Friday 17 January 2020

On This Day in Math - January 17

*New Horizons. August 2001. Artwork commissioned for the New Horizons mission to Pluto. Pluto's horizon spans the foreground, looking past its moon, Charon, toward the distant, star-like Sun. Painting by Dan Durda...who learned some math, but not his art, from me.

Whenever you can, count.
~Sir Francis Galton

The 17th day of the year; there are 17 prime partitions of 17. No other number is equal to its number of prime partitions. (for example, 7 has 3 prime partitions, 7, 3+2+2, and 5+2)

And 17 is the ONLY PRIME that is equal to the sum of four consecutive primes, 17 = 2 + 3 + 5 + 7

If you write out the numbers from 1 to 5000 in English (e.g., THREE THOUSAND EIGHT HUNDRED SEVENTY-THREE), it turns out that 17 is the only one that has a unique number of characters (nine). (Spaces and hyphens count as characters) .

Also, 17 is the only prime that is equal to the sum of the digits of its cube,173= 4913 *Mario Livio ‏@Mario_Livio

With any number of points less than 17, it is possible to color all the segments between them with two colors without any triangle having all three sides of the same color. With 17 or more, it is not possible.

The sum of the squares of the first seven primes (all primes up to 17) is 666, the "Number of the Beast." \(2^2 + 3^2 + 5^2 + 7^2 + 11^2 + 13^2 + 17^2 = 666 \)

17 mph is an unusual speed limit, but on the campus of Hampshire College in Amherst all the speed limit signs have been changed from 15 to 17 miles per hour to honor retired mathematics professor David Kelly. Kelly spent his career fascinated by the number 17. There is at least two others in the US, at Mountain View, California and Fiesta Mall in Mesa, Az. For those interested, this site lists 17 (of course) interesting facts about 17 from the Professor.
David Kelly at Hampshire College *MSN.COM

1672 (OS) James Gregory writes to John Collins in praise of Jan Hudde.

“I am confident that Huddenius (Latinized version of Hudde’s name) is able to perform what he has promised, for his two epistles, in my opinion, go beyond all who ever did write in Algebra, yea, Cates himself not being excepted. “ 

The “two epistles” he mentions were probably the two papers in Von Schooten’s Geometrie (1659 - 1661) including his De maximus et minimas. *Correspondence of Scientific Men of the Seventeenth Century

photograph from Lowell Observatory
1910 The Great January Comet of 1910, formally designated C/1910 A1 and often referred to as the Daylight Comet appeared in January 1910. It was already visible to the naked eye when it was first noticed, and many people independently "discovered" the comet. At its brightest, it outshone the planet Venus, and was possibly the brightest comet of the 20th century. The first astronomer to properly study the comet was Robert T. A. Innes at the Transvaal Observatory in Johannesburg on January 17, after having been alerted two days earlier by the editor of a Johannesburg newspaper.
The comet reached perihelion on January 17 and was at that time visible in daylight with the unaided eye; following perihelion, it declined in brightness but became a spectacular sight from the northern hemisphere in the evening twilight, its noticeably curved tail reaching up to 50 degrees by early February.
Halley's comet returned on schedule a few months later. *Wik

1929 Edwin Hubble publishes his classic paper,"A relation between distance and radial velocity among extra-galactic nebulae", showing the universe is expanding in The Proceedings of The National Academy of Sciences. *David Dickinson@Astroguyz

1940 In the presence of Alan Turing, Polish Mathematician Marian Rejewski broke the Enigma code at PC Bruno a Polish intelligence station outside Paris. The Polish team had broken the Enigma code as early as 1932. The PC Bruno team collaborated by teleprinter with counterparts at Bletchley Park in England. For their mutual communications security, the Polish, French, and British cryptologic agencies used the Enigma machine itself. Bruno closed its Enigma-encrypted messages to Britain with an ironic "Heil Hitler!"*Wik, *Polish Embassy, UK

In 1949, for the first time, full energy was released by the first synchrotron which was installed at the Radiation Laboratory, University of California, Berkeley. It was invented by Edwin Mattison of the same university, and would accelerate electrons by virtue of their negative charges, using a betatron-type magnet that weighed about 8 tons. The synchrotron was constructed at the General Electric Research Laboratory at Schnectady, N.Y. by Dr. Herbert C. Pollock and Willem F. Westendorp. *TIS

