Wednesday, 25 February 2026

On This Day in Math - February 25

  

Cathedral Church of St Paul the Apostle *Wik



People must understand that science is inherently neither a potential for good nor for evil. 
It is a potential to be harnessed by man to do his bidding.

~Glenn T. Seaborg

The 56th day of the year; There are 56 normalized 5x5 Latin Squares (First row and column have 1,2,3,4,5; and no number appears twice in a row or column. There are a much smaller number of 4x4 squares, try them first)

56 is the sum of the first six triangular numbers (56= 1 + 3 + 6 + 10 + 15 + 21) and thus the sixth tetrahedral number. It is also the sum of six consecutive primes. 3 + 5 + 7 + 11 + 13 + 17

Fifty-Six is a city in Stone County, Arkansas, United States. As of the 2020 census, the city had a total population of 158, an decrease of 15 persons from 2010.
When founding the community in 1918, locals submitted the name "Newcomb" for the settlement. This request was rejected, and the federal government internally named the community for its school district number (56)

As the sign says, the beautiful Blanchard Caverns are there. It is the only tourist site owned by the U S Forrest Service.



The Aubrey holes are a ring of fifty-six Chalk pits at Stonehenge, named after the seventeenth-century antiquarian John Aubrey. They date to the earliest phases of Stonehenge in the late fourth and early third millennium BC. Their purpose is still unknown. *Wik



EVENTS

1598 John Dee demonstrates the solar eclipse by viewing an image through a pinhole. Two versions from Ashmole and Aubrey give different details of who was present. Dee's Diary only contains the notation, "the eclips. A clowdy day, but great darkness about 9 1/2 maine " *Benjamin Wooley, The Queen's Conjuror


1606 Henry Briggs sends a Letter to Mr. Clarke, of Gravesend, dated from Gresham College, with which he sends him the description of a ruler, called Bedwell's ruler, with directions how to use it. (it seems from the letter to be a ruler for measuring the volume of timber. If you have information on where I could see a picture or other image of the device, please advise) *Augustus De Morgan, Correspondence of scientific men of the seventeenth century.  It seems to be similar to Gunter's scale,  a predecessor of the slide rule and calculating aid used from the 17th century until the 1970s. 

William Bedwell (1561 – 5 May 1632 near London) was an English priest and scholar, specializing in Arabic and other "oriental" languages as well as in mathematics. Bedwell also invented a ruler for geometrical purposes, similar to the Gunter's scale. He died at his vicarage at the age of 72.

BEDWELL, William (1563-1632, editor). The Turnament of Tottenham ... written long since in verse by Mr. Gilbert Pilkington ... taken out of an ancient manuscript ... by Wilhlm [sic] Bedwell. - BEDWELL, W. A Briefe Description of the Towne of Tottenham High-Crosse in Middlesex.



1702  Maria Margaretha Kirch (née Winckelmann, in historic sources named Maria Margaretha Kirchin; 25 February 1670 – 29 December 1720) was a German astronomer. She was one of the first famous astronomers of her period due to her writing on the conjunction of the sun with Saturn, Venus, and Jupiter in 1709 and 1712 respectively.  

Maria and Gottfried worked together as a team. In typical guild fashion she advanced from her position as Arnold's apprentice, to become assistant to her husband. Her husband had studied astronomy at the University of Jena and had served as apprentice to Johannes Hevelius.[5] At the academy she worked as his unofficial, but recognised assistant. Women's position in the sciences was akin to their position in the guilds, valued, but subordinate. Together they made observations and performed calculations to produce calendars and ephemerides.


During the first decade of her work at the academy as her husband's assistant Kirch would observe the heavens, every evening starting at 9 p.m. During such a routine observation she discovered a comet. On 21 April 1702 Kirch discovered the so-called "Comet of 1702" (C/1702 H1).Today there is no doubt about Kirch's priority in discovering C/1702 H1. However, at the time her husband was credited with the discovery. In his notes from that night her husband recorded:  "Early in the morning (about 2:00 AM) the sky was clear and starry. Some nights before, I had observed a variable star and my wife (as I slept) wanted to find and see it for herself. In so doing, she found a comet in the sky. At which time she woke me, and I found that it was indeed a comet... I was surprised that I had not seen it the night before".

