Wik Aluminum is abundant in the Earth's crust, but only as an oxide with bauxite ore.
In 1896, the Tootsie Roll was introduced by Austrian immigrant Leo Hirshfield to the U.S. In a small store in New York City, he began producing his a chocolaty, chewy candy, which he named after a nickname of "Tootsie" for his five-year-old daughter, Clara. He was America's first candy maker to individually wrap penny candy. By 1905, production moved to a four-story factory in New York. During World War II, Tootsie Rolls were added to American soldiers' rations because of their ability to withstand severe weather conditions and give quick energy. Tootsie Rolls are made from a base of sugar, corn syrup, soy-bean oil, skim milk and cocoa. Current production is over 49 million pieces a day.*TIS Every year in Calculus as we were introducing Rolle's Thm, I would mention to my class the important contribution of his daughter, Tootsie. Some nice "Tootsie Roll" math can be found at this blog from Christopher Danielson.
1912 Richard Courant gives his Inaugural lecture, "On Existence Proofs in Mathematics,” at Gottingen. Existence proofs would run through his life’s works. A common joke years later, when he was not loved by all who knew him, was that Courant had proved by Counterexample, “Courant does not exist.” *Reid, Courant
1927 German theoretical physicist Werner Heisenberg writes a letter to fellow physicist Wolfgang Pauli, in which he describes his uncertainty principle for the first time. In March he submitted his paper on the uncertainty principle for publication.
In quantum mechanics, the uncertainty principle (also known as Heisenberg's uncertainty principle) is any of a variety of mathematical inequalities asserting a fundamental limit to the accuracy with which the values for certain pairs of physical quantities of a particle, such as position, x, and momentum, p, can be predicted from initial conditions.
*APS News
1955 Germany issued a stamp for the centenary of the death of Gauss. [Scott #725] *VFR
In 1987, supernova 1987A in LMC was first seen. The brightest of the twentieth century, it was the first supernova visible with the naked eye since 1604. *TIS Approximately ten million billion neutrinos from supernova SN 1987A reached physicist Masatoshi Koshiba's water tank, of which his research group detected 12, confirming theories of supernovae. *@NobelPrize
Before and after:
2012 The near earth asteroid 2012 DA14 has an estimated diameter of about 44 meters and an estimated mass of about 120,000 metric tons. It was discovered on February 23, 2012, by the OAM Observatory, La Sagra in Spain (J75). Calculations show that on February 15, 2013, the distance between the asteroid and the Earth will be 0.07 LD (27,000 km; 17,000 mi) *Science Daily
BIRTHS
1583 Jean-Baptiste Morin (23 Feb 1583 in Villefranche, Beaujolais, France - 6 Nov 1656 in Paris, France) French astrologer and astronomer who attempted to solve the longitude problem using lunar observations. He was certainly not the first to propose the method but he did add one important new piece of understanding, namely he took lunar parallax into account. Since Morin put forward his method for a longitude prize, a committee was set up by Cardinal Richelieu to evaluate it. Étienne Pascal, Mydorge, Beaugrand, Hérigone, J C Boulenger and L de la Porte served on the committee and they were in dispute with Morin for the five years after he made his proposal. Morin realised that instruments had to be improved, improved methods of solving spherical triangles had to be found and better lunar tables were needed. He made some advances in these areas but his method, although theoretically sound, could not achieve either the computational or observational accuracy to succeed. Morin refused to listen to objections to his proposal. Even while the dispute was going on, in 1638, Morin attacked Descartes saying that he had realised as soon as they met how bad his philosophy was. These disputes alienated Morin from the scientific community. He was to spend the latter part of his life isolated from other scientists although Cardinal Richelieu's successor Cardinal Mazarin did award him a pension for his work on the longitude in 1645.*SAU
1723 Richard Price (23 February 1723 – 19 April 1791) was a British moral philosopher and preacher in the tradition of English Dissenters, and a political pamphleteer, active in radical, republican, and liberal causes such as the American Revolution. He fostered connections between a large number of people, including writers of the Constitution of the United States. He spent most of his adult life as minister of Newington Green Unitarian Church, where possibly the congregant he most influenced was early feminist Mary Wollstonecraft, who extended his ideas on the egalitarianism inherent in the spirit of the French Revolution to encompass women's rights as well. In addition to his work as a moral and political philosopher, he also wrote on issues of statistics and finance, and was inducted into the Royal Society for these contributions. Price was a friend of the mathematician and clergyman Thomas Bayes. He edited Bayes' most famous work "An Essay towards solving a Problem in the Doctrine of Chances" which contains Bayes' Theorem, one of the most fundamental theorems of probability theory, and arranged for its posthumous publication. Price wrote an introduction to Bayes' paper which provides some of the philosophical basis of Bayesian statistics. Besides the above-mentioned, Price wrote an Essay on the Population of England (2nd ed., 1780) which directly influenced Thomas Robert Malthus.*Wik
Joseph Priestley, Richard Price and Theophilus Lindsay in the pulpit, in a 1790 engraving satirising the campaign to have the Test Act repealed. The Test Acts were a series of penal laws originating in Restoration England, passed by the Parliament of England, that served as a religious test for public office and imposed various civil disabilities on Catholics and nonconformist Protestants.
