The Kiss Precise, Soddy's Circle Theorem

  Soddy's formula is another example of Stigler's law of eponymy, "No scientific discovery is named after its original discoverer." Stigler named the sociologist Robert K. Merton as the discoverer of "Stigler's law", so as to avoid this law about laws disobeying its very own decree.

Soddy's formula is about the relationship of the radii of four mutually tangent circles. The formula is sometimes called the "Kissing Circles Theorem". If four circles are all tangent to each other, then they must intersect at six distinct points. The first demonstration of this relationship between four mutually tangent circles (actually, one can be a line) was in 1643. Rene Descartes sent a letter to Princess Elisabeth of Bohemia in which he showed that the four radii, r₁, r₂, r₃, r₄, must be such that \( \frac{1}{r^2_{1}}+ \frac{1}{r^2_{2}}+\frac{1}{r^2_3}+\frac{1}{r^2_4}= \frac{1}{2}(\frac{1}{r_1}+\frac{1}{r_2}+\frac{1}{r_3}+\frac{1}{r_4} )^2\)

For this reason the theorem is often called Descarte's circle theorem. The figure shows four circles all externally tangent to each other, but could also be drawn with three tangent circles all inside, and tangent to, a fourth circle. The bend of this externally tangent circle is given a negative value, and thus the same equation provides its radius also.

The equation can be written much more easily, and usually is, using a notation of "bend". For each value let the "bend" equal the reciprocal of the radius, then \(\frac{1}{r_1} =b_1\)With this notation the formula can be written as \(b^2_1 + b^2_2+b^2_3+b^2_4=\frac{1}{2}(b_1+b_2+b_3+b_4)^2\).

It seems that it may also have been discovered about the same time in Japan. In the book, Sacred Mathematics: Japanese Temple Geometry, by Fukagawa Hidetoshi and Tony Rothman, there is an illustration of a complicated pattern of nested congruent circles, for which knowledge of the theorem would seem to be required, on a wooden tablet. It was a practice during the Edo period in Japan that people from every segment of society would inscribed geometry solutions on wooden tablets called sangaku and hang them as offerings in temples and shrines.
The Theorem was rediscovered and published in the 1841 The Lady's and Gentleman's diary by an amateur English Mathematician named Phillip Beecroft. Beecroft also observed that there exist four other circles that would each be mutually tangent at the same four points. These circles would have tangents perpendicular to the original circles tangents at each point of intersection. Both sets of Beecroft's circles are shown in this illustration from Mad Math.
Beecroft's circles are related to the use of a geometrical inversion in a circle which will invert the inner tangent circle to become an outer tangent circle. The circle of inversion between the two is the circle Beecroft uses that passes through the three points of tangent in the other three circles. (A nice explanation and illustration of this is at this AMS site.

In 1936 Sir Fredrick Soddy rediscovered the theorem again. Soddy may also be known to students of Science for receiving the Nobel Prize for Chemistry in 1921 for the discovery of the decay sequences of radioactive isotopes.  According to Oliver Sacks' wonderful book, Uncle Tungsten, Soddy also created the term "isotope" and was the first to use the term  "chain reaction".  In a strange "chain reaction" of ideas, Soddy played a part in the US developing an atomic bomb.  Soddy's book, The  Interpretation of Radium, inspired  H G Wells to write The World Set Free in 1914, and he dedicated the novel to Soddy's book. Twenty years later, Wells' book set Leo Szilard to thinking about the possibility of Chain reactions, and how they might be used to create a bomb, leading to his getting a British patent on the idea in 1936.  A few years later Szilard encouraged his friend, Albert Einstein, to write a letter to President Roosevelt about the potential for an atomic bomb.  The prize-winning science-fiction writer, Frederik Pohl, talks about Szilard's epiphany in Chasing Science (pg 25),

".. we know the exact spot where Leo Szilard got the idea that led to the atomic bomb.  There isn't even a plaque to mark it, but it happened in 1938, while he was waiting for a traffic light to change on London's Southampton Row.  Szilard had been remembering H. G. Well's old science-fiction novel about atomic power, The World Set Free and had been reading about the nuclear-fission experiment of Otto Hahn and Lise Meitner, and the lightbulb went on over his head."

Perhaps Soddy's name is appropriate for the formula if only for the unique way he presented his discovery. He presented it in the form of a poem which is presented below.

The Kiss Precise
by
Frederick Soddy

For pairs of lips to kiss maybe
Involves no trigonometry.
'Tis not so when four circles kiss
Each one the other three.

To bring this off the four must be
As three in one or one in three.
If one in three, beyond a doubt
Each gets three kisses from without.

If three in one, then is that one
Thrice kissed internally.

Four circles to the kissing come.
The smaller are the benter.
The bend is just the inverse of
The distance from the center.

Though their intrigue left Euclid dumb
There's now no need for rule of thumb.
Since zero bend's a dead straight line
And concave bends have minus sign,
The sum of the squares of all four bends
Is half the square of their sum.

To spy out spherical affairs
An oscular surveyor
Might find the task laborious,
The sphere is much the gayer,
And now besides the pair of pairs
A fifth sphere in the kissing shares.
Yet, signs and zero as before,
For each to kiss the other four,
The square of the sum of all five bends
Is thrice the sum of their squares.

In _Nature_, June 20, 1936

One may notice in the last verse that Soddy generalizes the theorem to five spheres. The extended theorem becomes: \[ b_1^2+b_2^2+b_3^2+b_4^2+b_5^2 = \frac13(b_1+b_2+b_3+b_4+b_5)^2. \]

Later   another verse was written by Thorold Gosset to describe the even more general   case in N dimensions for N+2 hyperspheres of the Nth dimension.

On August 15, 1936, only a few months after Soddy's poem had been published in Nature,  Gosset sent a copy of the poem to Donal Coxeter on the occasion of his wedding in the Round Church in Cambridge.  Gossett enclosed in his wedding congratulations, and his extension of the poem to the higher dimensions which were Coxeter's special area of study. It would be published in Nature the following year,
 

The Kiss Precise (Generalized) by Thorold Gosset

And let us not confine our cares
To simple circles, planes and spheres,
But rise to hyper flats and bends
Where kissing multiple appears,
In n-ic space the kissing pairs
Are hyperspheres, and Truth declares -
As n + 2 such osculate
Each with an n + 1 fold mate
The square of the sum of all the bends
Is n times the sum of their squares.

In _Nature_
    January 9, 1937.

Fred Lunnon sent me a kind note correcting a typing oversight, and adding that

"The original result generalizes nicely to curved n-space with
curvature v [e.g. v^2 = +1 for elliptic space, -1 for hyperbolic]
in the form



        \((\sum_i x_i)^2 - n \sum_i x_i^2 = 2n v^2\)




where \(x_i\) denote the curvatures of n+2 mutually tangent spheres.
Example: n = 2, v = 0, x = [-1,2,2,3] is one solution, corresponding to
a unit circle in the plane enclosing circles of radii 1/2,1/2,1/3.