1974 HP introduces the first programmable pocket calculator. The first desktop programmable calculators were produced in the mid-1960s by Mathatronics and Casio (AL-1000). These machines were, however, very heavy and expensive. The first programmable pocket calculator was the HP-65, in 1974; it had a capacity of 100 instructions, and could store and retrieve programs with a built-in magnetic card reader.Bill Hewlett's design requirement was that the calculator should fit in his shirt pocket. That is one reason for the tapered depth of the calculator. The magnetic program cards fed in at the thick end of the calculator under the LED display. The documentation for the programs in the calculator is very complete, including algorithms for hundreds of applications, including the solutions of differential equations, stock price estimation, statistics, and so forth.*Wik

1985 The last day for the card catalog at the New York Public Library. It contained 10 million dog-eared cards in 9,000 oak drawers. It was replaced by 800 bound volumes of photocopies of the cards and a computer catalog. *AP press release, 18 Jan 1985.

1996 Computer is Used in the Discovery of New Planets. Paul Butler and Geoffrey Marcy announced to the American Astronomical Society that they had discovered two new planets using an unconventional computer technique to analyze the movement of stars. Butler and Marcy let computers analyze spectrographic images of stars for eight years, looking for shifts in the light that would imply it is being pulled by the gravity of a planet. The first discovery, a planet orbiting the star 47 Ursae Majoris​, was announced in December 1995 and, since then, this team found 12 planets outside of our solar system.*CHM


1574 Robert Fludd, also known as Robertus de Fluctibus (17 January 1574; Bearsted, Kent, UK – 8 September 1637; London, UK), was a prominent English Paracelsian physician. He is remembered as an astrologer, mathematician, cosmologist, Qabalist and Rosicrucian apologist. He is credited by some with the invention of the thermometer (others credit Cornelis Drebbel, Galileo Galilei or Santorio Santorio).
Fludd is best known for his compilations in occult philosophy. He had a celebrated exchange of views with Johannes Kepler concerning the scientific and hermetic approaches to knowledge.
Between 1598 and 1604, Fludd studied medicine, chemistry and hermeticism on the European mainland. His itinerary is not known in detail. On his own account he spent a winter in the Pyrenees studying theurgy with the Jesuits.
On his return to England, Fludd entered Christ Church, Oxford. In 1605 he graduated M.B. and M.D. He then moved to London, settling in Fenchurch Street, and making repeated attempts to enter the College of Physicians. Fludd encountered problems with the College examiners, both because of his unconcealed contempt for traditional medical authorities, and because of his attitude. After at least six failures, he was admitted in 1609. Subsequently both his career and his standing in the College took a turn very much for the better. He was on good terms with Sir William Paddy. Fludd was one of the first to support in print the theory of the circulation of the blood of the College's William Harvey. To what extent Fludd may have actually influenced Harvey is still debated, in the context that Harvey's discovery is hard to date precisely. The term "circulation" was certainly ambiguous at that time
Fludd's works are mainly controversial. In succession he defended the Rosicrucians against Andreas Libavius, debated with Kepler (claiming the hermetic or "chemical" approach is deeper than the mathematical), argued against French natural philosophers including Gassendi and Mersenne, and engaged in the discussion of the weapon-salve, a form of sympathetic magic, current in the 17th century in Europe, whereby a remedy was applied to the weapon that had caused a wound in the hope of healing the injury it had made. (I suspect much of the success was having the doctors focus on the weapon rather than infecting the wounded body). *Wik

1624 Guarino Guarini (17 Jan 1624; 6 Mar 1683) Italian architect and theologian whose study of
mathematics led him to a career in architecture in which he created the most fantastic geometric elaboration of all baroque churches. In his Santissima Sindone, Guarini created a diaphanous dome - a geometrical optical illusion in the dome made through the use of the actual structure which creates the illusion that the dome recedes farther up into space than it really does. He wrote two architectural treatises and other works that concentrate on his mathematical knowledge. Therein, Guarini discusses Desargue's projective geometry, which reveal a scientific basis for his daring structures. He worked primarily in Turin and Sicily, with his influence stretching into Germany, Austria and Bohemia.*TIS