This comet was actually discovered a day prior by two astronomers in Rome, Italy, Francesco Bianchini and Giacomo Filippo Maraldi


1672 (NS) John Wallis collects his work on tangents in a letter to Oldenburg for publication in the Philosophical Transactions. According to a letter from Collins to James Gregory, "I mentioned Slusius (René-François de Sluse) his intent to publish his method de maximis et minimis et tangentibus, which Dr. Wallis hearing of hath sent up his owne Notations about the same, which should have been printed in the last Transactions, but is deferred to the next one newly come out." *John Wallis, Philip Beeley, Christoph J. Scriba, Correspondence of John Wallis (1616-1703)



1839 Appropriately, it was an astronomer who coined the term photography, but the question is, which one. Some credit Johann Heinrich von Madler for combining “photo” (from the Greek word for “light”) and “graphy” (“to write”). *APS.org  Madler's claim rests on a paper supposedly written on 25 February 1839 in the German newspaper Vossische Zeitung. Many still credit Sir John Herschel both for coining the word and for introducing it to the public. His uses of it in private correspondence prior to 25 February 1839 and at his Royal Society lecture on the subject in London on 14 March 1839 have long been amply documented and accepted as settled facts. *Wik

In 1830 Mädler began producing drawings of Mars which later became the first true maps of that planet. They were the first to choose what is today known as Sinus Meridiani as the prime meridian for Martian maps.  He made a preliminary determination for Mars's rotation period, which was off by almost 13 seconds. A later determination in 1837 was off by only 1.1 seconds.

He  also produced the first exact map of the Moon, Mappa Selenographica, published in four volumes in 1834–1836.

Title page to a 1861 first edition copy of "Der Wunderbau des Weltalls oder Populäre Astronomie"



1870 Hermann Amandus Schwarz sent his friend Georg Cantor a letter containing the first rigorous proof of the theorem that if the derivative of a function vanishes then the function is constant. See H. Meschkowski, Ways of Thought of Great Mathematicians, pp. 87–89 for an English translation of the letter. *VFR



1959 The APT Language is Demonstrated: The Automatically Programmed Tools language is demonstrated. APT is an English-like language that tells tools how to work and is mainly used in computer-assisted manufacturing.
NEW YORKER: Cambridge, Mass. - Feb. 25: The Air Force announced today that it has a machine that can receive instructions in English - figure out how to make whatever is wanted- and teach other machines how to make it. An Air Force general said it will enable the United States to build a war machine that nobody would want to tackle. Today it made an ashtray. *CHM


1976 Romania issued a stamp picturing the mathematician Anton Davidoglu (1876–1958). [Scott #2613] *VFR

a Romanian mathematician who specialized in differential equations. He studied under Jacques Hadamard at the École Normale Supérieure in Paris, defending his Ph.D. dissertation in 1900. His thesis — the first mathematical investigation of deformable solids — applied Émile Picard's method of successive approximations to the study of fourth order differential equations that model traverse vibrations of non-homogeneous elastic bars.

Davidoglu was a founding member of the Romanian Academy of Sciences, and was featured on a 1976 Romanian postage stamp. He died in 1958 in Bucharest.