See Ivars Petersen "Circle Game" in Science News (2001) \bf 159 (16) p.254"

 

Fred admits he wasn't the first to prove this, but did manage to replicate it on his own (which impresses the heck out of me)... but THEN....... wait for it.... He wrote another poem verse to accompany this extension to higher dimensions...

  The Kiss Precise (Further Generalized) by Fred Lunnon



    How frightfully pedestrian

    My predecessors were

    To pose in space Euclidean

    Each fraternising sphere!

    Let Gauss' k squared be positive

    When space becomes elliptic,

    And conversely turn negative

    For spaces hyperbolic:

    Squared sum of bends is sum times n

    Of twice k squared plus squares of bends.

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On This Day in Math - February 19

  

Copernicus statue at Olsztyn Castle

It is true that a mathematician who is not somewhat of a poet, will never be a perfect mathematician.
~Karl Weierstrass

The 50th day of the year; 50 is the smallest number that can be written as the sum of two squares in two distinct ways 50 = 49 + 1 = 25 + 25. *Tanya Khovanova, Number Gossip (What is the next, or what is the smallest number that can be written as the sum of two squares in three distinct ways? For solution from Ben Vitale, see bottom of post)

50 is also expressible as the sum of distinct primes in two ways so that all consecutive primes 2-23 are used :50 = 2 + 5 + 7 + 17 + 19 = 3 + 11 + 13 + 23.

Heron of Alexandria used \( \sqrt{50} = 7 + \frac{1}{14} = \frac {99}{14}\)  A solution to the Pell equation \( x^2 - 50 y^2 =1 \)  in the First century AD
 
The number 50 is somewhat responsible for the area of number theory about partitions. In 1740 Philip Naudé the younger (1684-1747) wrote Euler from Berlin to ask “how many ways can the number 50 be written as a sum of seven different positive integers?” Euler would give the answer, 522, within a few days but would return to the problem of various types of partitions throughout the rest of his life.

EVENTS

1003 al-Biruni observed two lunar eclipses from Gurgān,(Azerbaijan)  one on 19 February and the other on 14 August. On 4 June of the following year, 1004, he observed a third lunar eclipse.  *Encylopedia . com

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Tartaglia's Masterpiece

1512 The French invaded Brescia, in Northern Italy, during the War of the League of Cambrai. The militia of Brescia defended their city for seven days. When the French finally broke through, they took their revenge by massacring the inhabitants of Brescia. By the end of battle, over 45,000 residents were killed. During the massacre, a French soldier sliced Niccolò's jaw and palate with a saber. This made it impossible for Niccolò to speak normally, prompting the nickname "Tartaglia" Tartaglia is perhaps best known today for his conflicts with Gerolamo Cardano over the solution of cubics. (see this blog for the unfortunate common mistake about Tartaglia's family name.)

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1549 Osiander wrote of Michael Stifel: “He has devised new numbers for the alphabet, namely the triangular numbers, and his fantasies are more absurd than before.” *VFR  In 1553 Stifel published the Cours (algebra) Christoph Rudolph's. He was also steadily engaged on the computation of the numbers in Daniel and the Apocalypse, and became the zealous opponent of Andreas Osiander. Earlier, in 1532, Stiefel published a treatise on the numbers in Daniel, entitled Ein Rechenbuchlein vom End Christi, in which he fixed the last day and hour to be Oct. 19, 1533, at 8 o'clock in the morning with the result that the peasants neglected their labors and lost their harvests, but sued for damages when the prediction was not fulfilled.

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1600 The Inquisition brought Giordano Bruno to the Campo dei Fiori in Rome’s center where they chained him to an iron stake and burned him alive for his beliefs that the earth rotated on its axis. *Amir Aczel, Pendulum, pg 9 (This date seems wrong. Thony Christie noted that " Bruno was executed on 17th Feb and not for his cosmology but for his heretical theology." Thanks... several other sources agree with Feb 17th date))

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1616 On February 19, 1616, the Inquisition asked a commission of theologians, known as qualifiers, about the propositions of the heliocentric view of the universe after Nicollo Lorin had accused Galileo of Heretical remarks in a letter to his former student, Benedetto Castelli. 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

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1671/72 Newton’s first publication appears as a letter in the Philosophical Transactions. It deals with his new theory of light, showing that a prism separates white light into its component colors. Huygens, Hooke and others objected so strongly that he vowed not to publish again. Fortunately that vow was not kept. *VFR The full text of that publication is here.

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1787 William Herschel's 40-foot telescope, also known as the Great Forty-Foot telescope, was a reflecting telescope constructed between 1785 and 1789 at Observatory House in Slough, England. It used a 48-inch (120 cm) diameter primary mirror with a 40-foot-long (12 m) focal length (hence its name "Forty-Foot"). It was the largest telescope in the world for 50 years. It may have been used to discover Enceladus and Mimas, the 6th and 7th moons of Saturn. It was dismantled in 1840 by Herschel's son John Herschel due to safety concerns; today the original mirror and a 10-foot (3.0 m) section of the tube remain.

 The first observation with the telescope was on 19 February 1787, when Herschel pointed the then-incomplete telescope towards the Orion nebula, which he observed by crawling into the telescope and using a hand-held eyepiece: "The apparatus for the 40-foot telescope was by this time so far completed that I could put the mirror into the tube and direct it to a celestial object; but having no eye-glass fixed, not being acquainted with the focal length which was to be tried, I went into the tube, and laying down near the mouth of it I held the eye-glass in my hand, and soon found the place of the focus. The object I viewed was the nebula in the belt of Orion, and I found the figure of the mirror, though far from perfect, better than I had expected. It showed four small stars in the nebula and many more. The nebula was extremely bright."

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In 1855, M. Le Verrier presented the first weather map at the French Academy of Sciences.*TIS A storm on November 14, 1854 destroyed the French warship Henri IV and damaged other British and French vessels on the Black Sea involved in the Crimean War. A report from the state-supported Paris Observatory indicated that barometric readings showed that the storm had passed across Europe in about four days. Urban Leverrier, director of the Paris Observatory, concluded that had there been a telegraph line between Vienna and the Crimea, the British and French fleets could have received warnings. An earlier map is mentioned, but not shown in a letter dated Dec 1, 1816 in Gilbert's Annalen der Physik from Heinrich Wilhelm Brandes *Report of The International Meterological Congress, 1893

Meteorological map of the 16th of January 1865 — credits : Observatoire de Paris

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1876 Sylvester began his duties at the newly founded Johns Hopkins, *TIS

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1880, the photophone was demonstrated by Alexander Graham Bell and Charles Sumner Tainter. In their device, a mirrored silver disc was made to vibrate by speech from a speaking tube. Light reflected off the disc was focused by a parabolic dish onto a selenium photocell. The variations in the reflected light were converted into electrical signals carried to headphones.

 It was invented jointly by Alexander Graham Bell and his assistant Charles Sumner Tainter on February 19, 1880, at Bell's laboratory at 1325 L Street in Washington, D.C. Both were later to become full associates in the Volta Laboratory Association, created and financed by Bell.

