Saturday, 21 February 2026

On This Day in Math - February 21

   

Durer Perspective



My mother said, "Even you, Paul, can be in only one place at one time." Maybe soon I will be relieved of this disadvantage. Maybe, once I've left, I'll be able to be in many places at the same time. Maybe then I'll be able to collaborate with Archimedes and Euclid.
~Paul Erdos

The 52nd day of the year; The month and day are simultaneously prime a total of 52 times in a non-leap year. *Tanya Khovanova, Number Gossip How many times in a leap year ?

52 is also the maximum number of moves needed to solve the 15 puzzle from the worst possible start. *Mario Livio



52 is the number of 8-digit primes (on a calculator) that remain prime if viewed upside down, in a mirror, or upside down in a mirror. *Prime Curios

There are 52 letters in the names of the cards in a standard deck: ACE KING QUEEN JACK TEN
(This also works in Spanish. any other languages for which this is true?) *Futility Closet    (One correspondent suggested his names for cards in Spanish have 54 letters.  Any good Spanish speakers care to comment?)



EVENTS

1632 Galileo's epic Dialogue on the Two Chief World Systems is Published in Florence. After receiving, what Galileo viewed as permission to write about "the systems of the world" from the new pope, Urban VIII. Greeted with Praise from scholars across Europe, it would eventually be Galileo's downfall. *Brody & Brody, The Science Class You Wish You Had



1699 Newton elected the second foreign member of the French Academy. See January 28, 1699. [American Journal of Physics, 34(1966), 22] *VFR Thony Christie points out in a comment (below) that "Newton was appointed foreign associate of the Académie Royale des Sciences along with four others so to claim he was the second is more than somewhat dubious." (My Thanks)


1727/8 Isaac Greenwood began his “Publick” lectures at Harvard as the first Hollis Professor of Mathematics and Natural Philosophy. The lectures were open to the entire university. [I. B. Cohen, Some Early Tools of American Science, p. 35.] *VFR

A list of Hollis Professors up to 2025:

Isaac Greenwood (1727–1737)

John Winthrop (1737–1779)

Samuel Williams (1779–1789)

Samuel Webber (1789–1806)

John Farrar (1807–1838)

Joseph Lovering (1838–1888)

Benjamin Osgood Peirce (1888–1914)

Wallace Clement Sabine (1914–1919)

vacant (January 1919–September 1921)

Theodore Lyman (1921–1926)

Percy Williams Bridgman (1926–1950)

John Hasbrouck Van Vleck (1951–1969)

Andrew Gleason (1969–1992)

Bertrand Halperin (1992–2018)

Cumrun Vafa (2018–present)






1811, as Humphry Davy read a paper to the Royal Society, he introduced the name "chlorine" from the Greek word for "green," for the bright yellow green gas chemists then knew as oxymuriatic gas. In his paper, On a Combination of Oxymuriatic Gas and Oxygene Gas, Davy reported on his numerous experiments with oxymuratic gas, which appeared to have many of the reactive properties of oxygen. Hydrochloric acid was then known as muriatic acid, and when chlorine was first obtained from a reaction with the acid, the yellow green gas had been thought to be a compound containing oxygen. Later, Davy's careful work would show that the chlorine gas was in fact an element, unable to be decomposed into any simpler substances. *TIS

The element was first studied in detail in 1774 by Swedish chemist Carl Wilhelm Scheele, and he is credited with the discovery. Scheele produced chlorine by reacting MnO2 (as the mineral pyrolusite) with HCl:

4 HCl + MnO_2 → MnCl_2 + 2 H_2O + Cl_2

Scheele observed several of the properties of chlorine: the bleaching effect on litmus, the deadly effect on insects, the yellow-green color, and the smell similar to aqua regia.[14] He called it "dephlogisticated muriatic acid air" since it is a gas (then called "airs") and it came from hydrochloric acid (then known as "muriatic acid"). He failed to establish chlorine as an element. *Wik

Carl Wilhelm Scheele



1831 Michael Faraday in a letter to William Whewell regarding a recent publication by Whewell (Journal of the Royal Institution of England (1831), 437-453.), “Your remarks upon chemical notation with the variety of systems which have arisen, had almost stirred me up to regret publicly that such hindrances to the progress of science should exist. I cannot help thinking it a most unfortunate thing that men who as experimentalists, philosophers are the most fitted to advance the general cause of science; knowledge should by promulgation of their own theoretical views under the form of nomenclature, notation, or scale, actually retard its progress. *Isaac Todhunter, William Whewell, (1876), Vol. 1., 307.

Faraday, *Wik



1845 The ship Charles Heddle sailed north from Mauritius and encountered a terrible storm. Striking sails and scudding before the wind they proceeded four times around the center in clockwise loops hundreds of miles wide. After six days a clearing sky allowed the Captain to take a reading and realize that as they circled, they had also been driven back nearly to their starting point. Reading the log of the Charles Heddle and other reports of this storm, Henry Piddington coined the word cyclone, from the Greek for "coils of a snake,". After he used the term in his "The Sailor's Horn-Book for the Law of Storms" it became a common term.




1880 Noyes Chapman had applied for a patent on his "Block Solitaire Puzzle" (the 15 puzzle above in number facts) on February 21, 1880. However, that patent was rejected, likely because it was not sufficiently different from the August 20, 1878 "Puzzle-Blocks" patent (US 207124) granted to Ernest U. Kinsey 
His was a 6x6 square with letters, blanks and symbols.




1908 Birth date of Dr. Irving Joshua Matrix, the greatest numerologist who (n)ever lived. At the age of seven he astonished his minister Father when he pointed out that 8 is the holiest number of all: “The other numbers with holes are 0, 6, and 9, and sometimes 4, but 8 has two holes, therefore it is the holiest.” Martin Gardner first drew attention to Dr. Matrix in his January 1960 column “Mathematical Games,” in Scientific American. For more details, see The Incredible Dr. Matrix, by Martin Gardner [p. 3-4]. *VFR





1953, Francis Crick and James Watson reached their conclusion about the double helix structure of the DNA molecule. They made their first announcement on Feb 28, and their paper, A Structure for Deoxyribose Nucleic Acid, was published in the 25 Apr 1953 issue of journal Nature. *TIS

1958: The Peace symbol is designed and completed by Gerald Holtom #OTD.
*History Time

1996 Cox Enterprises announces it was buying a one-third interest in Digital Domain, a computer-generated special effects company, in order to heighten the use of special effects in media. The deal reflected "another step in the rapid convergence of various computer, software, entertainment and media companies," The New York Times wrote. *CHM

2012 The engineering profession's highest honors for 2012, presented by the National Academy of Engineering (NAE), recognize ground-breaking contributions to the development of the modern liquid crystal display and achievements that led to a curriculum that encourages engineering leadership. The awards, announced today, will be presented at a gala dinner event in Washington, DC on February 21, 2012.
George H. Heilmeier, Wolfgang Helfrich, Martin Schadt, and T. Peter Brody will receive the Charles Stark Draper Prize a $500,000 annual award that honors engineers whose accomplishments have significantly benefited society "for the engineering development of the Liquid Crystal Display (LCD) that is utilized in billions of consumer devices." *AAAS/Science Newsletter, January 19, 2012
The Draper prize is named for Charles Stark Draper, the "father of inertial navigation", an MIT professor and founder of Draper Laboratory.
The Priza was first presented in 1989 to Jack S. Kilby and Robert N. Noyce for their independent development of the monolithic integrated circuit.