BIRTHS

1304 Ibn Battuta, a Muslim traveler, was born Feb. 25, 1304, in Tangier, Morocco. Although nearly every Westerner has heard of Marco Polo, few are aware of Ibn Battuta, yet Ibn Battuta left Marco in the dust travel-wise (the proverbial dust, since Ibn Battuta sojourned some 50 years after Marco), travelling over three times as far, under much more difficult circumstances. When he was in his early 20s, like every good Muslim, Ibn Battuta prepared for his hajj, or pilgrimage to Mecca. He said goodbye to his parents, headed east along the Mediterranean coast of Africa, and made it to the Islamic holy land. The difference was that Ibn Battuta did not return home for almost 30 years. Travelling in caravans for protection, he toured much of the Middle East, then headed down to the horn of Africa, and then further on down the coast as far as Kilwa in Tanzania (as far south as any Muslim ever got). He journeyed up into Afghanistan, then on to India, Southeast Asia, and up into China, as far as Beijing 

Perhaps the most impressive leg of his travels was his last one, across the Sahara and down into West Africa and the kingdom of Mali, crossing 1000 miles of desert in the process. When he finally returned to Morocco in 1354, he dictated a narrative of his travels, which is known as the Rihla, or Journey, of Ibn Battuta. It survived in a number of manuscripts, but hardly anyone noticed until the French found several manuscripts in Algeria in the 19th century and translated the Rihla into French. *Linda Hall Org




1670 Maria Winckelmann (Maria Margarethe Winckelmann Kirch (25 Feb 1670 in Panitzsch, near Leipzig, Germany - 29 Dec 1720 in Berlin, Germany) was a German astronomer who helped her husband with his observations. She was the first woman to discover a comet.*SAU 

Kirch was original educated by her father and her uncle who believed that girls should receive the same education as boys. From them she learnt mathematics and astronomy going on to study with and work together with the amateur astronomer Christoph Arnold. Through Arnold she got to know the astronomer Gottfried Kirch and despite the fact that he was 30 years older than her they married. Kirch was official astronomer of the Berlin Royal Academy of Science and he and Maria ran the Academy’s observatory together for many years. In 1702 she became the first woman to discover a comet but the credit for the discovery was given to her husband. When Gottfried died in 1710 Maria applied for his position arguing correctly that she had done half of the work in the past. Despite her having published independently and having an excellent reputation as well as the active support of Leibniz the Academy refused to award her the post. She worked in various other observatories until 1717 when her son was appointed to his father's post, Maria once again becoming the assistant. Despite having more than proved her equality to any male astronomer Maria never really received the recognition she deserved." From Thony Christie's Renaissance Mathematicus blog on Daughters of Urania.



1827 Henry William Watson (25 Feb 1827 in Marylebone, London, England - 11 Jan 1903 in Berkswell (near Coventry), England) was an English mathematician who wrote some influential text-books on electricity and magnetism. *SAU

He was educated at King's College London and at Trinity College, Cambridge. He graduated as second wrangler and Smith's prizeman in 1850, Dr. W. H. Besant being senior wrangler. In 1851 he became fellow of Trinity college, and from 1851 to 1853 was assistant tutor there. Watson formed a close friendship with James Fitzjames Stephen, who entered Trinity in 1847. From 1853 he was mathematical master in the City of London School, and in 1857 he became mathematical lecturer at King′s College.*Wik




1902 Kenjiro Shoda (February 25, 1902 – March 3, 1977 *SAU gives March 20 for death) was a Japanese mathematician. He was interested in group theory, and went to Berlin to work with Issai Schur. After one year in Berlin, Shoda went to Göttingen to study with Emmy Noether. Noether's school brought a mathematical growth to him. In 1929 he returned to Japan. Soon afterwards, he began to write Abstract Algebra, his mathematical textbook in Japanese for advanced learners. It was published in 1932 and soon recognised as a significant work for mathematics in Japan. It became a standard textbook and was reprinted many times.*Wik



1915  Fr. James Robert C. McConnell (Dublin 25 February 1915;  13 February 1999) was an Irish Catholic priest and theoretical physicist. McConnell entered University College Dublin (UCD) in 1932 and graduated in 1936 with a first-class honours master's degree in mathematics. After leaving UCD, McConnell began his study for the priesthood, entering Clonliffe College. He moved to Rome after a year and earned a B.D., B.C.L., and S.T.L. and was ordained in 1939. He was made a Doctor of Mathematical Sciences by the Royal University of Rome (La Sapienza) in 1941.