1647 Elisabeth Catherina Koopmann Hevelius (in Polish also called Elżbieta Heweliusz) (17 Jan 1647 in Danzig, now Gdańsk, Poland - Died: 22 Dec 1693 in Danzig, now Gdańsk, Poland) was the second wife of Johannes Hevelius. Like her husband, she was also an astronomer.
The marriage of the sixteen year old to fifty two year old Hevelius in 1663 allowed her also to pursue her own interest in astronomy by helping him manage his observatory. They had a son, who died soon, and three daughters who survived. Following his death in 1687, she completed and published Prodromus astronomiae (1690), their jointly compiled catalogue of 1,564 stars and their positions.
She is considered one of the first female astronomers, and called "the mother of moon charts". Her life was recently novelized as The Star Huntress (2006).
The minor planet 12625 Koopman is named in her honour, as is the crater Corpman on Venus. *Wik

1706 Benjamin Franklin, (17 Jan 1706; 17 Apr 1790) American scientist. When he observed a balloon launch by the Montgolfier brothers he was asked of what use it was. He replied: Of what use is a new born baby? *VFR
While traveling on a ship, Franklin had observed that the wake of a ship was diminished when the cooks scuttled their greasy water. He studied the effects at Clapham common on a large pond there. "I fetched out a cruet of oil and dropt a little of it on the water...though not more than a teaspoon full, produced an instant calm over a space of several yards square." He later used the trick to "calm the waters" by carrying "a little oil in the hollow joint of my cane." *W. Gratzer, Eurekas and Euphorias, pgs 80,81
American printer and publisher, author, inventor and scientist, and diplomat. He become widely known in European scientific circles for his reports of electrical experiments and theories. He invented a type of stove, still being manufactured, to give more warmth than open fireplaces and the lightning rod, bifocal eyeglasses also were his ideas. Grasping the fact that by united effort a community may have amenities which only the wealthy few can get for themselves, he helped establish institutions people now take for granted: a fire company (1736), a library (1731), an insurance company (1752), an academy (1751), and a hospital (1751). In some cases these foundations were the first of their kind in North America. *TIS

1858 Gabriel Xavier Paul Koenigs (17 January 1858 Toulouse, France – 29 October 1931 Paris, France) was a French mathematician who worked on analysis and geometry. He was elected as Secretary General of the Executive Committee of the International Mathematical Union after the first world war, and used his position to exclude countries with whom France had been at war from the mathematical congresses.*Wik

1868 Louis Couturat (17 Jan 1868 in Ris-Orangis (near Paris), France - 3 Aug 1914 in Between Ris-Orangis and Melun, France), a logician whose historical researches led to the publication of Leibniz’s logical works in 1903.*VFR Couturat was killed in a car accident, his car being hit by the car carrying the orders for mobilization of the French army the day World War I broke out. Ironically he was a noted pacifist. *SAU

1889 Sir Ralph Howard Fowler (17 Jan 1889; 28 Jul 1944) was an English physicist and astronomer whose university education in mathematics led him to working on thermodynamics and statistical mechanics with important applications in physical chemistry. Turning to astronomy, he collaborated with Arthur Milne on the spectra of stars, and their temperatures, and pressures. He also worked on the statistical mechanics of white dwarf stars (1926) with P.A.M. Dirac, whom he had introduced to quantum theory. Fowler proposed that white dwarf stars consist of a degenerate gas of extremely high density. *TIS In 1921 he married Eileen Mary (1901–1930), the only daughter of Ernest Rutherford. They had four children, two sons and two daughters. Eileen died after the birth of their last child. One of his grandchildren is Mary Fowler, a geologist and current Master of Darwin College, Cambridge

1905 Dattaraya Ramchandra Kaprekar (17 Jan 1905 in Dahanu, India - Died: 1986 in Devlali, India) was an Indian mathematician who discovered several results in number theory, including a class of numbers and a constant named after him. Despite having no formal postgraduate training and working as a schoolteacher, he published extensively and became well-known in recreational mathematics circles. A Kaprekar number is a positive integer with the property that if it is squared, then its representation can be partitioned into two positive integer parts whose sum is equal to the original number (e.g. 45, since 452=2025, and 20+25=45, also 9, 55, 99 etc.) However, note the restriction that the two numbers are positive; for example, 100 is not a Kaprekar number even though 1002=10000, and 100+00 = 100. This operation, of taking the rightmost digits of a square, and adding it to the integer formed by the leftmost digits, is known as the Kaprekar operation.*Wik

1913 Shaun Wylie (17 January 1913 – 2 October 2009) was a British mathematician and World War II codebreaker. *Wik


1618 Luca Valerio (1552 in Naples, Italy - 17 Jan 1618 in Rome, Italy) was an Italian mathematician who applied methods of Archimedes to find volumes and centres of gravity of solid bodies. He corresponded with Galileo.*SAU