BIRTHS

1591 Girard Desargues (21 Feb 1591 in Lyon, France - ? Sept 1661 in Lyon, France) He did noted work in projective geometry. *VFR Desargues' most important work, the one in which he invented his new form of geometry, has the title Rough draft for an essay on the results of taking plane sections of a cone (Brouillon project d'une atteinte aux evenemens des rencontres du Cone avec un Plan). A small number of copies was printed in Paris in 1639. Only one is now known to survive, and until this was rediscovered, in 1951, Desargues' work was known only through a manuscript copy made by Philippe de la Hire (1640 - 1718). The book is short, but very dense. It begins with pencils of lines and ranges of points on a line, considers involutions of six points (Desargues does not use or define a cross ratio), gives a rigorous treatment of cases involving 'infinite' distances, and then moves on to conics, showing that they can be discussed in terms of properties that are invariant under projection. We are given a unified theory of conics.
Desargues' famous 'perspective theorem' - that when two triangles are in perspective the meets of corresponding sides are colinear - was first published in 1648, in a work on perspective by Abraham Bosse. *SAU


1764 Ruan Yuan (Chinese characters: 阮元) (21 Feb 1764 in Yangzhou, Jiangsu province, China - 27 Nov 1849 in Yangzhou, Jiangsu province, China), was a scholar official in the Qing Dynasty in Imperial China. He won jinshi (high) honors in the imperial examinations in 1789 and was subsequently appointed to the Hanlin Academy. He was famous for his work Biographies of Astronomers and Mathematicians and for his editing the Shi san jing zhu shu (Commentaries and Notes on the Thirteen Classics) for the Qing emperor.*Wik



1788 Francis Ronalds (21 February 1788 – 8 August 1873) came from a family of cheese purveyors, a profession he adopted for some years (while considering changing his name to Wensleydale).  But around 1810, he abruptly shifted his attention to electricity (this was 10 years after Volta's battery had opened up a new world for electrical investigators).  Ronalds invented a slew of ingenious electrical devices, including an electrograph that would measure the electricity in the atmosphere.  He also started collecting books and pamphlets on electricity, a collection that would grow into a sizable library.

In 1816, Ronalds built a working telegraph in the garden of the family house in Hammersmith in west London.  Part of it was underground, but above ground he strung out 8 miles of insulated wire in ribbon-candy fashion, with clocks at each end whose faces contained letters instead of numbers; the electrical signals in some way synchronized the clocks and spelled out a message.  Apparently, the device worked; he gave a demonstration on 5 August, 1816 for the Admiralty, offering it to them gratis, but the Secretary of the Admiralty, John Barrow, rejected it as an unnecessary invention, preferring the semaphore telegraph then in use.  Two years later, Barrow distinguished himself by sending out the first ships in search of a Northwest Passage, but he has never quite lived down the ignominy of rejecting the electrical telegraph as useless.  It would be 20 more years before England re-entered the telegraph business, and by that time, they were well behind the Americans.  Many today regard Ronalds as the true inventor of the telegraph, and there was considerable scholarly commotion in his behalf in 2016, the bicentennial of his invention.

Ronalds continued to invent and collect books throughout a very long life (he died in 1873, at age 85).  In the 1840s, with the invention of photography, he found a way to continuously photograph a full 24 hours of readings of his electrograph (second image).  His Library grew to accommodate 2000 books and 4000 pamphlets; after his death, it was deposited with the Institution of Engineering and Technology in London, and finally donated to that institution in 1976.

Ronalds published a book on his telegraph, Descriptions of an Electrical Telegraph, and of some other Electrical Apparatus (1823).  This work is surprisingly not in our collections, a deficiency we will try to remedy in the near future.  Ironically, we just last week acquired the principal book on semaphore telegraphy, the system that Barrow preferred to Ronalds’ electrical telegraph.

As a final note, the Ronalds house in Hammersmith, where his telegraph was first laid out, was acquired in the 1870s by designer William Morris, and is today known as Kelmscott House.  There is a plaque on the wall that commemorates Ronalds' garden telegraph (first image).  The only surviving portrait of Ronalds, painted not long before his death, is in the National Portrait Gallery, London (third image). *Linda Hall Org

*Wik





1849 Édouard Gaston (Daniel) Deville (21 Feb 1849; 21 Sep 1924 at age 75)
was a French-Canadian surveyor was a French-born Canadian surveyor of Canadian lands (1875-1924) who perfected the first practical method of photogrammetry, or the making of maps based on photography. His system used projective grids of images taken from photographs made with a camera and theodolite mounted on the same tripod. Photographs were taken from different locations, at precise predetermined angles, with measured elevations. Each photograph slightly overlapped the preceding one. With enough photographs and points of intersection, a map could be prepared, including contour lines. He also invented (1896) the first stereoscopic plotting instrument called the Stereo-Planigraph, though its complexity resulted in little use. *TIS




1965 Frances Evelyn Cave-Browne-Cave FRAS (21 February 1876–30 March 1965) was an English mathematician and educator.

Frances Cave-Browne-Cave was the daughter of Sir Thomas Cave-Browne-Cave and Blanche Matilda Mary Ann Milton. She was educated at home in Streatham Common with her sisters and entered Girton College, Cambridge, with her elder sister Beatrice Mabel Cave-Browne-Cave in 1895. She obtained a first-class degree and she would have been Fifth Wrangler in 1898 if she had been a man(Immediately behind G H Hardy.). She took Part II of the Mathematical Tripos in 1899.

Like her sister, she was usually known by the single surname Cave professionally. Along with Beatrice, she worked with Karl Pearson at University College London. Her work was funded by the first research grant offered at Girton: an Old Students' Research Studentship from Girton, provided by Florence Margaret Durham.Her research in the field of meteorology produced two publications in the Proceedings of the Royal Society which discussed barometric measurements, and was read to the British Association at Cambridge in 1904.

In 1903, Cave returned to Girton as a fellow. She prioritised teaching over research, and focused on developing the weakest students because she felt that was where the biggest difference could be made. She became the director of studies in 1918. She was on the executive council of the college and was largely responsible for drafting the charter of incorporation granted in 1924. On the 11 November 1921 she was elected a Fellow of the Royal Astronomical Society. Cave was made honorary fellow of Girton in 1942.

Cave received an MA from Trinity College, Dublin, in 1907 (since the rules of Cambridge University did not then permit women to take degrees) and from Cambridge in 1926.