While honeymooning in Europe with his bride Mabel Hubbard, Bell likely read of the newly discovered property of selenium having a variable resistance when acted upon by light, in a paper by Robert Sabine as published in Nature on 25 April 1878. In his experiments, Sabine used a meter to see the effects of light acting on selenium connected in a circuit to a battery. However Bell reasoned that by adding a telephone receiver to the same circuit he would be able to hear what Sabine could only see.

A photophone receiver and headset, one half of Bell and Tainter's optical telecommunication system of 1880

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1901 Messages from Mars reported in Collier's Magazine. While conducting experiments on high-frequency electrical transmission in 1899 in his Colorado Springs, Colorado laboratory, Nikola Tesla picked up cosmic radio waves on his instruments. Announcing this development, he publicly opined that the messages came from outer space, possibly from inhabitants of Mars. In a Collier’s Weekly article dated February 19, 1901, Tesla wrote, “At the present stage of progress, there would be no insurmountable obstacle in constructing a machine capable of conveying a message to Mars … What a tremendous stir this would make in the world! How soon will it come?” Later discoveries revealed that Tesla had actually picked up common radio waves emitted by interstellar gas clouds. *History. Com

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1940 Edwin Hubble wrote in a letter to Harlow Shapley that he had determined the distance to the "Andromeda nebula". He included this graph. HT Massimo

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1946 Alan Turing Presents the “Proposal for the Development in the Mathematics Division of an Automatic Computing Engine (ACE).”
This research proposal was presented to a meeting of the Executive Committee of the National Physical Laboratory (NPL) in Teddington, England, and approved at a second meeting held a month later.
Turing based this research on von Neumann’s First Draft of a Report on the EDVAC. He had studied it in summer 1945 when he was recruited by J.R. Womersley to join the staff of the NPL. *CHM

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1957 William H. Spencer obtained a patent on February 19, 1957 for a new "Method for Making Elastic Bands" which produced rubber bands in an Open Ring design. 

 The rubber band was patented in England on March 17, 1845 by Stephen Perry

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1971 The first warrant is issued to search a computer storage. Although the requirements for obtaining such a warrant were similar to those for searching a home, they ushered in a new era that would lead to increasingly sophisticated methods of encryption to hide computer files from law enforcement agents.*CHM

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1972 The New Yorker published an article by A. Adler on “Mathematics and Creativity” that was not well received by the mathematical community. See The [old] Mathematical Intelligencer, no. 2. *VFR An abstract is here

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BIRTHS

1473 Nicolaus Copernicus Polish astronomer who proposed that the planets have the Sun as the fixed point to which their motions are to be referred; that the Earth is a planet which, besides orbiting the Sun annually, also turns once daily on its own axis; and that very slow, long-term changes in the direction of this axis account for the precession of the equinoxes *TIS
An advance copy of his work De revolutionibus orbium coelestium was presented to Copernicus. On the same day he died. *VFR
Over 450 years after his death, Copernicus was reburied in the cathedral at Frombork on Poland’s Baltic coast. The astronomer whose ideas were once declared heresy by the Vatican—was reburied with full religious honors.

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1837 Aleksandr Nikolayevich Korkin (3 March [O.S. 19 February] 1837–September 1, 1908, all New Style) was a Russian mathematician. He made contribution to the development of partial differential equations. After Chebyshev, Korkin was the most important initiator of the formation of the Saint Petersburg Mathematical School*Wik

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1863 Axel Thue(19 Feb 1863 in Tönsberg, Norway - 7 March 1922 in Oslo, Norway) Thue studied Diophantine equations, showing that, for example, y³ - 2x² = 1 cannot be satisfied by infinitely many pairs of integers. Edmund Landau, in 1922, described Thue's work as, ".. the most important discovery in elementary number theory that I know. "
Thue's Theorem states, " If f (x, y) is a homogeneous polynomial with integer coefficients, irreducible in the rationals and of degree > 2 and c is a non-zero integer then  f (x, y) = c has only a finite number of integer solutions." *SAU

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1866 Thomas Jefferson Jackson See (19 Feb 1866 in Montgomery City, Missouri - 4 July 1962 in Oakland, California, USA) was an U S astronomer who studied in the University of Missouri and in Berlin. He fell out with his astronomical colleagues and was eventually banned from publishing. He spend the last part of his life arguing against Einstein's Theory of Relativity. *SAU

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1889 Sir Ernest Marsden (19 Feb 1889, 15 Dec 1970) British-born New Zealand nuclear physicist who worked under Ernest Rutherford investigating atomic structure with Hans Geiger. Marsden visually counted scintillations from alpha particles after passing through gold foil and striking a phosphorescent screen. That some of these were observed scattered at surprisingly large angles led to Rutherford's theory of the nucleus as the massive, tiny centre of the atom. Later, Marsden's own experiments, working in New Zealand, hinted suggested transmutation of elements was possible when alpha particles bombarding nitrogen nuclei produced scattered particles of greater speed than the original radiation. *TIS

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1924 Arnljot Høyland (19 February 1924 – 21 December 2002) was a Norwegian mathematical statistician.

Høyland was born in Bærum. He studied at the University of Oslo and later at the University of California, Berkeley in the USA. While a student he worked for the intelligence department at the Norwegian High Command, a military officer with the rank of Major. He lectured at the University of Oslo from 1959 to 1965, and then at the Norwegian Institute of Technology, eventually as a Professor of mathematical statistics. He published the textbooks Sannsynlighetsregning og statistisk metodelære (two volumes) in 1972 and 1973.

In 1944 Høyland composed the melody for Alf Prøysen's song "Julekveldsvise". 

He was decorated Knight, First Class of the Order of St. Olav in 1995. *Wik

Alf Prøysen (left) and Arnljot Høyland (right),

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1964  Jennifer Anne Doudna ForMemRS (born February 19, 1964  in Washington, D.C) is an American biochemist who has done pioneering work in CRISPR gene editing, and made other fundamental contributions in biochemistry and genetics. Doudna was one of the first women to share a Nobel in the sciences. She received the 2020 Nobel Prize in Chemistry, with Emmanuelle Charpentier, "for the development of a method for genome editing.