McConnell was appointed a scholar in the newly founded Dublin Institute for Advanced Studies in 1942. He was appointed Professor of Mathematical Physics in St. Patrick's College, Maynooth, having been awarded a D.Sc. from the National University of Ireland for his research there in 1949. He is best known for research on Rotational Brownian motion, the electric and magnetic properties of matter and the theory of the negative proton (or anti-proton).

McConnell was dean of the Faculty of Science, of Maynooth, from 1957 to 1968, and registrar of the college from 1966 to 1968.

McConnell was the 1986 recipient of the RDS Irish Times Boyle Medal for Scientific Excellence. He was appointed to the Pontifical Academy of Sciences in 1990, and honored with the title of Monsignor by Pope John Paul II in 1991 *Wik 




1922 Ernst Gabor Straus (February 25, 1922 – July 12, 1983) was a German-American mathematician who helped found the theories of Euclidean Ramsey theory and of the arithmetic properties of analytic functions. His extensive list of co-authors includes Albert Einstein and Paul Erdős as well as other notable researchers including Richard Bellman, Béla Bollobás, Sarvadaman Chowla, Ronald Graham, László Lovász, Carl Pomerance, and George Szekeres. It is due to his collaboration with Straus that Einstein has Erdős number 2. *Wik




1926 Masatoşi Gündüz İkeda (25 February 1926, Tokyo. - 9 February 2003, Ankara), was a Turkish mathematician of Japanese ancestry, known for his contributions to the field of algebraic number theory.

During his time in Japan , Ikeda conducted research on the theory of rings and the matrix representation of groups. In the 1970s, he turned to algebraic number theory and carried out important studies on the automorphisms and universality of the pure Galois group of the rational number field. In a study published in the famous mathematics journal Crelle's Journal , he showed that the Galois group has a very special structure. *Wik




DEATHS

1723 Sir Christopher Wren (20 Oct 1632; 25 Feb 1723) Architect, astronomer, and geometrician who was the greatest English architect of his time (Some may suggest Hooke as an equal) whose famous masterpiece is St. Paul's Cathedral, among many other buildings after London's Great Fire of 1666. Wren learned scientific skills as an assistant to an eminent anatomist. Through astronomy, he developed skills in working models, diagrams and charting that proved useful when he entered architecture. He inventing a "weather clock" similar to a modern barometer, new engraving methods, and helped develop a blood transfusion technique. He was president of the Royal Society 1680-82. His scientific work was highly regarded by Sir Isaac Newton as stated in the Principia. *TIS
Thony Christie points out that, "Most people don’t realise that as well as being Britain’s most famous 17th century architect, Wren was also a highly respected mathematician. In fact Isaac Newton named him along with John Wallace and William Oughtred as one of the three best English mathematicians of the 17th century. As a young man he was an active astronomer and was a highly vocal supporter of the then still relatively young elliptical astronomy of Johannes Kepler."

(I love the message on his tomb in the Crypt of St. Pauls: Si monumentum requiris circumspice ...."Reader, if you seek his monument, look about you." Lisa Jardine's book is excellent




1775 William Small (13 October 1734; Carmyllie, Angus, Scotland – 25 February 1775; Birmingham, England). He attended Dundee Grammar School, and Marischal College, Aberdeen where he received an MA in 1755. In 1758, he was appointed Professor of Natural Philosophy at the College of William and Mary in Virginia, then one of Britain’s American colonies.
Small is known for being Thomas Jefferson's professor at William and Mary, and for having an influence on the young Jefferson. Small introduced him to members of Virginia society who were to have an important role in Jefferson's life, including George Wythe a leading jurist in the colonies and Francis Fauquier, the Governor of Virginia.
Recalling his years as a student, Thomas Jefferson described Small as:

"a man profound in most of the useful branches of science, with a happy talent of communication, correct and gentlemanly manners, and a large and liberal mind... from his conversation I got my first views of the expansion of science and of the system of things in which we are placed."

