## Wednesday 26 February 2020

### On This Day in Math - February 26

Euler calculated without effort,
just as men breathe,
as eagles sustain themselves in the air.
~Francois Arago

The 57th day of the year; 57(base ten) is written with all ones in base seven. It is the last day this year that can be written in base seven with all ones.(What is the last day of the year that can be written with all ones in base two,... base three?)

57 is the maximum number of regions inside a circle formed by chords connecting 7 points on the circle. Students might ask themselves why this is the same as the first five numbers in the sixth row of Pascal's triangle.

57 is the number of permutations of the numbers 1 to 6 in which exactly 1 element is greater than the previous element (called a permutations with 1 "ascents").

57 is the maximum number of possible interior regions formed by 8 intersecting circles.

The number of ways of coloring the faces of a cube with 3 different colors is 57. For coloring a cube with n colors, the number of possible colorings is given by

57, is sometimes known as Grothendieck's prime.  The explanation is given in Amir D. Aczel's last book, Finding Zero.  Grothendieck had used primes as a framework on which to build some more general result when:

EVENTS
1616 Galileo is warned to abandon Copernican views. On February 19, 1616, the Inquisition had asked a commission of theologians, known as qualifiers, about the propositions of the heliocentric view of the universe 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 A transcript filed by the 1633 Inquisition indicates he was also enjoined from either speaking or writing about his theory. Yet Galileo remained in conflict with the Church. He was eventually interrogated by the Inquisition in Apr 1633. On 22 Jun 1633, Galileo was sentenced to prison indefinitely, with seven of ten cardinals presiding at his trial affirming the sentencing order. Upon signing a formal recantation, the Pope allowed him to live instead under house-arrest. From Dec 1633 to the end of his life on 8 Jan 1641, he remained in his villa at Florence.*TIS In 1992, the Vatican officially declared that Galileo had been the victim of an error.

1665 A letter from Christiaan Huygens to his father, Constantyn Huygens describes the discovery of synchronization between two pendulum clocks in his room.
While I was forced to stay in bed for a few days and made observations on my two clocks of the new workshop, I noticed a wonderful effect that nobody could have thought of before. The two clocks, while hanging [on the wall] side by side with a distance of one or two feet between, kept in pace relative to each other with a precision so high that the two pendulums always swung together, and never varied. While I admired this for some time, I finally found that this happened due to a sort of sympathy: when I made the pendulums swing at differing paces, I found that half an hour later, they always returned to synchronism and kept it constantly afterwards, as long as I let them go.

1849 Prince Albert visited the RI  for the 1st time to hear a lecture by Faraday. *Royal Institution ‏@ri_science Image

1855 Carl F. Gauss' body lay in state under the dome in the rotunda of the observatory in Gottingen two days after his death.  At nine o'clock a group of 12 students of science and mathematics, including Dedikind, carried the coffin out of the observatory and to his final resting place in St. Alben's Church Cemetery. After the casket was lowered it was covered with  covered with palms and laurel .

1885 “The Burroughs Company brought out their ﬁrst adding machine and announced that it would sell for $27.75$ plus $1.39$ shipping charges, for a total of whatever that came to.” *Tom Koch, 366 Dumb Days in History by Tom Koch

1962 A new teaching method based on “how and why things happen in mathematics rather than on traditional memorization of rules” is announced by the Educational Research Council of Greater Cleveland. This became the Cleveland Program of the New Math.*VFR

In 1896, Henri Becquerel stored a wrapped photographic plate in a closed desk drawer, and a phosphorescent uranium compound laid on top, awaiting a bright day to test his idea that sunlight would make the phosphorescent uranium emit rays. It remained there several days. Thus by sheer accident, he created a new experiment, for when he developed the photographic plate on 1 Mar 1896, he found a fogged image in the shape of the rocks. The material was spontaneously generating and emitting energetic rays totally without the external sunlight source. This was a landmark event. The new form of penetrating radiation was the discovery of the effect of radioactivity. He had in fact reported an earlier, related experiment to the French Academy on 24 Feb 1896, though at that time he thought phosphorescence was the cause.*TIS