Cave retired to Southampton in 1936. She died in Shedfield in a nursing home on 30 March 1965




1915 Evgeny Mikhailovich Lifshitz FRS (February 21, 1915 – October 29, 1985) was a leading Soviet physicist of Jewish origin and the brother of physicist Ilya Mikhailovich Lifshitz. (Some commonly encountered alternative transliterations of his names include Yevgeny or Evgenii and Lifshits or Lifschitz.) Lifshitz is well known in general relativity for coauthoring the BKL conjecture concerning the nature of a generic curvature singularity. As of 2006, this is widely regarded as one of the most important open problems in the subject of classical gravitation.
With Lev Landau, Lifshitz co-authored Course of Theoretical Physics, an ambitious series of physics textbooks, in which the two aimed to provide a graduate-level introduction to the entire field of physics. These books are still considered invaluable and continue to be widely used. Landau's wife strongly criticized his scientific abilities, hinting at how much of their joint work was done by Lifshitz and how much by Landau. Despite the sniping, he is well known for many invaluable contributions, in particular to quantum electrodynamics, where he calculated the Casimir force in an arbitrary macroscopic configuration of metals and dielectrics.*Wik
Offer Pade' added that The Course of Theoretical Physics is a ten-volume series of books covering theoretical physics that was initiated by Lev Landau and written in collaboration with his student Evgeny Lifshitz starting in the late 1930s. It is said that Landau composed much of the series in his head while in an NKVD prison in 1938–1939. (Wikipedia)
I have used several of the book in the series and found them excellent.




Landau(L) with Lifshitz(R) 




1984  Hannah Fry (born 21 February 1984-) is a British mathematician, author and broadcaster. She is Professor of the Public Understanding of Mathematics at the University of Cambridge, a fellow of Queens' College, Cambridge, and president of the Institute of Mathematics and its Applications. She was previously a professor at University College London.

Her work has included studies of patterns of human behaviour, such as interpersonal relationships and dating, and how mathematics can apply to them, the mathematics behind pandemics, and scientific explanations of modern appliances. She has had a particular focus on helping the public to improve their mathematical skills. Fry gave the Royal Institution Christmas Lectures in 2019 and has presented several television and radio programmes for the BBC, including The Secret Genius of Modern Life. She has received several awards for her work in mathematics, including the Asimov Prize and David Attenborough Award. *Wik

When Fry was a student at University College London, she was once invited to give a short public talk about her research on the mathematics of human behavior — specifically, how mathematical models can describe how people move through cities. She realized, though, that the audience would not be mathematicians. So instead of diving into equations, she brought along a bag of toy cars and began explaining how traffic patterns, crowd movements, and even riots could be understood through the same mathematical lens.

Her playful approach — literally rolling cars across a table to illustrate differential equations — so impressed the audience (and her department) that it launched her public-speaking career. That talk eventually led to her first BBC appearance, and she has said that it taught her one of her main lessons as a science communicator:
“If people can see the math in the world around them, they’ll fall in love with it — even if they think they hate equations.”






DEATHS

1900 Charles Piazzi Smyth FRSE FRS FRAS FRSSA (3 January 1819, Naples, Italy – 21 February 1900), was Astronomer Royal for Scotland from 1846 to 1888, well known for many innovations in astronomy and his pyramidological and metrological studies of the Great Pyramid of Giza. *Wik

1901 George Francis Fitzgerald (3 Aug 1851, 21 Feb 1901 at age 49) Irish physicist whose suggestion of a way to produce waves helped lay a foundation for wireless telegraphy. He also first developed a theory, independently discovered by Hendrik Lorentz, that a material object moving through an electromagnetic field would exhibit a contraction of its length in the direction of motion. This is now known as the Lorentz-FitzGerald contraction, which Einstein used in his own special theory of relativity. He also was first to propose the structure of comets as a head made of large stones, but a tail make of such smaller stones (less than 1-cm diam.) that the pressure of light radiation from the sun could deflect them. FitzGerald also studied electrolysis as well as electromagnetic radiation.*TIS
In his letter to Science dated May 2, 1889, which was quite brief, FitzGerald proposed that the best way to explain the null result of the Michelson-Morley experiment was to assume that the length of an object was not a constant, but that objects moving through the ether with a velocity v were contracted by a factor of v^2/c^2, where c is the speed of light. *Linda Hall Org




1912  Émile Michel Hyacinthe Lemoine (22 Nov 1840 in Quimper, France - 21 Feb 1912 in Paris, France) Lemoine work in mathematics was mainly on geometry. He founded a new study of properties of a triangle in a paper of 1873 where he studied the point of intersection of the symmedians of a triangle. He had been a founder member of the Association Française pour l'Avancement des Sciences and it was at a meeting of the Association in 1873 in Lyon that he presented his work on the symmedians.
A symmedian of a triangle from vertex A is obtained by reflecting the median from A in the bisector of the angle A. He proved that the symmedians are concurrent, the point where they meet now being called the Lemoine point. Among other results on symmedians in Lemoine's 1873 paper is the result that the symmedian from the vertex A cuts the side BC of the triangle in the ratio of the squares of the sides AC and AB. He also proved that if parallels are drawn through the Lemoine point parallel to the three sides of the triangle then the six points lie on a circle, now called the Lemoine circle. Its centre is at the mid-point of the line joining the Lemoine point to the circumcentre of the triangle. Lemoine gave up active mathematical research in 1895 but continued to support the subject. He had helped to found a mathematical journal, L'intermédiaire des mathématiciens., in 1894 and he became its first editor, a role he held for many years. *SAU   His mathematical recreation books are still popular in France.
Lemoine has been described by Nathan Altshiller Court as a co-founder (along with Henri Brocard and Joseph Neuberg) of modern triangle geometry, a term used by William Gallatly, among others. In this context, "modern" is used to refer to geometry developed from the late 18th century onward. Such geometry relies on the abstraction of figures in the plane rather than analytic methods used earlier involving specific angle measures and distances. The geometry focuses on topics such as collinearity, concurrency, and concyclicity, as they do not involve the measures listed previously.
The Lemoine point; L. The black lines are medians, the dotted lines are angle bisectors and the red lines are the symmedians (the reflections of the black lines in the dotted lines).