1670 Jean Leurechon (1591 – 17, Jan 1670) was a French Jesuit priest and mathematician. He often wrote under the pseudonym Hendrik van Etten.He was born in 1591 in Bar le Duc, and died  in Pont-à-Mousson.
At the age of 18, he entered the Jesuit college of Tournai in Belgium.
He joined the priesthood in 1624. In 1629, he became the rector of a college. He was a professor of theology for two years.
His most famous work is the Récréations Mathématiques written under the pseudonym Hendrik van Etten. The book is a collection of recreational mathematical puzzles. The book made him famous all over Europe. Math Historian Albrecht Heeffer has studied the book extensively and believers it was Not Leurechon, but Jean Appier dit Hanelett, a printer who wrote the book. He has also stated that he believes it is the first math book with the word "recreations" in the title.

Much of the mathematical content centers around Claude Bachet's problems and may have been copied from it or some common source. The book also gives the earliest known description of the operation of an ear trumpet and a very early description of the thermometer, which at the time was less than 30 years in existence.
Leurechon may well have created the term "thermometre" which he used in 1626. It made it's way into English through the translations of his work by William Oughtred.
His book led (indirectly) to the common belief that the instrument was "invented by a North Hollander peasant named Drebble. When Caspar Ens copied the problem from Leurechon's book, he inserted the adjective "Drebbvenanum" in front of the word instrument. This was repeated in Journal des sçavans (renamed Journal des savants) and became accepted as a popular truth.

A new edition is available on Amazon

1675 Bernard Frénicle de Bessy (c. 1605 in Paris, France - 17 Jan 1675 in Paris, France), wrote numerous mathematical papers, mainly in number theory and combinatorics. He is best remembered for Des quarrez ou tables magiques, a treatise on magic squares published posthumously in 1693, in which he described all 880 essentially different normal magic squares of order 4. The Frénicle standard form, a standard representation of magic squares, is named after him. He solved many problems created by Fermat and also discovered the cube property of the number 1729, later referred to as a taxicab number.(see "Births" 22 Dec,1887 )
Like Fermat, Frénicle was an amateur mathematician, but he still corresponded with the likes of Descartes, Huygens, Mersenne and also Fermat, who was his personal friend. His major contributions were in number theory.

He challenged Christiaan Huygens​ to solve the following system of equations in integers,

x2 + y2 = z2, x2 = u2 + v2, x − y = u − v.

A solution was given by Théophile Pépin in 1880.
In 1973, he was posthumously recognized by the American Mathematical Society for his work in structural combinatorics *Wik

1775 Vincenzo Riccati (Castelfranco Veneto, 11 January 1707 – Treviso, 17 January 1775) was an Italian mathematician and physicist. He was the brother of Giordano Riccati, and the second son of Jacopo Riccati.
Riccati's main research continued the work of his father in mathematical analysis, especially in the fields of the differential equations and physics. The Riccati equation is named after his father.*Wik

1910 Friedrich Wilhelm Georg Kohlrausch (14 Oct 1840, 17 Jan 1910)German physicist who investigated the properties of electrolytes (substances that conduct electricity in solutions by transfer of ions) and contributed to the understanding of their behaviour. Some of Kohlrausch's pioneering achievements include conductivity measurements on electrolytes, his work on the determination of basic magnetic and electrical quantities, and the enhancement of the associated measuring technologies. It was under his direction that the "Physikalisch-Technische Reichsanstalt" (the then Imperial Physical Technical Institute in Germany) created numerous standards and calibration standards which were also used internationally outside Germany.*TIS

1911 Sir Francis Galton (16 Feb 1822, 17 Jan 1911) English scientist, founder of eugenics, statistician and investigator of intellectual ability. He explored in south-western Africa. In meteorology, he was first to recognise and name the anticyclone. He interpreted the theory of evolution of (his cousin) Charles Darwin to imply inheritance of talent could be manipulated. Galton had a long-term interest in eugenics - a word he coined for scientifically selected parenthood to enable inheritance of beneficial characteristics. He coined the phrase "nature versus nurture." Galton experimentally verified the uniqueness of fingerprints, and suggested the first classification based on grouping the patterns into arches, loops, and whorls. On 1 Apr 1875, he published the first newspaper weather map - in The Times *TIS