1935 The first test of the ideas presented in Robert Watson-Watt's earlier memo, "Detection and location of aircraft by radio methods", were conducted on this date in a field near in Upper Stowe, about three miles south of Weedon Bec in Northhamptonshire. The tests were successful and on several occasions a clear signal was seen on the oscilloscopes hidden in the back of  an ambulance  from a Handley Page Heyford bomber being flown around the site by Bobby Blucke, who would later become Air Vice-Marshal Blucke. The tests were so secret that only three people were allowed to witness them, Watson-Watt, his colleague Arnold Wilkins, and a single member of the Air Ministry, A. P. Rowe

*Wik

1996 Silicon Graphics Inc. buys Cray Research for \$767 million, becoming the leading supplier of high-speed computing machines in the U.S. Over a forty year career, Cray founder Seymour Cray consistently produced most of the fastest computers in the world-- innovative, powerful supercomputers used in defense, meteorological, and scientific investigations. *CHM

2012 New world record distance for paper airplane throw: Joe Ayoob, a former Cal Quarterback, throws a John Collins paper airplane design, (which was named Suzanne), officially breaking the world record by 19 feet, 6 inches. The new world record was 226 feet, 10 inches. The previous record is 207 feet and 4 inches set by Stephen Kreiger in 2003. *ESPN

BIRTHS
1585 Federico Cesi (26 Feb OR 13 Mar 1585 (sources differ, but Thony Christie did some research to suggest the Feb date is the correct one); 1 Aug 1630 at age 45) Italian scientist who founded the Accademia dei Lincei (1603, Academy of Linceans or Lynxes), often cited as the first modern scientific society, and of which Galileo was the sixth member (1611). Cesi first announced the word telescope for Galileo's instrument. At an early age, while being privately educated, Cesi became interested in natural history and that believed it should be studied directly, not philosophically. The name of the Academy, which he founded at age 18, was taken from Lynceus of Greek mythology, the animal Lynx with sharp sight. He devoted the rest of his life to recording, illustrating and an early classification of nature, especially botany. The Academy was dissolved when its funding by Cesi ceased upon his sudden death(at age 45). *TIS It was revived in its currently well known form of the Pontifical Academy of Sciences, by the Vatican, Pope Pius IX in 1847.

1664 Nicolas Fatio de Duillier (alternative names are Facio or Faccio;) (26 February 1664 – 12 May 1753) was a Swiss mathematician known for his work on the zodiacal light problem, for his very close (some have suggested "romantic" ) relationship with Isaac Newton, for his role in the Newton v. Leibniz calculus controversy , and for originating the "push" or "shadow" theory of gravitation.
[Le Sage's theory of gravitation is a kinetic theory of gravity originally proposed by Nicolas Fatio de Duillier in 1690 and later by Georges-Louis Le Sage in 1748. The theory proposed a mechanical explanation for Newton's gravitational force in terms of streams of tiny unseen particles (which Le Sage called ultra-mundane corpuscles) impacting all material objects from all directions. According to this model, any two material bodies partially shield each other from the impinging corpuscles, resulting in a net imbalance in the pressure exerted by the impact of corpuscles on the bodies, tending to drive the bodies together.]

He also developed and patented a method of perforating jewels for use in clocks.
When Leibniz sent a set of problems for solution to England he mentioned Newton and failed to mention Faccio among those probably capable of solving them. Faccio retorted by sneering at Leibniz as the ‘second inventor’ of the calculus in a tract entitled ‘Lineæ brevissimæ descensus investigatio geometrica duplex, cui addita est investigatio geometrica solidi rotundi in quo minima fiat resistentia,’ 4to, London, 1699. Finally he stirred up the whole Royal Society to take a part in the dispute (Brewster, Memoirs of Sir I. Newton, 2nd edit. ii. 1–5).
In 1707, Fatio came under the influence of a fanatical religious sect, the Camisards, which ruined Fatio's reputation. He left England and took part in pilgrim journeys across Europe. After his return only a few scientific documents by him appeared. He died in 1753 in Maddersfield near Worcester, England. After his death his Geneva compatriot Georges-Louis Le Sage tried to purchase the scientific papers of Fatio. These papers together with Le Sage's are now in the Library of the University of Geneva.
Eventually he retired to Worcester, where he formed some congenial friendships, and busied himself with scientific pursuits, alchemy, and the mysteries of the cabbala. In 1732 he endeavoured, but it is thought unsuccessfully, to obtain through the influence of John Conduitt [q. v.], Newton's nephew, some reward for having saved the life of the Prince of Orange. He assisted Conduitt in planning the design, and writing the inscription for Newton's monument in Westminster Abbey. *Wik