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DEATHS

1553 Erasmus Reinhold (October 22, 1511 – February 19, 1553) was a German astronomer and mathematician, considered to be the most influential astronomical pedagogue of his generation. He was born and died in Saalfeld, Saxony.
He was educated, under Jacob Milich, at the University of Wittenberg, where he was first elected dean and later became rector. In 1536 he was appointed professor of higher mathematics by Philipp Melanchthon. In contrast to the limited modern definition, "mathematics" at the time also included applied mathematics, especially astronomy. His colleague, Georg Joachim Rheticus, also studied at Wittenberg and was appointed professor of lower mathematics in 1536.
Reinhold catalogued a large number of stars. His publications on astronomy include a commentary (1542, 1553) on Georg Purbach's Theoricae novae planetarum. Reinhold knew about Copernicus and his heliocentric ideas prior to the publication of De revolutionibis and made a favourable reference to him in his commentary on Purbach. However, Reinhold (like other astronomers before Kepler and Galileo) translated Copernicus' mathematical methods back into a geocentric system, rejecting heliocentric cosmology on physical and theological grounds.
It was Reinhold's heavily annotated copy of De revolutionibus in the Royal Observatory, Edinburgh that started Owen Gingerich on his search for copies of the first and second editions which he describes in The Book Nobody Read.[5] In Reinhold's unpublished commentary on De revolutionibus, he calculated the distance from the Earth to the sun. He "massaged" his calculation method in order to arrive at an answer close to that of Ptolemy.*Wik

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1622 Sir Henry Savile (30 Nov 1549 in Bradley (near Halifax), Yorkshire, England - 19 Feb 1622 in Eton, Berkshire, England) Savile was an English mathematician who founded professorships of geometry and astronomy at Oxford. It is interesting to read Savile's comments in these lectures on why he felt that mathematics at that time was not flourishing. Students did not understand the importance of the subject, Savile wrote, there were no teachers to explain the difficult points, the texts written by the leading mathematicians of the day were not studied, and no overall approach to the teaching of mathematics had been formulated. Of course, as we shall see below, fifty years later Savile tried to rectify these shortcomings by setting up two chairs at the University of Oxford. *SAU

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1799 Jean-Charles Borda, (4 May 1733 in Dax, France - 19 Feb 1799 in Paris, France) a major figure in the French navy who participated in sev­eral scientific voyages and the American revolution. Besides his contributions to navigational instruments he did important work on fluid mechanics, even showing that Newton’s theory of fluid resistance was untenable. He is best known for the voting system he created in 1770.*VFR (The Borda count is a single-winner election method in which voters rank candidates in order of preference. The Borda count determines the winner of an election by giving each candidate a certain number of points corresponding to the position in which he or she is ranked by each voter. Once all votes have been counted the candidate with the most points is the winner. Because it sometimes elects broadly acceptable candidates, rather than those preferred by the majority, the Borda count is often described as a consensus-based electoral system, rather than a majoritarian one.The Borda count is a popular method for granting awards for sports in the United States, and is used in determining the Most Valuable Player in Major League Baseball, and by the Associated Press and United Press International to rank teams in NCAA sports, to determine the winner of the Heisman Trophy.) [He was one of the main driving forces in the introduction of the decimal system. Borda made good use of calculus and experiment to unify areas of physics. For his surveying, he also developed a series of trigonometric tables. In 1782, while in command of a flotilla of six French ships, he was captured by the British. Borda's health declined after his release. He is one of 72 scientists commemorated by plaques on the Eiffel tower.]*TIS

With the advent of the metric system, after the French Revolution it was decided that the quarter circle should be divided into 100 angular units, currently known as the gradian, instead of 90 degrees, and the gradian into 100 centesimal minutes of arc (centigrades) instead of 60 arc-minutes. This required the calculation of trigonometric tables and logarithms corresponding to the new unit and instruments for measuring angles in the new system.

Borda constructed instruments for measuring angles in the new units (the instrument could no longer be called a "sextant") which was later used in the arc measurement of the meridian between Dunkirk and Barcelona by Delambre to determine the radius of the Earth and thus define the length of the metre.  *Wik 

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1897 Karl (Theodor Wilhelm) Weierstrass (31 Oct 1815, 19 Feb 1897 at age 81) was a German mathematician who is known as the "father of modern analysis" for his rigour in analysis led to the modern theory of functions, and considered one of the greatest mathematics teachers of all-time. He was doing mathematical research while a secondary school teacher, when in 1854, he published a paper on Abelian functions in the famous Crelle Journal. The paper so impressed the mathematical community that he shortly received an honorary doctorate and by 1856, he had a University appointment in Berlin. In 1871, he demonstrated that there exist continuous functions in an interval which have no derivatives nowhere in the interval. He also did outstanding work on complex variables.*TIS Weierstrass died peacefully at the age of 82 at his home in Berlin after a long illness culminating in influenz. It is reported that his last wish was that the priest say nothing in his praise at the funeral, but to restrict the services to the customary prayers. *VFR

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1908 Paul Matthieu Hermann Laurent (2 Sept 1841 in Echternach, Luxembourg - 19 Feb 1908 in Paris, France) He developed statistical formulas for the calculation of actuarial tables and studied heat conduction. *VFR

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1916 Ernst Mach (18 Feb 1838; 19 Feb 1916 at age 77) Austrian physicist and philosopher who established important principles of optics, mechanics, and wave dynamics. His early physical works were devoted to electric discharge and induction. Between 1860 and 1862 he studied in depth the Doppler Effect by optical and acoustic experiments. He introduced the "Mach number" for the ratio of speed of object to speed of sound is named for him. When supersonic planes travel today, their speed is measured in terms that keep Mach's name alive. His lifetime interest, however, was in psychology and human perception. He supported the view that all knowledge is a conceptual organization of the data of sensory experience (or observation). *TIS

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1842 Joseph Valentin Boussinesq (13 March 1842 – 19 February 1929) was a French mathematician and physicist who made significant contributions to the theory of hydrodynamics, vibration, light, and heat.
In 1897 he published Théorie de l' écoulement tourbillonnant et tumultueux des liquides, a work that greatly contributed to the study of turbulence and hydrodynamics.

John Scott Russell experimentally observed solitary waves in 1834 and reported it during the 1844 Meeting of the British Association for the advancement of science. Subsequently, this was developed into the modern physics of solitons. In 1871, Boussinesq published the first mathematical theory to support Russell's experimental observation, and in 1877 introduced the Korteweg–De Vries equation. In 1876, Lord Rayleigh published his mathematical theory to support Russell's experimental observation. At the end of his paper, Rayleigh admitted that Boussinesq's theory came before his.

In 1897, he published Théorie de l'écoulement tourbillonnant et tumultueux des liquides ("Theory of the swirling and agitated flow of liquids"), a work that greatly contributed to the study of turbulence and hydrodynamics.

The word "turbulence" was never used by Boussinesq. He used sentences such as "écoulement tourbillonnant et tumultueux" (vortex or tumultuous flow). The first mention of the word "turbulence" in French or English scientific fluid mechanics literature (the word "turbulence" existed in other context) can be found in a paper by Lord Kelvin in 1887 *Wik

(While Kelvin is credited with introducing the term, Leonardo da Vinci is recognized for early observations and descriptions of turbulent flow in water, even using the Italian word "turbolenza" to describe it.)

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1938 Edmund Georg Hermann Landau (14 Feb 1877 in Berlin, Germany - 19 Feb 1938 in Berlin, Germany) Although famous as a number theorist, he is best known for his textbooks which are written in an austere definition-theorem-proof style. His Grundlagen der Analysis is an excellent treatment of the development of our number systems from the Peano postualates. Reading this book is a good way to learn mathematical German. But if you are lazy, it has been translated into English. *VFR Landau gave the first systematic presentation of analytic number theory and wrote important works on the theory of analytic functions of a single variable.*SAU Legend has it that at the age of three, when is mother forgot her umbrella in a carriage, he replied, "It was number 354," and the umbrella was quickly re-acquired.

