Euler calculated without effort,
just as men breathe,
as eagles sustain themselves in the air.
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.
57 letters and spaces (not counting commas) are required to write the famous prime number 6700417 in English. The number was one of the factors of \(F(5)=2^{2^5}+1 \) Fermat had conjectured that all such "Fermat Numbers" were prime. In 1732, Euler showed that F(5) was the product or 641 times 6700417. Euler never stated that both numbers were prime, and historians still disagree about whether he knew, or even suspected, that it was.
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
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| Costa San Giorgio, near Ponte Vecchio ... |
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
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 .
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| Gauss' Headstone *Wik |
After posting this, I was informed by *Keenan Patterson that "William Burroughs lived in St. Louis when he designed his calculating machine. His namesake grandson was a novelist ." And Thony Christie sites the younger as " one of the great authors of the second half of the twentieth century "
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 The Image of Becquerel's photographic plate which has been fogged by exposure to radiation from a uranium salt. The shadow of a metal Maltese Cross placed between the plate and the uranium salt is clearly visible.*Wik
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 The Image of Becquerel's photographic plate which has been fogged by exposure to radiation from a uranium salt. The shadow of a metal Maltese Cross placed between the plate and the uranium salt is clearly visible.*Wik
*Wik
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
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| *Wik |
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
As happens with records, after over a decade their had record remained unassailable. But a team of three paper airplane experts worked together to take a shot at the title, and on April 16, 2022, Kim Kyu Tae threw a paper glider 252 feet and 7 inches (77.134 meters), utterly shattering the record that stood for so long. (They said they had done much better in practices, and warned of more to come.)
BIRTHS
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
The "Flammarion engraving" first appeared in Flammarion's 1888 edition of L’Atmosphère. In 1907, he wrote that he believed that dwellers on Mars had tried to communicate with Earth in the past. He also believed in 1907 that a seven-tailed comet was heading toward Earth. In 1910, for the appearance of Halley's Comet, he was widely but falsely reported as believing the gas from the comet's tail "would impregnate [the Earth’s] atmosphere and possibly snuff out all life on the planet".
In 1862 he published his first book, The Plurality of Inhabited Worlds, and was dismissed from his position at the Paris Observatory later the same year. It is not quite clear if these two incidents are related to each other.
La Fin du Monde (The End of the World), 1893 (translated into English as Omega: The Last Days of the World in 1894), is a science fiction novel about a comet colliding with the Earth, followed by several million years leading up to the gradual death of the planet, and has recently been brought back into print. It was adapted into a film in 1931 by Abel Gance.
George Gamow cited Flammarion as having had a significant influence on his childhood interest in science.
A traveller puts his head under the edge of the firmament in the original (1888) printing of the Flammarion wood engraving. And below "Telefonoscope" from his La Fin du Monde, 1894. A telephonoscope was an early concept of videophone and television, conceptualized in the late 1870s through the 1890s. It was mentioned in various early science fiction works
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 surfaces. 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
The Indian Institute of Astrophysics commemorated the discovery with an international conference entitled 'Magnetic Coupling between the Interior and the Atmosphere of the Sun', during Dec 2-5, 2008. To mark the discovery, a commemorative stamp and a first day cover on the Evershed Effect were released in a special function at the Institute on Dec 2, 2008 by Shri M P Rajan, Chief Post Master General, Karnataka.
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 (Let a and b be integers with greatest common divisor d. Then there exist integers x and y such that ax + by = d. ).Title page of the 1621 edition of Diophantus' Arithmetica, translated into Latin by Claude Gaspard Bachet de Méziriac.
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.
While at Cambridge, Scarburgh became acquainted with Seth Ward (1617–1689), who shared his interest in mathematics. Ward would later go on to become the Savilian Professor of Astronomy at Oxford, as well as the Bishop of Exeter. Both Ward and Scarburgh taught mathematics classes, and one mathematics textbook that we know they both used was Clavis mathematicae (The Key to Mathematics), first published in 1631 by William Oughtred , who was perhaps most famous for constructing the first slide rule. Clavis mathematicae was written while Oughtred was serving as the tutor to the son of a nobleman, and it included algorithms and problem solving in arithmetic, algebra and geometry
In order to ask questions about the text, Ward and Scarburgh actually visited Oughtred in Albury, which is located southwest of London and about 100 miles from Cambridge. Oughtred mentioned both of them in the 1652 edition of his work, and he particularly praised Scarburgh’s skill in mathematics as well as his mastery of the work of Euclid and Archimedes.
The relationship between Oughtred and Scarburgh continued throughout their lives, and Scarburgh completed the posthumous revision and publication of Oughtred’s remaining papers in a single volume in 1676. While these last manuscripts were not considered to be major works, Oughtred still must have had a high opinion of Scarburgh’s scholarship to entrust him with the task
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
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
On this day in 1765, Nevil Maskelyne was appointed the fifth Astronomer Royal to succeed Nathaniel Bliss who had only held the post for two years. Bliss was successor to Edmund Halley in the position.
Bliss studied at Oxford University and later became the Savilian Professor of Geometry. He made important meridian observations of a comet and a solar eclipse visible from Greenwich, and many of his observations proved useful in solving the longitude problem, and were bought by the Board of Longitude after his death. *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
2017 Ludvig Dmitrievich Faddeev ( 23 March 1934 – 26 February 2017) was a Soviet and Russian mathematical physicist. He is known for the discovery of the Faddeev equations in the quantum-mechanical three-body problem and for the development of path-integral methods in the quantization of non-abelian gauge field theories, including the introduction of the Faddeev–Popov ghosts (with Victor Popov). He led the Leningrad School, in which he along with many of his students developed the quantum inverse scattering method for studying quantum integrable systems in one space and one time dimension. This work led to the invention of quantum groups by Drinfeld and Jimbo.
Faddeev was born in Leningrad to a family of mathematicians. His father, Dmitry Faddeev, was a well-known algebraist, professor of Leningrad University and member of the Russian Academy of Sciences. His mother, Vera Faddeeva,(20 Sept, 1906 - 15 April, 1983) was known for her work in numerical linear algebra. Faddeev attended Leningrad University, receiving his undergraduate degree in 1956. He enrolled in physics, rather than mathematics, "to be independent of [his] father". Nevertheless, he received a solid education in mathematics as well "due to the influence of V. A. Fock and V. I. Smirnov". His doctoral work on scattering theory was completed in 1959 under the direction of Olga Ladyzhenskaya
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