1912 Osborne Reynolds (23 Aug 1842 in Belfast, Ireland - 21 Feb 1912 in Watchet, Somerset, England) was an Irish mathematician best known for introducing the Reynolds number classifying fluid flow.*SAU
 British innovator in the understanding of fluid dynamics. Separately, his studies of heat transfer between solids and fluids brought improvements in boiler and condenser design. He spent his entire career at what is now the University of Manchester. *Wik




1926 Heike Kamerlingh Onnes (21 Sep 1853, 21 Feb 1926 at age 72)Dutch physicist who was awarded the 1913 Nobel Prize for Physics for his work on low-temperature physics in which he liquified hydrogen and helium. From his studies of the resistance of metals at low temperatures, he discovered superconductivity (a state in which certain metals exhibit almost no electrical resistance at a temperature near absolute zero).*TIS




1932 James Mercer FRS (15 January 1883 – 21 February 1932) was a mathematician, born in Bootle, close to Liverpool, England. He was educated at University of Manchester, and then University of Cambridge. He became a Fellow, saw active service at the Battle of Jutland in World War I, and after decades of suffering ill health died in London, England.
He proved Mercer's theorem, which states that positive definite kernels can be expressed as a dot product in a high-dimensional space. This theorem is the basis of the kernel trick (applied by Aizerman), which allows linear algorithms to be easily converted into non-linear algorithms. *Wik




1938 George Ellery Hale (29 Jun 1868, 21 Feb 1938 at age 69). U S astronomer known for his development of important astronomical instruments. To expand solar observations and promote astrophysical studies he founded Mt. Wilson Observatory (Dec 1904). He discovered that sunspots were regions of relatively low temperatures and high magnetic fields. Hale hired Harlow Shapley and Edwin Hubble as soon as they finished their doctorates, and he encouraged research in galactic and extragalactic astronomy as well as solar and stellar astrophysics. Hale planned and tirelessly raised funds for the 200-inch reflecting telescope at the Palomar Mountain Observatory completed in 1948, after his death, and named for him—the Hale telescope. *TIS
Originally, the Hale Telescope was going to use a primary mirror of fused quartz manufactured by General Electric, but instead the primary mirror was cast in 1934 at Corning Glass Works in New York State using Corning's then new material called Pyrex (borosilicate glass). Pyrex was chosen for its low expansion qualities so the large mirror would not distort the images produced when it changed shape due to temperature variations (a problem that plagued earlier large telescopes).
The 5 meter (16 ft. 8 in.) mirror in December 1945 at the Caltech Optical Shop when grinding resumed following World War 2. The honeycomb support structure on the back of the mirror is visible through the surface.*Wik

Gavin Putland added , "Hale co-invented the spectroheliograph."





1962 Julio Rey Pastor (14 August 1888 – 21 February 1962) was a Spanish mathematician and historian of science. Rey proposed the creation of a "seminar in mathematics to arouse the research spirit of our school children.” His proposal was accepted and in 1915 the JAE created the Mathematics Laboratory and Seminar, an important institution for the development of research on this field in Spain.
In 1951, he was appointed director of the Instituto Jorge Juan de Matemáticas in the CSIC. His plans in Spain included two projects: the creation, within the CSIC, of an Institute of Applied Mathematics, and the foundation of a Seminar on the History of Science at the university. *Wik




1993 Inge Lehmann  (13 May 1888 – 21 February 1993) was a Danish seismologist and geophysicist. In 1936, she discovered that the Earth has a solid inner core inside a molten outer core. Before that, seismologists believed Earth's core to be a single molten sphere, being unable, however, to explain careful measurements of seismic waves from earthquakes, which were inconsistent with this idea. Lehmann analysed the seismic wave measurements and concluded that Earth must have a solid inner core and a molten outer core to produce seismic waves that matched the measurements. Other seismologists tested and then accepted Lehmann's explanation. Lehmann was also one of the longest-lived scientists, having lived for over 104 years 

Lehmann's parents enrolled both her and her sister at Fællesskolen in 1904, a liberal and progressive school that offered the same curriculum to both boys and girls, a practice uncommon at the time. This school was led by Hanna Adler, Niels Bohr's aunt, a pioneering woman scholar and firm believer in gender equality. A year after earning her degree, Adler launched her school, inspired by innovative teaching practices in the US.*Wik 

Lehmann Memorial





1996 Hans-Joachim Bremermann​ (14 September, 1926 - 21 February, 1996) was a German-American mathematician and biophysicist. He worked on computer science and evolution, introducing new ideas of how mating generates new gene combinations. Bremermann's limit, named after him, is the maximum computational speed of a self-contained system in the material universe.
 Bremermann's limit, named after him, is the maximum computational speed of a self-contained system in the material universe.
Bremermann came to the United States in 1952 and held a research associate position at Stanford University. In 1953, he was appointed a research fellow at Harvard University. He returned to Münster for 1954–55.

After returning to the United States, he was a mathematics researcher at the Institute for Advanced Study in Princeton (1955–57), and then appointed assistant professor at the University of Washington, Seattle (1957–58). He then spent another year researching at Princeton (1958–59), this time in physics.

In 1959, he became an associate professor of mathematics at University of California, Berkeley, where he remained for the rest of his career, being promoted to full professor in 1966. He held chairs at Berkeley in mathematics and biophysics. By the 1960s, his work had turned towards the theory of computation and evolutionary biology, in which he studied complexity theory, genetic search algorithms, and pattern recognition.

In 1978 he gave the "What Physicists Do" series of lectures at Sonoma State University, discussing physical limitations to mathematical understanding of physical and biological systems. He continued work in mathematical biology through the 1980s, developing mathematical models of parasites and disease, neural networks, and AIDS epidemiology and pathology. He retired from the University of California in 1991.*Wik



2009 Ilya Piatetski-Shapiro (30 March 1929 – 21 February 2009) was a Russian-Jewish mathematician. During a career that spanned 60 years he made major contributions to applied science as well as theoretical mathematics. In the last forty years his research focused on pure mathematics; in particular, analytic number theory, group representations and algebraic geometry. His main contribution and impact was in the area of automorphic forms and L-functions.
For the last 30 years of his life he suffered from Parkinson's disease. However, with the help of his wife Edith, he was able to continue to work and do mathematics at the highest level, even when he was barely able to walk and speak.*Wik



2012 Vera Nikolaevna Kublanovskaya (née Totubalina; November 21, 1920 – February 21, 2012) was a Russian mathematician noted for her work on developing computational methods for solving spectral problems of algebra. She proposed the QR algorithm for computing eigenvalues and eigenvectors in 1961, which has been named as one of the ten most important algorithms of the twentieth century. This algorithm was proposed independently by the English computer scientist John G.F. Francis in 1961.
Kublanovskaya was born in November 1920 in Krokhona, a village near Belozersk in Vologda Oblast, Russian Soviet Federative Socialist Republic. She was born in a farming and fishing family as one of nine siblings. She died at the age of 91 years old in February 2012. 

Kublanovskaya started her tertiary education in 1939 at the Gertzen Pedagogical Institute in Leningrad.[4] There, she was encouraged to pursue a career in mathematics. She moved on to study mathematics at Leningrad State University in 1945 and graduated in 1948. Following her graduation, she joined the Leningrad Branch of the Steklov Mathematical Institute of the USSR Academy of Sciences. She remained there for 64 years of her life.

In 1955, she got her first doctorate degree on the application of analytic continuation to numeric methods. In 1972 she obtained a secondary doctorate on the use of orthogonal transformations to solve algebraic problems.
In October 1985, she was awarded an honorary doctorate at Umeå University, Sweden, with which she has collaborated.
During her first PhD, she joined Leonid Kantorovich's group that was working on developing a universal computer language in the USSR. Her task was to select and classify matrix operations that are useful in numerical linear algebra. *Wik

*SAU



2025   Ioan Mackenzie James FRS (23 May 1928 – 21 February 2025) was a British mathematician working in the field of topology, particularly in homotopy theory.