1786 Dominique François Jean Arago (26 Feb 1786, 2 Oct 1853) was a French physicist and astronomer who discovered the chromosphere of the sun (the lower atmosphere, primarily composed of hydrogen gas), and for his accurate estimates of the diameters of the planets. Arago found that a rotating copper disk deflects a magnetic needle held above it showing the production of magnetism by rotation of a nonmagnetic conductor. He devised an experiment that proved the wave theory of light, showed that light waves move more slowly through a dense medium than through air and contributed to the discovery of the laws of light polarization. Arago entered politics in 1848 as Minister of War and Marine and was responsible for abolishing slavery in the French colonies. *TIS A really great blog about Arago, With the catchy title, "François Arago: the most interesting physicist in the world!" is posted here. Read this introduction, and you will not be able to resist:

When he was seven years old, he tried to stab a Spanish solider with a lance
When he was eighteen, he talked a friend out of assassinating Napoleon
He once angered an archbishop so much that the holy man punched him in the face
He has negotiated with bandits, been chased by a mob, broken out of prison
He is:
François Arago, the most interesting physicist in the world

1799 Benoit Clapeyron (26 Feb 1799, 28 Jan 1864) French engineer who expressed Sadi Carnot's ideas on heat analytically, with the help of graphical representations. While investigating the operation of steam engines, Clapeyron found there was a relationship (1834) between the heat of vaporization of a fluid, its temperature and the increase in its volume upon vaporization. Made more general by Clausius, it is now known as the Clausius-Clapeyron formula. It provided the basis of the second law of thermodynamics. In engineering, Clayeyron designed and built locomotives and metal bridges. He also served on a committee investigating the construction of the Suez Canal and on a committee which considered how steam engines could be used in the navy.*TIS

1842 Nicolas Camille Flammarion (26 Feb 1842; 3 Jun 1925 at age 83) was a French astronomer who studied double and multiple stars, the moon and Mars. He is best known as the author of popular, lavishly illustrated, books on astronomy, including Popular Astronomy (1880) and The Atmosphere (1871). In 1873, Flammarion (wrongly) attributed the red color of Mars to vegetation when he wrote “May we attribute to the color of the herbage and plants which no doubt clothe the plains of Mars, the characteristic hue of that planet...” He supported the idea of canals on Mars, and intelligent life, perhaps more advanced than earth's. Flammarion reported changes in one of the craters of the moon, which he attributed to growth of vegetation. He also wrote novels, and late in life he turned to psychic research. *TIS

1843 Karl Friedrich Geiser (26 Feb 1843 in Langenthal, Bern, Switzerland, 7 May 1934 in Küsnacht, Zürich, Switzerland) Swiss mathematician who worked in algebraic geometry and minimal sufaces. He organised the first International Mathematical Congress in Zurich.*SAU

1864 John Evershed (26 Feb 1864, 17 Nov 1956) English astronomer who discovered (1909) the Evershed effect - the horizontal motion of gases outward from the centres of sunspots. While photographing solar prominences and sunspot spectra, he noticed that many of the Fraunhofer lines in the sunspot spectra were shifted to the red. By showing that these were Doppler shifts, he proved the motion of the source gases. This discovery came to be known as the Evershed effect. He also gave his name to a spectroheliograph, the Evershed spectroscope.*TIS