1954 Leonard Eugene Dickson (22 Jan 1874,Independence, Iowa, 17 Jan 1954, Harlingen, Texas)American mathematician who made important contributions to the theory of numbers and the theory of groups. He published 18 books including Linear groups with an exposition of the Galois field theory. The 3-volume History of the Theory of Numbers (1919-23) is another famous work still much consulted today. *TIS

1997 Clyde William Tombaugh (4 Feb 1906 on Ranch near Streator, Illinois, 17 Jan 1997) was an American astronomer who discovered what was then recognized as the planet Pluto, which he photographed on 23 Jan 1930, the only planet discovered in the twentieth century, after a systematic search instigated by the predictions of other astronomers. Tombaugh was 24 years of age when he made this discovery at Lowell Observatory in Flagstaff, Ariz. He also discovered several clusters of stars and galaxies, studied the apparent distribution of extragalactic nebulae, and made observations of the surfaces of Mars, Venus, Jupiter, Saturn, and the Moon.Born of poor farmers, his first telescope was made of parts from worn-out farming equipment. *TIS
From my personal blog after a visit to Mars Hill, Flagstaff, Az. (much material from Wikipedia)
In the late 19th and early 20th century, observers of Mars drew long straight lines that appeared on the surface between 60 degrees north and south of the martian equator. Italian astronomer Giovanni Schiaparelli called these lines canali, which became canals in English. Lowell extended this observation to a theory that Mars had polar ice caps that would melt in the martian spring and fill the canals. He even extended the theory to include intelligent life on Mars that had designed the canals.
Eventually it became clear that there were no martian canals, but Mars hill went on to be the sight where a self educated Kansas schoolboy found his dream of working in astronomy in 1929, when the observatory director, V M Slipher, "handed the job of locating Planet X to Clyde Tombaugh, a 23-year-old Kansas man who had just arrived at the Lowell Observatory after Slipher had been impressed by a sample of his astronomical drawings."
On the nights of Jan 23 and 30th of January, 1930, he found a planet in the images that he thought was the Planet X. "The discovery made front page news around the world. The Lowell Observatory, who had the right to name the new object, received over 1000 suggestions, from "Atlas" to "Zymal". Tombaugh urged Slipher to suggest a name for the new object quickly before someone else did. Name suggestions poured in from all over the world. Constance Lowell proposed Zeus, then Lowell, and finally her own first name. These suggestions were disregarded.
The name "Pluto" was proposed by Venetia Burney (later Venetia Phair), an eleven-year-old schoolgirl in Oxford, England. Venetia was interested in classical mythology as well as astronomy, and considered the name, one of the alternate names of Hades, the Greek god of the Underworld, appropriate for such a presumably dark and cold world. She suggested it in a conversation with her grandfather Falconer Madan, a former librarian of Oxford University's Bodleian Library. Madan passed the name to Professor Herbert Hall Turner, who then cabled it to colleagues in America. The object was officially named on March 24, 1930."
Among the many awards Tombaugh received was a scholarship to the Univ of Kansas, where he would eventually earn a Bachelors and Masters Degree. It is said that the Astronomy Dept head refused to allow him to take the introductory astronomy class because it would be undignified for the discoverer of a planet.

When New Horizons rocketed away from Cape Canaveral on Jan. 19, 2006, Pluto was the ninth planet in our solar system. It was demoted to dwarf planet a scant seven months later.
Tombaugh's widow and two children offered up an ounce of his ashes for the journey to Pluto. The ashes of the farm boy-turned-astronomer are in a 2-inch aluminum capsule inscribed with these words:

"Interned herein are remains of American Clyde W. Tombaugh, discoverer of Pluto and the solar system's 'third zone.' Adelle and Muron's boy, Patricia's husband, Annette and Alden's father, astronomer, teacher, punster, and friend: Clyde Tombaugh (1906-1997)"

2000 Eugène Ehrhart (29 April 1906 Guebwiller – 17 January 2000 Strasbourg) was a French mathematician who introduced Ehrhart polynomials in the 1960s. Ehrhart received his high school diploma at the age of 22. He was a mathematics teacher in several high schools, and did mathematics research on his own time. He started publishing in mathematics in his 40s, and finished his PhD thesis at the age of 60. The theory of Ehrhart polynomials can be seen as a higher-dimensional generalization of Pick's theorem. *Wik

Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell

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