James was born in Croydon, Surrey, England, and was educated at St Paul's School, London and Queen's College, Oxford. In 1953 he earned a D. Phil. from the University of Oxford for his thesis entitled Some problems in algebraic topology, written under the direction of J. H. C. Whitehead.

In 1957 he was appointed reader in pure mathematics, a post which he held until 1969. From 1959 until 1969 he was a senior research fellow at St John's College, Oxford. He held the Savilian Chair of Geometry at the University of Oxford from 1970 to 1995. He was a professor emeritus, and later an honorary fellow of St John's.

He was elected a Fellow of the Royal Society in 1968. In 1978 the London Mathematical Society awarded him the Senior Whitehead Prize, which was established in honor of his doctoral supervisor, Whitehead. In 1984 he became President of the London Mathematical Society.

James married Rosemary Stewart, a writer and researcher in business management and healthcare management, in 1961. She died in 2015, aged 90. James died on 21 February 2025, aged 96.






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

Friday, 20 February 2026

Pick's Theorem, some history.

 


*Wik


 
Georg Pick was a Jewish Austrian mathematician (murdered during The Holocaust).  In 1880 he received his PhD from University of Vienna under Leo Konigsberger. In 1899 he published a formula for finding the area of a polygon if all the vertices are on lattice points (points whose x and y coordinates on the plane are both integers, although if they are only rational, you can adapt the theorem.)  He presented the formula he created in 1899, in Geometries zur Zahlenlehre in Prague.  He worked at University of Prague and was on the appointments committee and pushed hard for Einstein to get a position in physics there. He was also instrumental in introducing Einstein to Ricci-Curbastro and Levi-Civita which helped him work out the mathematics in the general theory of relativity.  

Hugo Steinhaus caused a surge in the popularity (and knowledge) of the theorem when he used it in his popular, Mathematical Snapshots, in 1969.  (see Google n-gram below)It probably would have been much more popular in 1899 if graph paper had been more in mathematics education, but thirty to fifty years would pass before the paper became popular in geometry and algebra classes. I also think the appearance of the Geoboard created by Egyptian Educator Caleb Gattegno in the fifties was important in applications of Pick's theorem in elementary and middle schools.  I don't know if these still are used much, or any, so I popped an image of one below. My first geoboard was a crude piece of wood with a 6x6 array nails driven by a terrible carpenter, then and now, the writer. 

Pick would never be aware of this late surge of popularity, he died after two weeks in the Theresiestadt prison camp in 1942.  










*Art of Problem Solving

The formula gives the area in two variables, N and B .  N is the number of lattice points inside the polygon (many teachers, and some books, use I, for inside), and B is the number on the boundary.  The area is given by Area = N + B/2 - 1.  The example at the right shows N=3 for the inside points, B= 14 for the inside points, so our Area = 3 + 13/2 - 1, or 8 1/2 square units.  You can, of course verify this to yourself by counting connecting lines inside and dividing into squares, rectangles, and triangles that are easy to compute.

There is not a higher dimensional analogy of this theorem, counting points inside and on the boundary, but the Ehrhart Polynomial, created by French high school teacher Eugene Ehrhart in the 60's, describes an expression for the volume in terms of the number of interior points in the polytope and dilations.  

You can find more about the theorem and links to some of its extensions at Drexel University where I also found that the original theorem was published in "Geometrisches zur Zahlenlehre" Sitzungber. Lotos, Naturwissen Zeitschrift Prague, Volume 19 (1899) pages 311-319.  


Here are some more sources for information om the method:  


W. W. Funkenbusch
“From Euler’s Formula to Pick’s Formula using an Edge Theorem”
The American Mathematical Monthly
Volume 81 (1974) pages 647-648

In this short paper Funkenbusch shows that Pick's theorem is derived from Euler's Gem using the theorem that Edges = 3I +2B -3, with I and B for inside lattice points and B for boundary points.

Dale E. Varberg
“Pick’s Theorem Revisited”
The American Mathematical Monthly
Volume 92 (1985) pages 584-587

Varberg extends the theorem to cases with polygons with holes in them.  An interesting read.


Branko Grünbaum and G. C. Shephard
“Pick’s Theorem”
The American Mathematical Monthly
Volume 100 (1993) pages 150-161

For young students, the best part of this is the introduction in which the authors describe an applied mathematical approach to timber management, which unknown to the speaker, was Pick's Theorem.

My favorite article to date is by an Eighth grade student, Chris Polis, from Papua, New Guinea in 1991.  He found generalizations of Pick's Thm to several different lattices, Triangular, hexagonal, and a tesselation of the plain by isosceles trapezoids.  He found individual formulas for these, then found a general one for all of them including Pick's Thm, \( A = \frac{e + 2 (i - 1)}{P-2}\) where P is the number of edges in the lattice, e is boundary points and i is interior points.  For a square this would give P=4 and the formula becomes \( A = \frac{e + 2 (i - 1)}{4-2}\) which simplifies to Pick's Thm.  (Wonder what he is doing today?)

You can use this Desmos lattice I plucked from google to try the triangular formula with the 9 boundary points on the edge and 3 in the interior, and confirm that the interior has 13 unit equilateral triangles in area.  



I recently saw another use of the theorem on twitter to answer the following question.  Several people found the right answer with trig, but one saw a different easy solution.  





Draw the lattice and use Pick's Theorem.  


Did you notice the triangle is a right triangle?  


Recently I came across an extension of Pick's theorem that would cover shapes with holes and such that make the original theorem not work (although in many cases a little common sense will still solve them.)  

.The new approach was in the article "Counting Parallel Segments: New Variants of Pick’s Area Theorem" by Alexander Belyaev & Pierre-Alain Fayolle.  I found it in the Mathematical Intelligencer ,Volume 41, pages 1–7, (2019).  


The method counts parallel line segments and parts of segments to find the area of such non-traditional figures.  


The line segments in dark blue are called interior segments,  They contribute one unit each to the area.  In the figure (a) there are eight of them.  The red line segments are called exterior segments, and they add 1/2 a unit.  The light blue segments are partial segments and also count 1/2 unit each. [Notice in the one passing through an interior point (blue) there are two partial segments, one above and one below. ]  So the area would be 8 + 2/2 +4/2 = 11. sq units
Try the (b) image for yourself.  I'll put the answer below after a brief side note; do take time to try one diagram that does work with the regular Pick method, such as the one near the beginning of this article.  It should work for them also.


How many red(edge) lines did you use?  How many drk blue(interior) segments ?  How many partials?
I had two reds on the left edge, two drk blue and one partial on the next vertical row, four drk blue on the third vertical row, and one drk blue on the fourth edge.  That should add up to the same 8 1/2 units as we got the "Pick" way.