In 1764 Small returned to Britain, with a letter of introduction to Matthew Boulton from Benjamin Franklin. Through this connection Small was elected to the Lunar Society, a prestigious club of scientists and industrialists.
In 1765 he received his MD and established a medical practice in Birmingham, and shared a house with John Ash, a leading physician in the city. Small was Boulton's doctor and became a close friend of Erasmus Darwin, Thomas Day, James Keir, James Watt, Anna Seward and others connected with the Lunar Society. He was one of the best-liked members of the society and an active contributor to their debates.
Small died in Birmingham on 25 February 1775 from malaria contracted during his stay in Virginia. He is buried in St. Philips Church Yard, Birmingham.
The William Small Physical Laboratory, which houses the Physics department at the College of William & Mary, is named in his honor. *Wik





1786 Thomas Wright (22 September 1711 – 25 February 1786) was an English astronomer, mathematician, instrument maker, architect and garden designer. He was the first to describe the shape of the Milky Way and speculate that faint nebulae were distant galaxies.

Wright's publication An Original Theory or New Hypothesis of the Universe (1750) explained the appearance of the Milky Way as "an optical effect due to our immersion in what locally approximates to a flat layer of stars." This work influenced Immanuel Kant in writing his Universal Natural History and Theory of the Heavens (1755). The theory was later empirically advanced by William Herschel in 1785,[6] leading to galactocentrism (a form of heliocentrism, with the Sun at the center of the Milky Way). Another of Wright's ideas, which is also often attributed to Kant, was that many faint nebulæ are actually incredibly distant galaxies. Wright wrote:

...the many cloudy spots, just perceivable by us, as far without our Starry regions, in which tho' visibly luminous spaces, no one star or particular constituent body can possibly be distinguished; those in all likelihood may be external creation, bordering upon the known one, too remote for even our telescopes to reach. *Wik

Wright's observatory/folly at Westerton, County Durham





1947 Louis Carl Heinrich Friedrich Paschen (22 Jan 1865; 25 Feb 1947) was a German physicist who was an outstanding experimental spectroscopist. In 1895, in a detailed study of the spectral series of helium, an element then newly discovered on earth, he showed the identical match with the spectral lines of helium as originally found in the solar spectrum by Janssen and Lockyer nearly 40 years earlier. He is remembered for the Paschen Series of spectral lines of hydrogen which he elucidated in 1908. *TIS




1950 Nikolai Nikolaevich Luzin, (also spelled Lusin) (9 December 1883, Irkutsk – 28 January 1950, Moscow), was a Soviet/Russian mathematician known for his work in descriptive set theory and aspects of mathematical analysis with strong connections to point-set topology. He was the eponym of Luzitania, a loose group of young Moscow mathematicians of the first half of the 1920s. They adopted his set-theoretic orientation, and went on to apply it in other areas of mathematics.*Wik




1972 Władysław Hugo Dionizy Steinhaus (January 14, 1887 – February 25, 1972) was a Polish mathematician and educator. Steinhaus obtained his PhD under David Hilbert at Göttingen University in 1911 and later became a professor at the University of Lwów, where he helped establish what later became known as the Lwów School of Mathematics. He is credited with "discovering" mathematician Stefan Banach, with whom he gave a notable contribution to functional analysis through the Banach-Steinhaus theorem. After World War II Steinhaus played an important part in the establishment of the mathematics department at Wrocław University and in the revival of Polish mathematics from the destruction of the war.
Author of around 170 scientific articles and books, Steinhaus has left its legacy and contribution on many branches of mathematics, such as functional analysis, geometry, mathematical logic, and trigonometry. Notably he is regarded as one of the early founders of the game theory and the probability theory preceding in his studies, later, more comprehensive approaches, by other scholars. *Wik
His Mathematical Snapshots is a delight to read, but get the first English edition if you can—there are lots of surprises there. *VFR

"When Steinhaus failed to attend an important meeting of the Committee of the Polish Academy of Sciences in 1960, he received a letter chiding him for "not having justified his absence." He immediately wired the President of the Academy that "as long as there are members who have not yet justified their presence, I do not need to justify my absence."