1861 George Ballard Mathews, FRS (February 23, 1861 — March 19, 1922) was a London born mathematician who specialized in number theory. After receiving his degree (as Senior Wrangler) from St John's College, Cambridge in 1883, he was elected a Fellow of St John's College. *Wik Mathews also wrote Algebraic equations (1907) which is a clear exposition of Galois theory, and Projective geometry (1914). This latter book develops the subject of projective geometry without using the concept of distance and it bases projective geometry on a minimal set of axioms. The book also treats von Staudt's theory of complex elements as defined by real involutions. The book contains a wealth of information concerning the projective geometry of conics and quadrics. *SAU
1905 Prime Number Theorist Derrick Lehmer (February 23, 1905 – May 22, 1991) Derrick Lehmer, one of the world's best known prime number theorists, is born in Berkeley, California. Before World War II, Lehmer invented a number of electromechanical sieves for finding prime numbers and made many important contributions in prime number theory throughout his life. Prime numbers are of interest in themselves as mathematical curiosities but are also of great importance to cryptography. The Computer Museum History Center has three Lehmer sieves in its permanent collection. Lehmer died in 1991.*CHM Lehmer's peripatetic career as a number theorist, with he and his wife taking numerous types of work in the United States and abroad to support themselves during the Great Depression, fortuitously brought him into the center of research into early electronic computing.His father Derrick Norman Lehmer, known mainly as a pioneer in number theory computing, also made major contributions to combinatorial computing.
He married Emma Markovna Lehmer (née Trotskaia) whose father had been her professor. She was known for her work on reciprocity laws in algebraic number theory. She preferred to deal with complex number fields and integers, rather than the more abstract aspects of the theory.*Wik
1922 Anneli Cahn Lax (23 Feb 1922 in Katowice, Poland - 24 Sept 1999 in New York City, New York, USA) Anneli Cahn was born in Katowice, then a German city, but now part of Poland, on February 23, 1922. Her family fled Hitler’s regime in 1935 and settled in New York. She married Peter Lax, a fellow mathematician, in 1948. Their lives together included a shared love for mathematics. Perhaps her most important contribution to mathematics was as editor of the New Mathematics Library. The launch of the Soviet satellite Sputnik in 1957 was a shock to the American scientific community, a shock felt on every level. Much thought was devoted to the education of a new generation who would accelerate the pace of American scientific productivity. Out of this endeavor grew the New Mathematical Library. The notion was to make accessible to interested high school students, and to a more general public, deep results in mathematics described by research mathematicians. (This sort of work had long been going on in Eastern Europe.) Lax was asked to take over as general editor for this series, and under her guidance it grew to be the foremost mathematical expository series in the language. Upon her death it was renamed in her honor. *Mark Saul, Obituary for the AMS VOl 47,#7
1930 Gorō Shimura (23 February 1930 – 3 May 2019) was a Japanese mathematician and Michael Henry Strater Professor Emeritus of Mathematics at Princeton University who worked in number theory, automorphic forms, and arithmetic geometry. He was known for developing the theory of complex multiplication of abelian varieties and Shimura varieties, as well as posing the Taniyama–Shimura conjecture which ultimately led to the proof of Fermat's Last Theorem.
Gorō Shimura was born in Hamamatsu, Japan, on 23 February 1930.[2] Shimura graduated with a B.A. in mathematics and a D.Sc. in mathematics from the University of Tokyo in 1952 and 1958, respectively.
After graduating, Shimura became a lecturer at the University of Tokyo, then worked abroad — including ten months in Paris and a seven-month stint at Princeton's Institute for Advanced Study — before returning to Tokyo, where he married Chikako Ishiguro. He then moved from Tokyo to join the faculty of Osaka University, but growing unhappy with his funding situation, he decided to seek employment in the United States.[4][2] Through André Weil he obtained a position at Princeton University. Shimura joined the Princeton faculty in 1964 and retired in 1999, during which time he advised over 28 doctoral students and received the Guggenheim Fellowship in 1970, the Cole Prize for number theory in 1977, the Asahi Prize in 1991, and the Steele Prize for lifetime achievement in 1996.
Shimura described his approach to mathematics as "phenomenological": his interest was in finding new types of interesting behavior in the theory of automorphic forms. He also argued for a "romantic" approach, something he found lacking in the younger generation of mathematicians. Shimura used a two-part process for research, using one desk in his home dedicated to working on new research in the mornings and a second desk for perfecting papers in the afternoon.