OK  so did you get 3 + 2/2 + 4/2 for a total of six square units for the figure (b)?

I think this is an interesting method, and the parallels Don't have to be vertical, horizontal or diagonal at any slope.  try those and see if you get the same area each time.
Good luck!


On This Day in Math - February 20

 



A mathematician will recognise Cauchy, Gauss, Jacobi or Helmholtz after reading a few pages, just as musicians recognise, from the first few bars, Mozart, Beethoven or Schubert.
~Ludwig Boltzmann

The 51st day of the year; 51 is the number of different paths from (0,0) to (6,0) made up of segments connecting lattice points that can only have slopes of 1, 0, or -1 but so that they never go below the x-axis. These are called Motzkin Numbers.

\(\pi(51) = 15\), the number of primes less than 51 is given by it's reversal, 15.

Jim Wilder pointed out that 51 is the smallest number that can be written as a sum of primes  with the digits 1 to 5 each used once  2 + 3 + 5 + 41 = 51 (Students might explore similar problems using first n digits 2-9)

A triangle with sides 51, 52 and 53 has an integer area 1170 units2.

Diophantus (around 250 AD) solved 26y^2 +1 = x^2 for (x,y) = (51, 10)

You may recognize the sequence of Perfect Numbers 6, 28, 496, 8128...(and then they start getting really big).  The fifth is 33,550,336, and if you have this one or the next memorized you are a very unusual person.  But how many are there? As of December of 2018, there are only 51 known.  The largest presently known is   282589932 × (282589933 − 1).  It has just a little less than 50 million digits.  

And like any odd number, 51 is the sum of two consecutive numbers, 25+26 , and the difference of their squares \(26^2 - 25^2\)

And I just found this unusual reference, "Don’t be baffled if you see the number 51 cropping up in Chinese website names, since 51 sounds like 'without trouble' or 'carefree' in Chinese." at
 the Archimedes Lab


EVENTS

1639  Responding to Mersenne's comment that the sum of the divisors of 360 form a ratio of 9/4 with 360, Fermat responds that 2016 has the same property. For 2024 the ratio is 540/253, about 2.134


1648 A letter from Fermat through Frenicle to Digby reached Wallis saying that Fermat had solved equations of the type x2-Ay2 = 1 for all non-square values up to 150. Thus begins the saga of the mis-naming of Pell's equation. *Edward Everett Whitford, The Pell Equation.  
As early as 400 BC in India and Greece, mathematicians studied the numbers arising from the n = 2 case of Pell's equation, probably as approximations for square roots.

Pell's equation for n = 2 and six of its integer solutions *Wik




1729 A Letter from Gabriel Cramer, Prof. Math. Genev. to James Jurin, M. D. and F. R. S. to be read at the Royal Society, gives an “account of an Aurora Borealis Attended with Unusual Appearances” . The borealis occurred on Feb 15, and the letter was sent on Feb 20. *Transactions of RSI




1807 Sophie Germain writes to Gauss informing him that she is the person who had written to him using the name M. LeBlanc. In closing she writes her hope that this will not change their correspondence. His Response on April 30 would assure her it had not.
*Sophie Germain: An Essay in the History of the Theory of Elasticity


In 1835, Charles Darwin, on his H.M.S. Beagle voyage reached Chile, and experienced a very strong earthquake and shortly afterward saw evidence of several feet of uplift in the region. He repeated measurement a few days later, and found the land had risen several feet. He had proved that geological changes occur even in our own time. Lyell's principles were based on the concept of a steady-state, nondirectional earth whereby uplift, subsidence, erosion, and deposition were all balanced. Thereby, Darwin coupled in his mind this dramatic evidence of elevation with accompanying subsidence and deposition. Thus he hypothesized that coral reefs of the Pacific developed on the margins of subsiding land masses, in the three stages of fringing reef, barrier reef, and atoll.*TIS





1905 Lise Meitner had entered the University of Vienna in October 1901. She was particularly inspired by Boltzmann, and was said to often speak with contagious enthusiasm of his lectures. Her dissertation was supervised by Franz Exner and his assistant Hans Benndorf. Her thesis, titled Prüfung einer Formel Maxwells ("Examination of a Maxwell Formula"), was submitted on 20 November 1905 and approved on 28 November. She was examined orally by Exner and Boltzmann on 19 December, and her doctorate was awarded on 1 February 1906.
 She became the second woman to earn a doctoral degree in physics at the University of Vienna, after Olga Steindler who had received her degree in 1903; the third was Selma Freud, who worked in the same laboratory as Meitner, and received her doctorate later in 1906.Freud is also known as  founder of the first official Salvation Army corps in Vienna.



1913 It was on, or around, this day that the Three Sisters Radio towers near Arlington, Va went into service. In an area called Radio, near the Columbia Pike and Courthouse Road. Virginia. It was a neighborhood named for the old U.S. Navy Wireless Station. The tallest of the three towers was 45 feet taller than the Washington Monument, and second only to the Eiffel Tower in the world.
The Navy opened Radio Arlington, call sign NAA, in 1913, launching the U.S. military’s global communications system on Fort Myers. A streetcar stop was even named “Radio.’’ Old Radio Arlington marked the first time the term “radio’’ was used in communications, according to Nan and Ross Netherton’s book “Arlington County in Virginia: A Pictorial History,” which was published in 1987. In the days of Marconi and other radio pioneers, the new communications mode was called “wireless telegraphy.’’
*The 625 Sentinal

At Tenwatts Blog I found that there is a marker outside the present Dept. of Defense facility there:
"Three radio towers similar to the Eiffel tower were erected here in 1913. One stood 600 feet, and the other two 450 feet above the 200-foot elevation of the site. The word "radio" was first used instead of "wireless" in the name of this naval communications facility. The first trans-Atlantic voice communication was made between this station and the Eiffel tower in 1915. The nation set its clocks by the Arlington Radio time signal and listened for its broadcast weather reports. The towers were dismantled in 1941, as a menace to aircraft approaching the new Washington National Airport."
I also found the nice postcard showing the three sisters (and some additions) taken from Arlington National Cemetery. His post suggests that the towers were eventually dismantled.


1947   Before John Glenn, Neil Armstrong, or Sally Ride could step into a spacesuit and rocket into the annals of history, an intrepid bunch of fruit flies had to pave the way.

Of course, the flies didn’t have much of a say when they blasted off on a V-2 rocket launched from New Mexico’s White Sands Proving Grounds on Feb. 20, 1947. But as the first animals intentionally shot into and returned alive from space, the insects’ journey heralded a new age in space research and exploration. The flies’ flight traces to the summer of 1945, when a load of German-made V-2 rocket parts arrived at White Sands, a newly established military testing area that is “almost as isolated as a valley of the Moon, which it resembles,” wrote Lloyd Mallan in Men, Rockets and Space Rats, an on-the-ground chronicle of early spaceflight efforts published in 1955. The U.S. also imported a group of scientists and engineers from postwar Germany to assist with experiments using the V-2s, part of the intelligence operation later known as Operation Paperclip.