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1940 Otto Toeplitz died in Jerusalem, after having left Germany in the Spring of 1939. He made lasting contributions to the theory of integral equations and the theory of functions of infinitely many variables. Today he is best remembered for two popular works which have been translated into English: The Enjoyment of Mathematics (original 1930, 1957), and The Calculus: A Genetic Approach (first published 1949; English 1963). These are some of the most successful attempts to bring higher mathematics to the general public. The later shows his deep interest in the history of mathematics; every calculus teacher could profit from reading it. *VFR

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1990 Otto Neugebauer, historian of ancient and medieval mathematics and astronomy. *VFR
(May 26, 1899 – February 19, 1990) He was an Austrian-American mathematician and historian of science who became known for his research on the history of astronomy and the other exact sciences in antiquity and into the Middle Ages. By studying clay tablets he discovered that the ancient Babylonians knew much more about mathematics and astronomy than had been previously realized. The National Academy of Sciences has called Neugebauer "the most original and productive scholar of the history of the exact sciences, perhaps of the history of science, of our age." *Wik

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  1937 Robert Coleman Richardson (June 26, 1937 – February 19, 2013) was an American physicist who (with Douglas Osheroff and David Lee) was awarded the 1996 Nobel Prize for Physics for their discovery of superfluidity in the isotope helium-3. As helium is reduced in temperature toward almost absolute zero, a strange phase transition occurs, and the helium takes on the form of a superfluid. The atoms had until that point had moved with random speeds and directions. But as a superfluid, the atoms then move in a co-ordinated manner! 

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@BenVitale: smallest number w/ 3 representations: \( 325 = 1^2 + 18^2 = 6^2 + 17^2 = 10^2+ 15^2\)


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

On This Day in Math - February 18

  

Leon Battista Alberti, De pictura and Elementa *Museo Galileo

The power of mathematics rests on its evasion of all unnecessary thought and on its wonderful saving of mental operations.
~Ernst Mach

The 49th day of the year; lots of numbers are squareful (divisible by a square number) but 49 is the smallest number so that it, and both its neighbors are squareful. (Many interesting questions arise for students.. what's next, can there be four in a row?, etc)

And Prof. William D Banks of the University of Missouri has recently proved that every integer in base ten is the sum of 49 or less palindromes. (August 2015) (Building on Prof. Banks groundbreaking work, by February 22, 2016 JAVIER CILLERUELO AND FLORIAN LUCA had proved that for any base > 4   EVERY POSITIVE INTEGER IS A SUM OF THREE PALINDROMES )

1 / 49 = 0.0204081632 6530612244 8979591836 7346938775 51 and then repeats the same 42 digits.  It's better than it looks.  Write down all the powers of two, and then index them two to the right and add.

 

The 49th Mersenne prime is discovered. On Jan 19th, 2016 The GIMPS program announced a new "largest known" prime, 2^74,207,281 -1. called M74,207,281 for short, the number has 22,338,618 digits.

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EVENTS

3102 B.C. The Kaliyuga begins according to the Indian mathematician Aryabhata (born A.D. 476). He believed all astronomical phenomena were periodic, with period 4,320,000= 20 × 603 years, and that all the planets had mean longitude zero on this date. [College Mathematics Journal, 16 (1985), p. 169.] *VFR

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1670 “Joannes Georgius Pelshower [Regimontanus Borussus] giving me a visit, and desiring an example of the like, I did that night propose to myself in the dark without help to my memory a number in 53 places: 2468135791011121411131516182017192122242628302325272931 of which I extracted the square root in 27 places: 157103016871482805817152171 proxim´e; which numbers I did not commit to paper till he gave me another visit, March following, when I did from memory dictate them to him.” So wrote John Wallis. [American Journal of Psychology, 4(1891), 38] *VFR

Wallis made significant contributions to trigonometry, calculus, geometry, and the analysis of infinite series. In his Opera Mathematica I (1695) he introduced the term "continued fraction".  He was one of the finest cryptographers of the period.

Wallis has been credited as the originator of the number line "for negative quantities" and "for operational purposes." This is based on a passage in his 1685 treatise on algebra in which he introduced a number line to illustrate the legitimacy of negative quantities.

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1673: Robert Hooke writes in his Journal: "Bought Copernicus tower hill 2sh " *‏@HookesLondon Thony Christie points out that current first editions run about \( 2,500,000 \) GB Pounds.

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1727 Leonhard Euler defends his De Sono essay in a public disputation at the law auditorium at Basal. His paper had been submitted as his "habilitationsschrift", part of his application for the Physics Professorship at Basal. Fortunately, he did not get the position, and soon departed for a position at Petersburg Academy of Science in Russia. Among other competitors overlooked for the position was Jakob Hermann. *Ronald S. Calinger; Leonhard Euler: Mathematical Genius in the Enlightenment

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1772 the Royal Danish Academy of Sciences and Letters presented Alexander Wilson with a gold medal for his work on sunspots. Wilson was a Scottish surgeon, type-founder, astronomer, mathematician and meteorologist and the first scientist to record the use of kites in meteorological investigations. Wilson noted that sunspots viewed near the edge of the Sun's visible disk appear depressed below the solar surface, a phenomenon referred to as the Wilson effect. When the Royal Danish Academy of Sciences and Letters announced a prize to be awarded for the best essay on the nature of solar spots, Wilson submitted an entry which won. *Wik  Regius Professor of Practical Astronomy at the University of Glasgow.

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1879 “I will do the same for the young women that I do for the young men. I shall take pleasure in giving gratuitous instruction to any person whom I find competent to receive it. I give no elementary instruction, but only in the higher mathematics.” Benjamin Peirce to Arthur V. Gilman, president of Harvard. [Scripta Mathematica, 11(1945), 259
*VFR

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1879 J. J. Sylvester, in a lecture at the Peabody Institute in Baltimore, read “Rosalind”, a mock-sentimental poem of four hundred lines all ending in “ind”. For the first few lines of this dreadful poem, see Osiris, 1(1936), p. 106. *VFR Encyclopedia.com says that Sylvester was the author of this poem, and another which had two hundred lines rhyming with “Winn.” These were products of his later residence in Baltimore. Sylvester had perhaps a better appreciation of music.

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In 1913, chemist Frederick Soddy introduced the term "isotope". Soddy was an English chemist and physicist who received the Nobel Prize for Chemistry in 1921 for investigating radioactive substances. He suggested that different elements produced in different radioactive transformations were capable of occupying the same place on the Periodic Table, and on 18 Feb 1913 he named such species "isotopes" from Greek words meaning "same place." He is credited, along with others, with the discovery of the element protactinium in 1917. *TIS He also wrote the mathematical poem, The Kiss Precise, which includes a solution to Descartes Circle Problem. the poem begins:

For pairs of lips to kiss maybe
Involves no trigonometry.
'Tis not so when four circles kiss
Each one the other three.
To bring this off the four must be
As three in one or one in three.
If one in three, beyond a doubt
Each gets three kisses from without.
If three in one, then is that one
Thrice kissed internally.