[ Told by Mark Kac in "Hugo Steinhaus -- A Remembrance and a Tribute," Amer. Math. Monthly 81 (June-July 1974) 578. ] * http://komplexify.com

The Scottish Book from the Lwów School of Mathematics, which Steinhaus contributed to and probably saved during World War II.

photo: Contents of the rear pocket of Mathematical Snapshots, by Hugo Steinhaus, 1938 (Linda Hall Library)






1988 Kurt Mahler (26 July 1903, Krefeld, Germany – 25 February 1988, Canberra, Australia) was a mathematician and Fellow of the Royal Society. Mahler proved that the Prouhet–Thue–Morse constant and the Champernowne constant 0.1234567891011121314151617181920... are transcendental numbers.
He was a student at the universities in Frankfurt and Göttingen, graduating with a Ph.D. from Johann Wolfgang Goethe University of Frankfurt am Main in 1927. He left Germany with the rise of Hitler and accepted an invitation by Louis Mordell to go to Manchester. He became a British citizen in 1946.
He was elected a member of the Royal Society in 1948 and a member of the Australian Academy of Science in 1965. He was awarded the London Mathematical Society's Senior Berwick Prize in 1950, the De Morgan Medal, 1971, and the Thomas Ranken Lyle Medal, 1977. *Wik




1999 Glenn Theodore Seaborg (April 19, 1912,Ishpeming, Michigan – February 25, 1999) was an American scientist who won the 1951 Nobel Prize in Chemistry for "discoveries in the chemistry of the transuranium elements", contributed to the discovery and isolation of ten elements, and developed the actinide concept, which led to the current arrangement of the actinoid series in the periodic table of the elements. He spent most of his career as an educator and research scientist at the University of California, Berkeley where he became the second Chancellor in its history and served as a University Professor. Seaborg advised ten presidents from Harry S. Truman to Bill Clinton on nuclear policy and was the chairman of the United States Atomic Energy Commission from 1961 to 1971 where he pushed for commercial nuclear energy and peaceful applications of nuclear science.
The element seaborgium was named after Seaborg by Albert Ghiorso, E. Kenneth Hulet, and others, who also credited Seaborg as a co-discoverer. It was so named while Seaborg was still alive, which proved controversial. He influenced the naming of so many elements that with the announcement of seaborgium, it was noted in Discover magazine's review of the year in science that he could receive a letter addressed in chemical elements: seaborgium, lawrencium (for the Lawrence Berkeley Laboratory where he worked), berkelium, californium, americium
(Once when being aggressively cross-examined during testimony on nuclear energy for a senate committee, the Senator asked, “How much do you really know about Plutonium.” Seaborg quietly answered, “Sir, I discovered it.” , Which he did as part of the team at the Manhattan Project. *Wik





2022 Richard Steven Varga (October 9, 1928 - February 25, 2022) was an American mathematician who specialized in numerical analysis and linear algebra. He was an Emeritus University Professor of Mathematical Sciences at Kent State University and an adjunct Professor at Case Western Reserve University. Varga was known for his contributions to many areas of mathematics, including matrix analysis, complex analysis, approximation theory, and scientific computation. He was the author of the classic textbook Matrix Iterative Analysis. Varga served as the Editor-in-Chief of the journal Electronic Transactions on Numerical Analysis (ETNA).





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

Tuesday, 24 February 2026

The Shoelace Formula and a Formulas for Shoelaces

 


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.

Remember if the coordinates are all integers, you can use Pick's theorem as well.    https://pballew.blogspot.com/2022/02/picks-theorem-some-history.html

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:


You can also order the book from Amazon 

On This Day in Math - February 24

   


3D Lichtenberg Figures *Wik


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