Shimura had two children, Tomoko and Haru, with his wife Chikako. Shimura died on 3 May 2019 in Princeton, New Jersey at the age of 89.
Shimura was a colleague and a friend of Yutaka Taniyama, with whom he wrote the first book on the complex multiplication of abelian varieties and formulated the Taniyama–Shimura conjecture. Shimura then wrote a long series of major papers, extending the phenomena found in the theory of complex multiplication of elliptic curves and the theory of modular forms to higher dimensions (e.g. Shimura varieties). This work provided examples for which the equivalence between motivic and automorphic L-functions postulated in the Langlands program could be tested: automorphic forms realized in the cohomology of a Shimura variety have a construction that attaches Galois representations to them. *Wik
1947 Rufus Bowen (23 February 1947 - 30 July 1978) worked on dynamical systems. Rufus died of a cerebral hemorrhage at the age of 31. *SAU
In 1970, Bowen completed his doctorate in Mathematics at Berkeley under Stephen Smale, and joined the faculty as assistant professor in that year. At this time he began calling himself Rufus,the nickname he had been given because of his red hair and beard.He was an invited speaker at the 1974 International Mathematical Conference in Vancouver, British Columbia.He was promoted to full professorship in 1977. Bowen's mature work dealt with dynamical systems theory, a field which Smale, Bowen's dissertation advisor, explored and broadened in the 1960s.
1951 Shigefumi Mori (23 Feb 1951 Nagoya, Japan, ) Japanese mathematician who has made important contributions to the field of algebraic geometry. His major work, in which he proved the existence of minimal models for all three-dimensional algebraic varieties (Jan 1988), has been dubbed Mori's Program. Within ten years since his first published paper, Mori had thereby completed what many said could never be done. In 1979, Mori published his first major results, a proof of the Hartshorne conjecture, which stated that a certain class of algebraic varieties are projective in nature. In other words, these varieties or sets of solutions to given polynomial equations could be described using projective geometry. He was awarded the Fields Medal in 1990 for his work in algebraic geometry.*TIS
DEATHS
1468 Johannes Gutenberg, printer, died. *VFR
1560 Gaspar Lax (1487 in Sarinena, Aragon, Spain - 23 Feb 1560 in Zaragoza, Spain) Lax published several good mathematics books based on works by Boethius, Euclid, Jordanus and Campanus. He was one of the Spanish school of "calculatores" who studied mechanics, being particularly involved with numerical examples, and using as their main tools the elements of proportion theory and infinitesimal arithmetic. This school seems to have originated with Lax and other students of Maior who studied in Paris, then returned to Spain. *SAU
1603 François Viète (1540 – 23 February 1603), Seigneur de la Bigotière, was a French mathematician whose work on new algebra was an important step towards modern algebra, due to its innovative use of letters as parameters in equations. He was a lawyer by trade, and served as a privy Councillor to both Henry III and Henry IV. A popular story about Viete as a codebreaker for Henry III is worth resharing: "While working for King Henry III, he discovered the key to a Spanish cipher of 500 characters, and so was able to read the secret correspondence of his enemies. Philipp II of Spain was so sure that his code was invulnerable that when he heard of this, he complained to the Pope that the French were using sorcery against him, contrary to good Christian morals." Vieta's most significant contributions were in algebra. While letters had been used to describe an unknown quantity by earlier writers, Vieta was the first to also use letters for the parameters or constant coefficients in an equation. Vieta gave a solution of the problem of Apollonius, to construct a circle tangent to three given circles, and also made a study of ``solid" problems such as the trisection of the angle and the construction of the regular heptagon, which use a marked ruler in addition to the Euclidean tools of ruler and compass. (His method was similar to the Greek method called "neusis" {neuein "incline towards"} which had been used by early mathematicians such as Archimedes but gradually the technique dropped out of favor and use.) Vieta calculated the value of \( \pi \) to ten decimal places, using the method of Archimedes, and also gave an infinite product formula for \( \pi \) one of the earliest occurrences of an infinite product.
*Robin Hartshorne
1844 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
1855 Karl Friedrich Gauss (30 Apr 1777 in Brunswick, Germany , 23 Feb 1855 at age 77). His poorly educated mother couldn’t remember his birthdate, but could relate it to a movable religious feast. To confirm the date of his birth Gauss developed a formula for the date of Easter. *VFR He transformed nearly all areas of mathematics, for which his talent showed from a very early age. For his contributions to theory in magnetism and electricity, a unit of magnetic field has been named the gauss. He devised the method of least squares in statistics, and his Gaussian error curve remains well-known. He anticipated the SI system in his proposal that physical units should be based on a few absolute units such as length, mass and time. In astronomy, he calculated the orbits of the small planets Ceres and Pallas by a new method. He invented the heliotrope for trigonometric determination of the Earth's shape. With Weber, he developed an electromagnetic telegraph and two magnetometers. *TIS; He proved that the heptadecagon (17 gon) was constructable (see April 8) with straight-edge and compass. Because of difficulties engraving the 17gon on his memorial, a seventeen pointed star was used instead. The Star is located below his foot on the right of the monument pedestal. Dave Renfro has provided me a complete and elementary proof of the construction.