The complete link is here

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1930 Clyde Tombaugh (1906–1997) discovered Pluto on photographic plates under the direction of V M Slipher at the Lowell Observatory at Flagstaff, Az. For 45 minutes, before he showed his superiors, he was the only person in the world who knew it existed. When he later went to college he was not allowed to take Astronomy I, the instructor thinking it unsuitable for the discoverer of a planet. (On August 24th of 2006 the International Astronomical Union decided to rescind Pluto’s status as a planet and reclassify it as another entity called a “dwarf planet”. ) *FFF, pg 537

And from @MAAnow " Clyde Tombaugh proved the existence of what would become Pluto, but the woman whose calculations made that possible has been largely forgotten by history. Meet Elizabeth Williams, the mathematician behind our favorite tiny (non?)planet. Williams' role in the Planet X project was that of head human computer, performing mathematical calculations on where Lowell should search for an unknown object and its size based on the differences in the orbits of Neptune and Uranus. Her calculations led to predictions for the location of the unknown planet, :

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2006 The game of Connect Four was first solved by James D. Allen (Oct 1, 1988), and independently by Victor Allis (Oct 16, 1988). First player can force a win. Strongly solved by John Tromp's 8-ply database (Feb 4, 1995). It was weakly solved for all boardsizes where width+height is at most 15 (Feb 18, 2006). *Wik

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BIRTHS

1201 Muhammad ibn Muhammad ibn al-Hasan al-Tusi (18 Feb 1201; 26 Jun 1274 at age 73) Persian philosopher, scientist, mathematician and astronomer who made outstanding contributions in his era. When The Mongol invasion, started by Genghis Khan, reached him in 1256, he escaped likely death by joining the victorious Mongols as a scientific adviser. He used an observatory built at Maragheh (finished 1262), assisted by Chinese astronomers. It had various instruments such as a 4 meter wall quadrant made from copper and an azimuth quadrant which was Tusi's own invention. Using accurately plotted planetary movements, he modified Ptolemy's model of the planetary system based on mechanical principles. The observatory and its library became a center for a wide range of work in science, mathematics and philosophy. He was known by the title Tusi from his place of birth (Tus)*TIS
Iranian stamp for the 700th anniversary of his death

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1404 Leon Battista Alberti (18 Feb 1404; 25 Apr 1472 at age 68) Italian artist and geometrist who “wrote the book,” the first general treatise Della Pictura (1434) on the the laws of perspective, establishing the science of projective geometry. Alberti also worked on maps (again involving his skill at geometrical mappings) and he collaborated with Toscanelli who supplied Columbus with the maps for his first voyage. He also wrote the first book on cryptography which contains the first example of a frequency table. *TIS
. This noted architect took up the study of mathematics for relaxation. He contributed to the study of perspective. *VFR

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1677 Jacques Cassini (18 Feb 1677; 16 Apr 1756 at age 79) French astronomer whose direct measurement of the proper motions of the stars (1738) disproved the ancient belief in the unchanging sphere of the stars. He also studied the moons of Jupiter and Saturn and the structure of Saturn's rings. His two major treatises on these subject appeared in 1740: Elements of Astronomy and Astronomical Tables of the Sun, Moon, Planets, Fixed Stars, and Satellites of Jupiter and Saturn. He also wrote about electricity, barometers, the recoil of firearms, and mirrors. He was the son of astronomer, mathematician and engineer Giovanni Cassini (1625-1712) with whom he made numerous geodesic observations. Eventually, he took over his father's duties as head of the Paris Observatory.*TIS Cassini was born at the Paris Observatory and died at Thury, near Clermont. Admitted at the age of seventeen to membership of the French Academy of Sciences, he was elected in 1696 a fellow of the Royal Society of London, and became maître des comptes in 1706. *Wik

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1745 Count Alessandro Giuseppe Antonio Anastasio Volta (18 Feb 1745; 5 Mar 1827 at age 82) Italian physicist who invented the electric battery (1800), which for the first time enabled the reliable, sustained supply of current. His voltaic pile used plates of two dissimilar metals and an electrolyte, a number of alternated zinc and silver disks, each separated with porous brine-soaked cardboard. Previously, only discharge of static electricity had been available, so his device opened a new door to new uses of electricity. Shortly thereafter, William Nicholson decomposed water by electrolysis. That same process later enabled Humphry Davy to isolate potassium and other metals. Volta also invented the electrophorus, the condenser and the electroscope. He made important contributions to meteorology. His study of gases included the discovery of methane. The volt, a unit of electrical measurement, is named after him.*TIS

Volta battery at the Tempio Voltiano museum, Como

*Wik

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1832 Octave Chanute(18 Feb 1832, 23 Nov 1910) U.S. aeronaut whose work and interests profoundly influenced Orville and Wilbur Wright and the invention of the airplane. Octave Chanute was a successful engineer who took up the invention of the airplane as a hobby following his early retirement. He designed and built the Hannibal Bridge with Joseph Tomlinson and George S. Morison. In 1869, this bridge established Kansas City, Missouri as the dominant city in the region, as the first bridge to cross the Missouri River there. He designed many other bridges during his railroad career, including the Illinois River rail bridge at Chillicothe, Illinois, the Genesee River Gorge rail bridge near Portageville, New York (now in Letchworth State Park), the Sibley Railroad Bridge across the Missouri River at Sibley, Missouri, the Fort Madison Toll Bridge at Fort Madison, Iowa, and the Kinzua Bridge in Pennsylvania.

Knowing how railroad bridges were strengthened, Chanute experimented with box kites using the same basic strengthening method, which he then incorporated into wing design of gliders. Through thousands of letters, he drew geographically isolated pioneers into an informal international community. He organized sessions of aeronautical papers for the professional engineering societies that he led; attracted fresh talent and new ideas into the field through his lectures; and produced important publications. *TIS The town of Chanute, Kansas is named after him, as well as the former Chanute Air Force Base near Rantoul, Illinois, which was decommissioned in 1993. The former Base, now turned to peacetime endeavors, includes the Octave Chanute Aerospace Museum, detailing the history of aviation and of Chanute Air Force base. He was buried in Springdale Cemetery, Peoria, Illinois. *Wik

Chanute's 12 wing glider, Katydid.

Chanute's 1896 biplane hang glider is a trailblazing design adapted by the Wright brothers, who "contrived a system consisting of two large surfaces on the Chanute double-deck plan".

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1838 Ernst Mach (18 Feb 1838; 19 Feb 1916 at age 77) Austrian physicist and philosopher who established important principles of optics, mechanics, and wave dynamics. His early physical works were devoted to electric discharge and induction. Between 1860 and 1862 he studied in depth the Doppler Effect by optical and acoustic experiments. He introduced the "Mach number" for the ratio of speed of object to speed of sound is named for him. When supersonic planes travel today, their speed is measured in terms that keep Mach's name alive. His lifetime interest, however, was in psychology and human perception. He supported the view that all knowledge is a conceptual organization of the data of sensory experience (or observation). *TIS

Ernst Mach's historic 1887 photograph (shadowgraph) of a bow shockwave around a supersonic bullet.