1946 Ahmed Hassan Zewail (February 26, 1946 – August 2, 2016) was an Egyptian-American scientist, known as the "father of femtochemistry". He was awarded the 1999 Nobel Prize in Chemistry for his work on femtochemistry and became the first Egyptian and the first Arab to win a Nobel Prize in a scientific field. He was the Linus Pauling Chair Professor of Chemistry, Professor of Physics, and the director of the Physical Biology Center for Ultrafast Science and Technology at the California Institute of Technology.
Zewail died aged 70 on the evening of August 2, 2016, after a long battle with cancer. *Wik

DEATHS
1638 Claude-Gaspar Bachet de M´eziriac (9 Oct 1581, 26 Feb 1638), noted for his work in number theory and mathematical recreations. He published the Greek text of Diophantus’s Arithmetica in 1621. This is the translation that Fermat used and in which he wrote the famous afghan note for FLT. He asked the ﬁrst ferrying problem: Three jealous husbands and their wives wish to cross a river in a boat that will only hold two persons, in such a manner as to never leave a woman in the company of a man unless her husband is present. (With four couples this is impossible.)*VFR (I admit that I don't know how this differs from the similar river crossings problems of Alcuin in the 800's, Help someone?)His books on mathematical puzzles formed the basis for almost all later books on mathematical recreations.*SAU He was also the first to use continued fractions in the solution of indeterminate equations. Some have given him credit for Bezot's identity.

1693 Sir Charles Scarborough MP FRS FRCP (19 December 1615 – 26 February 1693) was an English physician and mathematician.
He was born in St. Martin's-in-the-Fields, London in 1615, the son of Edmund Scarburgh, and was sent to St. Paul's School, whence he proceeded to Caius College, Cambridge, and educated at St Paul's School, Gonville and Caius College, Cambridge (BA, 1637, MA, 1640) and Merton College, Oxford (MD, 1646). While at Oxford he was a student of William Harvey, and the two would become close friends. Scarborough was also tutor to Christopher Wren, who was for a time his assistant.
Following the Restoration in 1660, Scarborough was appointed physician to Charles II, who knighted him in 1669; Scarborough attended the king on his deathbed, and was later physician to James II and William and Mary. During the reign of James II, Scarborough served (from 1685 to 1687) as Member of Parliament for Camelford in Cornwall.
Scarborough was an original fellow of the Royal Society and a fellow of the Royal College of Physicians, author of a treatise on anatomy, Syllabus Musculorum, which was used for many years as a textbook, and a translator and commentator of the first six books of Euclid's Elements (published in 1705). He also was the subject of a poem by Abraham Cowley, An Ode to Dr Scarborough.
Scarborough died in London in 1693. He was buried at Cranford, Middlesex, where there is a monument to him in the parish church erected by his widow. *Wik

1878 Pietro Angelo Secchi (18 Jun 1818, 26 Feb 1878 at age 59) Italian Jesuit priest and astrophysicist, who made the first survey of the spectra of over 4000 stars and suggested that stars be classified according to their spectral type. He studied the planets, especially Jupiter, which he discovered was composed of gasses. Secchi studied the dark lines which join the two hemispheres of Mars; he called them canals as if they where the works of living beings. (These studies were later continued by Schiaparelli.) Beyond astronomy, his interests ranged from archaeology to geodesy, from geophysics to meteorology. He also invented a meteorograph, an automated device for recording barometric pressure, temperature, wind direction and velocity, and rainfall.*TIS

1985 Tjalling Charles Koopmans (August 28, 1910 – February 26, 1985) was the joint winner, with Leonid Kantorovich, of the 1975 Nobel Memorial Prize in Economic Sciences. Koopmans' early works on the Hartree–Fock theory are associated with the Koopmans' theorem, which is very well known in quantum chemistry. Koopmans was awarded his Nobel prize (jointly with Leonid Kantorovich) for his contributions to the field of resource allocation, specifically the theory of optimal use of resources. The work for which the prize was awarded focused on activity analysis, the study of interactions between the inputs and outputs of production, and their relationship to economic efficiency and prices.*SAU

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