Up they went on Feb. 20, 1947. The flies reached an altitude of 109 kilometers in 190 seconds (space starts at 100 kilometers, according to NASA), then parachuted back down to Earth, where they were recovered alive and examined by biologists. “Analysis made by Harvard on recovered seeds and flies has shown that no detectable changes are produced by the radiation,” wrote U.S. Naval Research Laboratory nuclear physicist Ernst H. Krause in a report published that same year.

*APS Org



1947 Computer pioneer Alan Turing suggests testing artificial intelligence with the game of chess in a lecture to the London Mathematical Society. Computers, he argued, must, like humans, be given training before their IQ is tested. A human mathematician has always undergone an extensive training. This training may be regarded as not unlike putting instruction tables into a machine, he said. One must therefore not expect a machine to do a very great deal of building up of instruction tables on its own.*CHM



1966 The only verified example of a family producing five single children with coincidental birthdays is that of Catherine (1952), Coral (1953), Charles (1956), Claudia (1961), and Cecelia (1966), born to Ralph and Carolyn Cummins of Clintwood, VA. All on Feb 20th.  What is the probability of this happening? *VFR (RALPH? He should have changed his name.)



1979 The German Democratic Republic issued a stamp commemorating the centenary of Einstein’s birth. It shows the Einstein tower in Potsdam and his famous formula E = mc2. [Scott #1990]*VFR




In 1996, a bright "new" star was discovered in Sagittarius by Japanese amateur astronomer Yukio Sakurai. It was found not to be a usual nova, but instead was a star going through a dramatic evolutionary state, re-igniting its nuclear furnace for one final blast of energy called the "final helium flash." It was only the second to be identified in the twentieth century. A star like the Sun ends its active life as a white dwarf star gradually cooling down into visual oblivion. Sakurai's Object had a mass a few times that of the Sun. Its collapse after fusing most of its hydrogen fuel to helium raised its temperature so much higher it began nuclear fusion of its helium remains. This was confirmed using its light spectrum to identify the elements present.*TIS
Sakurai's Object is surrounded by a planetary nebula created following the star's red giant phase around 8300 years ago.[26] It has been determined that the nebula has a diameter of 44 arcseconds and expansion velocity of roughly 32 km/s.




2013 In celebration of the 100th anniversary of the publication of the three-volume version of Bertrand Russell and Alfred North Whitehead's Principia Mathematica, a London theater company staged the world premiere of a musical based on the epic mathematics text.
Performed by the Conway Collective based out of London's historic Conway Hall and written by Tyrone Landau, the play was described as "fascinating and unusual." *MAA DL





BIRTHS

 1844 Ludwig Eduard Boltzmann (February 20, 1844 – September 5, 1906) was an Austrian physicist famous for his founding contributions in the fields of statistical mechanics and statistical thermodynamics. He was one of the most important advocates for atomic theory at a time when that scientific model was still highly controversial. *Wik Trivia: Boltzmann's famous equation S = K log W (where S = entropy, K = Boltzmann's constant, and W = probability of a particular state) was inscribed as an epitaph on Boltzmann's tombstone. *Wik After obtaining his doctorate, he became an assistant to his teacher Josef Stefan. Boltzmann's fame is based on his invention of statistical mechanics, independently of Willard Gibbs. Their theories connected the properties and behaviour of atoms and molecules with the large scale properties and behaviour of the substances of which they were the building blocks. He also worked out a kinetic theory of gases, and the Stefan-Boltzmann law concerning a relationship between the temperature of a body and the radiation it emits. His firm belief and defense of atomism (that all matter is made of atoms) against hostile opposition to this new idea, may have contributed to his suicide in 1906. *TIS

He was an incredible physicist, but an equally talented teacher.  "In her (Lise Meitner) second university year (1902), ....A fairly typical curriculum, ... unusual in one respect, it was taught by ... Ludwig Boltzmann."  Fifty years later the former student would recall his lectures as "the most beautiful and stimulating I have ever heard.....He himself was so enthusiastic about everything he taught us that one left every lecture with the feeling that a new and beautiful world had been revealed." Lise Meitner by Ruth Lewin Sime




1860 Mathias Lerch​ (20 February 1860, Milínov - 3 August 1922, Schüttenhofen) was an eminent Czech mathematician who published about 250 papers, largely on mathematical analysis and number theory. He studied in Prague and Berlin, and held teaching positions at the Czech Technical Institute in Prague, the University of Fribourg in Switzerland, the Czech Technical Institute in Brno, and Masaryk University in Brno; he was the first mathematics professor at Masaryk University when it was founded in 1920. In 1900, he was awarded the Grand Prize of the French Academy of Sciences for his number-theoretic work. The Lerch zeta-function is named after him as is the Appell–Lerch sum.*Wik




1910 Esther (Klein) Szekeres (20 February 1910 – 28 August 2005) was a Hungarian–Australian mathematician with an Erdős number of 1. She was born to Ignaz Klein in a Jewish family in Budapest, Kingdom of Hungary in 1910. As a young woman in Budapest, Klein was a member of a group of Hungarians including Paul Erdős, George Szekeres and Paul Turán that convened over interesting mathematical problems.
In 1933, Klein proposed to the group a combinatorial problem that Erdős named as the Happy Ending problem as it led to her marriage to George Szekeres in 1937, with whom she had two children.
Following the outbreak of World War II, Esther and George Szekeres emigrated to Australia after spending several years in Hongkew, a community of refugees located in Shanghai, China. In Australia, they originally settled in Adelaide before moving to Sydney in the 1960s.
In Sydney, Esther lectured at Macquarie University and was actively involved in mathematics enrichment for high-school students. In 1984, she jointly founded a weekly mathematics enrichment meeting that has since expanded into a program of about 30 groups that continue to meet weekly and inspire high school students throughout Australia and New Zealand.
In 2004, she and George moved back to Adelaide, where, on 28 August 2005, she and her husband passed away within an hour of each other *Wik



1926 Kenneth Harry Olsen (February 20, 1926 – February 6, 2011) was an American engineer who co-founded Digital Equipment Corporation (DEC) in 1957 with colleague Harlan Anderson *Wik

1929 Madan Lal Puri ( Sialkot in Pakistan , 20 February 1929 ) is an India statistician important in the context of nonparametric statistics and also occupied the fuzzy sets .
He built his career in the United States. He was born on February 20, 1929 in Sialkot, and is known for his work in mathematics which has had profound effects on the way statistics is understood and applied. He has won many honors and awards, including the Bicentennial Medal from Indiana University, Bloomington.
*Wik




1931 John Willard Milnor (20 Feb 1931, )American mathematician who was awarded the Fields Medal in 1962 for his his proof that a 7-dimensional sphere can have 28 different differential structures. This work opened up the new field of differential topology. Milnor's theorem shows that the total curvature of a knot is at least 4. In the 1950's, Milnor did a substantial amount of work on algebraic topology in which he constructed the classifying space of a topological group and gave a geometric realisation of a semi-simplicial complex. Since the 1970's his interest is in dynamics, especially holomorphic dynamics. Milnor served the American Mathematical Society as vice president (1975-76) and was awarded the Wolf Prize in 1989. *TIS