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1844 Jacob Lueroth (18 Feb 1844 in Mannheim, Germany - 14 Sept 1910 in Munich, Germany) Lüroth was taught by Hesse and Clebsch and continued to develop their work on geometry and invariants. He published results in the areas of analytic geometry, linear geometry and continued the directions of his teachers in his publications on invariant theory. In 1869 Lüroth discovered the "Lüroth quartic". This came out of an investigation he was carrying out into when a ternary quartic form could be represented as the sum of five fourth powers of linear forms.
Some of his work on rational curves, published in Mathematische Annalen in 1876, was extended to surfaces by Castelnuovo in 1895. In 1883 Lüroth published his method on constructing a Riemann surface for a given algebraic curve.
Lüroth also worked on the big problem of the topological invariance of dimension. He made some useful progress but this difficult problem was not completely solved until the work of Brouwer in 1911.
Among his other work, Lüroth undertook editing. He was an editor of the complete works of Hesse and of Grassmann. He also has some fine results on logic, a topic he worked on in collaboration with his friend Ernst Schröder.
Von Staudt's ideas of geometry interested Lüroth and he further developed von Staudt's complex geometry. He published Grundriss der Mechanik in 1881. This mechanics book makes heavy use of the vector calculus. *sau

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1922 Ferdinand Wittenbauer (18 February 1857 in Maribor – 16 February 1922 in Graz) was an Austrian mechanical engineer and writer. He is known for introducing graphic methods in dynamics.

Ferdinand Wittenbauer was born on 18 February 1857 in Maribor as third child to Ferdinand Wittenbauer, a military doctor. His parents died early. He then lived in Graz with his uncle and attended Realschule, where he was always top of his class. He did his Matura at the early age of fifteen and later studied at the School of Engineering at Technische Hochschule Graz.  In 1879, he graduated from the Technische Hochschule with honours.  From 1883 to 1884 he undertook a study trip through Germany visiting the universities of Berlin and Freiburg im Breisgau. In 1887, he was appointed to the chair Reine und Technische Mechanik und Theoretische Maschinenlehre which relates to mechanics and machine science at the Technische Hochschule Graz. He succeeded Franz Stark who was appointed professor at the Deutsche Technische Hochschule in Prague.[ From 1894 to 1896 and from 1903 to 1905, Wittenbauer served as dean to the faculty of mechanical engineering, from 1911 to 1912 as rector to his alma mater.

Ferdinand Wittenbauer married Hermine née Weiß in 1882. His wife died in 1914. Their only son Ferdinand was born in 1886, became an engineer as well and died by suicide in September 1922. Ferdinand Wittenbauer died on 16 February 1922 in Graz due to the consequences of a stroke he suffered earlier that year.

At the beginning of his scientific career, Wittenbauer worked on kinematic geometry. His main contribution lay in applying graphic methods of kinematic geometry to dynamics. In 1904, he started publishing treatises which were preliminary works for his almost 800-page book on Graphische Dynamik (Graphical Dynamics), which he completed only shortly before his death. In 1905, Wittenbauer first published his internationally acclaimed and still valid method for a graphic determination of the flywheel moment of inertia.

You may come across posts that mention Wittenbaur's parallelogram, without ever commenting on why he chose such an unusual way to form a parallelogram, a pretty trivial process.  His method was to take any quadrilateral and by trisecting each side, and then construction of a parallelogram with sides parallel to the diagonals of the original quadrilateral.  The center of gravity of a random quadrilateral is harder to arrive at than the center of gravity of a parallelogram. But by creating a parallelogram with the same center of gravity as the original quadrilateral it made the centroid (centre of mass) easy. 

Ferdinand Wittenbauer also discovered an easy method to calculate the centroid (centre of mass) of any quadrangle, known as Wittenbauer's  Theorem or Wittenbauer's Parallelogram. 

In addition, Wittenbauer is known for his Aufgaben aus der technischen Mechanik, a collection of exercises in technical mechanics including solutions published in three volumes. Co-author was mathematician and engineer Theodor Pöschl (son to Jakob Pöschl, Nikola Tesla’s teacher). Finished in 1911, it served as very first and then most prominent set of problems in the fields of mechanics in the German-speaking area for some decades. It was translated into several languages, in 1965 a Spanish edition still appeared. *Wik * PB

Draw an arbitrary quadrilateral and divide each of its sides into three equal parts. Draw a line through adjacent points of trisection on either side of each vertex and you'll have a parallelogram. *Futility Closet

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1871 George Udny Yule (18 Feb 1871 in Morham (near Haddington), Scotland - 26 June 1951 in Cambridge, Cambridgeshire, England) graduated in Engineering from University College London and then studied in Bonn. He worked with Karl Pearson on the statistics of regression and correlation. He took a post with an examinations board before being appointed to a Cambridge fellowship. He is best known for his book: Introduction to the Theory of Statistics.*SAU

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DEATHS

901 Al-Sabi Thabit ibn Qurra al-Harrani (born c. 836, 18 Feb 901) was a Mesopotamian scholar and mathematician who greatly contributed to preparing the way for such important mathematical discoveries as the extension of the concept of number to (positive) real numbers, integral calculus, theorems in spherical trigonometry, analytic geometry, and non-euclidean geometry. In astronomy he was one of the first reformers of the Ptolemaic system, writing Concerning the Motion of the Eighth Sphere. He believed (wrongly) that the motion of the equinoxes oscillates. Including observations of the Sun, eight complete treatises by Thabit on astronomy have survived. In mechanics he was a founder of statics. He wrote The Book on the Beam Balance in which he finds the conditions for the equilibrium of a heavy beam. *TIS

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1851 Karl Gustav Jacob Jacobi (10 Dec 1804; 18 Feb 1851) German mathematician who, with the independent work of Niels Henrik Abel of Norway, founded the theory of elliptic functions. He also worked on Abelian functions and discovered the hyperelliptic functions. Jacobi applied his work in elliptic functions to number theory. He also investigated mathematical analysis and geometry. Jacobi carried out important research in partial differential equations of the first order and applied them to the differential equations of dynamics. His work on determinants is important in dynamics and quantum mechanics and he studied the functional determinant now called the Jacobian. *TIS He died from smallpox, in his 47th year.*VFR

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1856 Baron Wilhelm von Biela (19 Mar 1782, 18 Feb 1856 at age 73) Austrian astronomer who was known for his measurement (1826) of a previously known comet as having an orbital period of 6.6 years. Subsequently, known as Biela's Comet, it was observed to break in two (1846), and in 1852 the fragments returned as widely separated twin comets that were not seen again. However, in 1872 and 1885, bright meteor showers (known as Andromedids, or Bielids) were observed when the Earth crossed the path of the comet's known orbit. This observation provided the first concrete evidence for the idea that some meteors are composed of fragments of disintegrated comets.*TIS