An old story says that Gaoss died at 1:05 A. M. on this date and the pocket watch he had carried for his entire adult life stopped at "almost" exactly the same time. Having heard this anecdote perhaps a hundred or more times, I have never heard an estimate of the amount of variation from exact was displayed on the watch. PB
1917 Jean-Gaston Darboux (14 Aug 1842, 23 Feb 1917 at age 74)French mathematician whose work on partial differential equations introduced a new method of integration (the Darboux integral) and contributed to infinitesimal geometry. He wrote a paper in 1870 on differential equations of the second order in which he presented the Darboux integral. In 1873, Darboux wrote a paper on cycloids and between 1887-96 he produced four volumes on infinitesimal geometry, including a discussion of one surface rolling on another surface. In particular he studied the geometrical configuration generated by points and lines which are fixed on the rolling surface. He also studied the problem of finding the shortest path between two points on a surface.*TIS
1961 Mary Ann Elizabeth Stephansen (10 March 1872 in Bergen, Norway - 23 Feb 1961 in Espeland, Norway)received her Ph.D. in mathematics from the University of Zurich in 1902. She was the first woman from Norway to receive a doctoral degree in any subject. Her thesis area was in partial differential equations. It was not until 1971 that another Norwegian woman obtained a doctorate in mathematics. Stephansen taught at the Norwegian Agricultural College from 1906 until her retirement in 1937. She began as an assistant in physics and mathematics, then was appointed to a newly created docent position in mathematics in 1921. She published four mathematical research papers on partial differential equations and difference equations. A extensive biography of Elizabeth Stephansen is available as a pdf document at the web site of Professor Kari Hag. This also includes description of her mathematical work. *Agnes Scott College Web site
1963 Antonio Signorini (2 April 1888 – 23 February 1963) was an influential Italian mathematical physicist and civil engineer of the 20th century. He is known for his work in finite elasticity, thermoelasticity and for formulating the Signorini problem. The Signorini problem is the first variational inequality problem, : it consists in finding the elastic equilibrium configuration of an anisotropic non-homogeneous elastic body, resting on a rigid frictionless surface and subject only to its mass forces. The name was coined by Gaetano Fichera to honour his teacher, Antonio Signorini: the original name coined by him is problem with ambiguous boundary conditions. The problem was posed by Antonio Signorini during a course taught at the Istituto Nazionale di Alta Matematica in 1959. The problem was taken up, in particular, by one of his students, Gaetano Fichera. On the first days of January 1963, Fichera was able to give a complete proof of the existence and uniqueness of a solution for the problem with ambiguous boundary condition, which he called "Signorini problem" to honour his teacher. The preliminary note later published as Fichera 1963 was written up and submitted to Signorini exactly a week before his death: He was very satisfied to see a positive answer to his question. *Wik
2016 Hendrika Cornelia Scott (Henda) Swart FRSSAf (born 1939, died February 23, 2016 [age 77-78]) was a South African mathematician, a professor emeritus of mathematics at the University of KwaZulu-Natal and a professor at the University of Cape Town.
Born Hendrika Cornelia Scott, she married John Henry Swart. They had three children Christine, Sandra and Gustav.
Swart began teaching at the University of Natal in 1962. She was the first person to earn a doctorate in mathematics from Stellenbosch University, in 1971, with a dissertation on the geometry of projective planes supervised by Kurt-Rüdiger Kannenberg. In 1977, her research interests shifted from geometry to graph theory, which she continued to publish in for the rest of her career.
She was the editor-in-chief of the journal Utilitas Mathematica, and was vice president of the Institute of Combinatorics and its Applications. In 1996 she became a fellow of the Royal Society of South Africa.
Swart was a part-time lecturer at the University of Cape town from 2014 until her death.
She published under the name Henda C Swart, and published nearly 100 papers from 1980 to 2018.*Wik
Credits : *CHM=Computer History Museum *FFF=Kane, Famous First Facts *NSEC= NASA Solar Eclipse Calendar *RMAT= The Renaissance Mathematicus, Thony Christie *SAU=St Andrews Univ. Math History *TIA = Today in Astronomy *TIS= Today in Science History *VFR = V Frederick Rickey, USMA *Wik = Wikipedia *WM = Women of Mathematics, Grinstein & Campbell
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