1948 Andrew Christopher Fabian, OBE, FRS (20 February 1948 - ) is a British astronomer and astrophysicist. He is a Royal Society Research Professor at the Institute of Astronomy, Cambridge, and Vice-Master of Darwin College, Cambridge. He was the President of the Royal Astronomical Society from May 2008 through to 2010. He is an Emeritus Professor of Astronomy at Gresham College, a position in which he delivered free public lectures within the City of London between 1982 and 1984. He was also editor-in-chief of the astronomy journal Monthly Notices of the Royal Astronomical Society. He was educated at King's College London (BSc, Physics) and University College London (PhD).
His current areas of research include galaxy clusters, active galactic nuclei, strong gravity, black holes and the X-ray background. He has also worked on X-ray binaries, neutron stars and supernova remnants in the past. Much of his research involves X-ray astronomy and high energy astrophysics. His notable achievements include his involvement in the discovery of broad iron lines emitted from active galactic nuclei, for which he was jointly awarded the Bruno Rossi Prize. He is author of over 800 refereed articles and head of the X-ray astronomy group at the Institute of Astronomy. Fabian was awarded the Dannie Heineman Prize for Astrophysics by the American Astronomical Society in 2008 and the Gold Medal of the Royal Astronomical Society in 2012 *Wik




DEATHS

1762 Tobias Meyer (17 Feb 1723; 20 Feb 1762 at age 38) German astronomer who developed lunar tables that greatly assisted navigators in determining longitude at sea. Mayer also discovered the libration (or apparent wobbling) of the Moon. Mayer began calculating lunar and solar tables in 1753 and in 1755 he sent them to the British government. These tables were good enough to determine longitude at sea with an accuracy of half a degree. Mayer's method of determining longitude by lunar distances and a formula for correcting errors in longitude due to atmospheric refraction were published in 1770 after his death. The Board of Longitude sent Mayer's widow a payment of 3000 pounds as an award for the tables. *TIS Leonhard Euler described him as 'undoubtedly the greatest astronomer in Europe'. 

In 1748, he began a study of the lunar surface. He decided to improve the accuracy of luar maps by measuring the position of each lunar crater with a micrometer built into his telescope. The result was a kind of lunar gazetteer, with longitudes and latitudes for hundreds of lunar features, which he intended to turn into both a lunar globe and a lunar map. The globe was never finished, but a prospectus was issued in 1750 with two sample engravings.
*Wik



More notes on Meyer can be found on this blog at the Board of Longitude Project from the Royal Museums at Greenwich. Another nice blog by Thony Christie, The Renaissance Mathematicus tells of Meyer's measurement of the Moon's distance, and the importance of that measurement.

1778 Laura Maria Catarina Bassi (31 Oct 1711 in Bologna, Papal States, 20 Feb 1778 in Bologna,
Portrait of Laura Bassi at
 the University of Bologna.*Wik

Papal States) was an Italian physicist and one of the earliest women to gain a position in an Italian university. *SAU She was the first woman in the world to earn a university chair in a scientific field of studies. She received a doctoral degree from the University of Bologna in May 1732, only the third academic qualification ever bestowed on a woman by a European university, and the first woman to earn a professorship in physics at a university in Europe. She was the first woman to be offered an official teaching position at a university in Europe.
In 1738, she married Giuseppe Veratti, a fellow academic with whom she had twelve children. After this, she was able to lecture from home on a regular basis and successfully petitioned the University for more responsibility and a higher salary to allow her to purchase her own equipment.
One of her principal patrons was Pope Benedict XIV. He supported less censorship of scholarly work, such as happened with Galileo, and he supported women figures in learning, including Agnesi.
She was mainly interested in Newtonian physics and taught courses on the subject for 28 years. She was one of the key figures in introducing Newton's ideas of physics and natural philosophy to Italy. She also carried out experiments of her own in all aspects of physics. In order to teach Newtonian physics and Franklinian electricity, topics that were not focused in the university curriculum, Bassi gave private lessons.[6] In her lifetime, she authored 28 papers, the vast majority of these on physics and hydraulics, though she did not write any books. She published only four of her papers.[2] Although only a limited number of her scientific works were left behind, much of her scientific impact is evident through her many correspondents including Voltaire, Francesco Algarotti, Roger Boscovich, Charles Bonnet, Jean Antoine Nollet, Giambattista Beccaria, Paolo Frisi, Alessandro Volta. Voltaire once wrote to her saying "There is no Bassi in London, and I would be much happier to be added to your Academy of Bologna than that of the English, even though it has produced a Newton". *Wik

1846 Antonio Abetti (19 Jun 1846, 20 Feb 1928 at age 81) Italian astronomer who was an authority on minor planets. At first a civil engineer, he became an astronomer at the University of Padua (1868-93), with an interest in positional astronomy and made many observations of small planets, comets and star occultations. In 1874, Abetti went to Muddapur, Bengal, to observe the transit of Venus across the sun's disk where his use of a spectroscope was the first use of this kind. Later, he became director at the Arcetri Observatory and Professor of astronomy at the University of Florence (1894-1921). The observatory had been founded by G. B. Donati in 1872, and Abetti equipped it with a new telescope that he had built in the workshops at Padua. He was active after retirement, until his death, and was followed by his son Giorgio.*TIS



1955 Arthur Lee Dixon FRS (27 November 1867 — 20 February 1955) was a British mathematician and holder of the Waynflete Professorship of Pure Mathematics at the University of Oxford. The younger brother of Alfred Cardew Dixon, he was educated at Kingswood School and Worcester College, Oxford, becoming a Tutorial Fellow at Merton College in 1898 and the Waynflete Professor in 1922. Dixon was the last mathematical professor at Oxford to hold a life tenure, and although he was not particularly noted for his mathematical innovations he did publish many papers on analytic number theory and the application of algebra to geometry, elliptic functions and hyperelliptic functions. Elected a Fellow of the Royal Society in 1912 and serving as President of the London Mathematical Society from 1924 to 1926, *Wik




1972 Maria Goeppert-Mayer (28 Jun 1906, 20 Feb 1972 at age 65) German physicist who shared one-half of the 1963 Nobel Prize for Physics with J. Hans D. Jensen of West Germany for their proposal of the shell nuclear model. (The other half of the prize was awarded to Eugene P. Wigner of the United States for unrelated work.) In 1939 she worked at Columbia University on the separation of uranium isotopes for the atomic bomb project. In 1949, she devised the shell nuclear model, which explained the detailed properties of atomic nuclei in terms of a structure of shells occupied by the protons and neutrons. This explained the great stability and abundance of nuclei that have a particular number of neutrons (such as 50, 82, or 126) and the same special number of protons. *TIS




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