Biela's Comet in February 1846, soon after it split into two pieces, and the biela meteor showers as seen on Nov 27, 1872

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1877 Charles Henry Davis (16 Jan 1807; 18 Feb 1877) U.S. naval officer and scientist who published several hydrographic studies, was a superintendent of the Naval Observatory (1865–67, 1874–77) and worked to further scientific progress. Between his naval duties at sea, he studied mathematics at Harvard. He made the first comprehensive survey of the coasts of Massachusetts, Rhode Island, and Maine, including the intricate Nantucket shoals area. He helped establish and then supervised the preparation of the American Nautical Almanac (1849) for several years. Davis was a co-founder of the National Academy of Sciences (1863), and wrote several scientific books.*TIS

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1899 (Marius) Sophus Lie (17 Dec 1842; 18 Feb 1899) was a Norwegian mathematician who made significant contributions to the theories of algebraic invariants, continuous groups of transformations and differential equations. Lie groups and Lie algebras are named after him. Lie was in Paris at the outbreak of the French-German war of 1870. Lie left France, deciding to go to Italy. On the way however he was arrested as a German spy and his mathematics notes were assumed to be coded messages. Only after the intervention of French mathematician, Gaston Darboux, was Lie released and he decided to return to Christiania, Norway, where he had originally studied mathematics to continue his work. *TIS

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1900 Eugenio Beltrami (November 16, 1835, Cremona – February 18, 1900, Rome) was an Italian mathematician notable for his work concerning differential geometry and mathematical physics. His work was noted especially for clarity of exposition. He was the first to prove consistency of non-Euclidean geometry by modeling it on a surface of constant curvature, the pseudosphere, and in the interior of an n-dimensional unit sphere, the so-called Beltrami–Klein model. He also developed singular value decomposition for matrices, which has been subsequently rediscovered several times. Beltrami's use of differential calculus for problems of mathematical physics indirectly influenced development of tensor calculus by Gregorio Ricci-Curbastro and Tullio Levi-Civita.*Wik
Beltrami studied elasticity, wave theory, optics, thermodynamics, and potential theory, and was among the first to explore the concepts of hyperspace and time as a fourth dimension. His investigations in the conduction of heat led to linear partial differential equations. Some of Beltrami's last work was on a mechanical interpretation of Maxwell's equations. *TIS

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1944 Charles Benedict Davenport (1 Jun 1866, 18 Feb 1944 at age 77) American zoologist who contributed substantially to the study of eugenics (the improvement of populations through breeding) and heredity and who pioneered the use of statistical techniques in biological research. Partly as a result of breeding experiments with chickens and canaries, he was one of the first, soon after 1902, to recognize the validity of the newly discovered Mendelian theory of heredity. In Heredity in Relation to Eugenics (1911), he compiled evidence concerning the inheritance of human traits, on the basis of which he argued that the application of genetic principles would improve the human race. These data were at the heart of his lifelong promotion of eugenics, though he muddled science with social philosophy. *TIS

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1957 Henry Norris Russell (25 Oct 1877; 18 Feb 1957) American astronomer and astrophysicist who showed the relationship between a star's brightness and its spectral type, in what is usually called the Hertzsprung-Russell diagram, and who also devised a means of computing the distances of binary stars. As student, professor, observatory director, and active professor emeritus, Russell spent six decades at Princeton University. From 1921, he visited Mt. Wilson Observatory annually. He analyzed light from eclipsing binary stars to determine stellar masses. Russell measured parallaxes and popularized the distinction between giant stars and "dwarfs" while developing an early theory of stellar evolution. Russell was a dominant force in American astronomy as a teacher, writer, and advisor. *TIS

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1967 Julius Robert Oppenheimer (22 Apr 1904, 18 Feb 1967 at age 62) was an American theoretical physicist and science administrator, noted as director of the Los Alamos laboratory during development of the atomic bomb (1943-45) and as director of the Institute for Advanced Study, Princeton (1947-66). Accusations as to his loyalty and reliability as a security risk led to a government hearing that resulted the loss of his security clearance and of his position as adviser to the highest echelons of the U.S. government. The case became a cause célèbre in the world of science because of its implications concerning political and moral issues relating to the role of scientists in government. *TIS

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1995 Walter Samuel McAfee (September 2, 1914 – February 18, 1995) was an American scientist and astronomer, notable for participating in the world's first lunar radar echo experiments with Project Diana.

McAfee was born in Ore City, Texas to African-American parents Luther F. McAfee and Susie A. Johnson; he was the second of their nine children. When McAfee was three months old, the family moved to Marshall, Texas, where McAfee would grow up and attend undergraduate school. He graduated high school in Marshall in 1930, and later noted that his high school physics and chemistry teacher, Freeman Prince Hodge, was a great influence of his.[4] Following the completion of his master's degree, McAfee took a job in 1939 teaching science and mathematics in Columbus, Ohio. In 1941, he married Viola Winston, who taught French at the same junior high school in Columbus, Ohio where McAfee taught. McAfee and Winston had two daughters.[5] McAfee died at his home in South Belmar, New Jersey, on February 18, 1995.

McAfee attended Wiley College, where his mother studied, graduating with a B.S. in mathematics in 1934. Following his undergraduate work, McAfee attended Ohio State University and earned his M.S. in physics in 1937. After his work on Project Diana with the United States Army Signal Corps Engineering Laboratories, McAfee returned to school, receiving the Rosenwald Fellowship to continue his doctoral studies at Cornell University. In 1949, McAfee was awarded his PhD in Physics for his work on nuclear collisions under Hans Bethe.

In 1956 President Dwight D. Eisenhower presented him with one of the first Secretary of the Army Research and Study Fellowships. The fellowship enabled McAfee to spend two years studying radio astronomy at Harvard University.

McAfee left his teaching position in Columbus when he was hired by the Army Signal Corps to work at the Electronics Research Command at Fort Monmouth, New Jersey, in May 1942.[8] It was here that he participated in Project Diana, completing the first calculations showing that radar signals could be successfully bounced from a ground-based antenna to the Moon and back; this prediction was verified experimentally in 1946.

During his time at Fort Monmouth, he lectured in physics and electronics at Monmouth College (now Monmouth University) from 1958 to 1975, and served as a trustee at Brookdale Community College. McAfee also served on the Curriculum Advisory Council of the electronics engineering department at Monmouth and was recognized with an honorary doctorate of science in 1985.

In 1961, McAfee received the first U.S. Army Research and Development Achievement Award. He was eventually promoted to GS-16, making him the first African-American person to achieve this "super grade" civil service position.[7] After his death, a building at Fort Monmouth was renamed the McAfee Center, marking the first time a civilian was so honored at the site.[9] A research building at Aberdeen Proving Ground was named in his honor (2011), and he was inducted into the United States Army Materiel Command's Hall of Fame (2015), becoming the first African American to receive that honor.[5] Wiley College inducted McAfee into its Science Hall of Fame. *Wik

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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