## Saturday 10 February 2024

### On This Day in Math - February 10

 Newton First Day Cover *BFDC.co.uk

It is impossible to be a mathematician without being a poet in soul.

~Sofya Kovalevskaya

The 41st day of the year; Euler (1772) observed that the polynomial f(x)= x2 + x + 41 will produce a prime for any integer value of x in the interval 0 to 39. In 1778 Legendre realized that x2 - x + 41 will give the same primes for interval (1-40).
n^2 + n + 41 is prime for n = 0 ... 39 and Is prime for nearly half the values of n up to 10,000,000. *John D. Cook

If you multiply 41 by any three digit number to produce a five digit number, every cyclic representation of that number formed by moving the last digit to the front is also divisible by 41. (for example 41*378 = 15,498. 41 will also divide 81,549; 98154; 49815; and 54,981 *The Moscow Puzzles
41 can be expressed as the sum of consecutive primes in two ways, (2 + 3 + 5 + 7 + 11 + 13), and the  (11 + 13 + 17).

41 is the smallest integer whose reciprocal has a 5-digit repeating decimal.  $\frac{1}{41} = \overline{.02439}$

And even more from @Math Year-Round 41=1!+2!+3!+1¹+2²+3³

Found this on Twitter(X) by Abakcus

The Expanded Number Facts collection for year days 1-60 are now available here

EVENTS

1676/7 “The truth of it is, mathematical learning will not go off without a dowry; the booksellers have lost so much by the works of Drs. Wallis and ... Barrow ... that it is no easy task to persuade booksellers to undertake any thing but toys that are mathematical.” [Collins to Baker, The Correspondence of Isaac Newton, Vol. 2, p. 192]

In 1720, Edmund Halley was appointed second Astronomer Royal of England. Halley succeeded John Flamsteed as Astronomer Royal, a position he would hold until his death in 1742 at the age of 85. *Wik  On the 300th anniversary of his trip to St Helena, the island issued three stamps. The 5p value shows Halley’s comet as it appeared on the Bayeux Tapestry.

Flamsteed may still be spinning in his grave over the choice.  John Flamsteed revealed his irritation with the choice of Edmond Halley as successor to Wallis as the Savilian Professor of Geometry. In a letter to Abraham Sharpe he wrote:-

Dr Wallis is dead – Mr Halley expects his place – who now talks, swears and drinks brandy like a sea-captain.

1734 The Marquise de Chatelet writes to ask Maupertuis to explain his claim in a 1732 paper that "God preferred the inverse square law of attraction over all others." Apparently he failed to convince her. *J. B. Shank, The Newton Wars and the Beginning of the French Enlightenment

1747  "On the acceptance of trigonometry in wasan: Evidence from a text of Aida Yasuaki" [Born 10 February 1747 Yamagata, Japan ]  J. Marshall Unger; Historia Mathematica Volume 52, August 2020, Pages 51-65  .  Wasan, or wanska was a term used for great mathematicians of the 18th and 19th century.  their geometric methods avoided the use of trigonometry tables.

The diagonals of a cyclic quadrilateral divide it into four non-overlapping quarter-triangles and its circumcircle into four skewed sectors.1 Each quarter-triangle and each skewed sector has an incircle. Japanese mathematicians of the 18th and 19th centuries (wasanka) discovered how to find the radius of the circumcircle given the radii of the incircles either of the four quarter-triangles or of the four skewed-sectors.

"Aida was hard-working and strong-willed and produced as many as fifty to sixty works a year. Nearly 2000 works survived him, including many on non-mathematical subjects. He was a distinguished teacher of traditional mathematics and a successful populariser of that discipline."

*mathshistory.st-andrews

1860 Joseph Toynbee (English otologist, whose career was dedicated to pathological and anatomical studies of the ear.) writes to ask Faraday for tickets to Thomas Henry Huxley's lecture.

18 Savile Row. Burlington Gardens. W | 10 Feb 1860

Having been unsuccessful in my attempts to obtain a ticket for Mr. Huxley’s lecture tonight I shall esteem it a favour if you can give me one.

Believe me yours sincerely ; obliged,

Joseph Toynbee

*JAIPREET VIRDI, From the Hands of Quacks

WEEKLY EVENING MEETING,

Friday, February 10, 1860.

SIR HENRY HOLLAND, BART. M.D. F.R.S. Vice-President,

in the Chair.

PROFESSOR T. H. HUXLEY, F.R.S.

On Species and Races, and their origin.

The speaker opened his discourse by stating that its object was to place the fundamental propositions of Mr. Darwin's work "On the Origin of Species by Natural Selection," in a clear light, and to consider whether, as the question at present stands, the evidence adduced in their favour is, or is not, conclusive.

1860  Published #OTD 1860 by the Linnean Society, Alfred Russel Wallace's  paper : "On the Zoological Geography of the Malay Archipelago". The paper having been communicated on his behalf by Charles Darwin to the Society on 3/11/1859.

1880 On 10 February 1880, an article ran in the Daily Times (of Bethlehem, Pennsylvania) describing a remarkable invention recently demonstrated by a local inventor, Dr. H.E. Licks. The invention allowed images to be transmitted by telegraph. In other words, it resembled what people today would recognize as a television. However, Licks called his invention a "diaphote," from the Greek dia meaning "through" and photos meaning "light".
Despite the excitement it generated, the diaphote turned out to be a hoax. However, it wasn't until 1917 that "Dr. H.E. Licks" revealed the hoax in a book, Recreations in Mathematics. Licks himself is believed to have been the pseudonym of Mansfield Merriman (1848-1925), a professor of engineering at Lehigh University. *Museum of Hoaxes

He published Recreations in Mathematics in 1917 (a wonderful book) under the pseudonym H. E. Licks, which included a story, "The Diaphote Hoax", a republication of a detailed newspaper report from February 10, 1880 which purported to describe the scientific demonstration of a device that transmitted images by electricity. The report is peppered throughout with scientific jokes including mentions of "Dr. H. E. Licks" ('helix'), "Prof. M. E. Kannick" ('mechanic'), "Col. A. D. A. Biatic" ('adiabatic'), and "Prof. L. M. Niscate" ('lemniscate').

1914 The Girl Scout’s patent the trefoil design for their membership badge. The badge was designed by the founder of Girl Guides (renamed in 1913), Juliette "Daisy" Gordon Low who began the program in Savannah, Ga. with a group of 18. This (2012) is the centennial year of the Girl Scouts. The organization has declared 2012 the "Year of the Girl", and the Smithsonian's National Portrait Gallery opened a year-long exhibit "Juliette Gordon Low and 100 Years of Girl Scouts" on January 13, 2012.*Wik

 Juliette Gordon Low in 1887 *Wik

1946 War Department revealed the development of ENIAC, an electronic numerical integrator and computer. It is 1000 times faster than human computation. *VFR

In 1958, radar signals were bounced off the planet Venus by MIT engineers at Lincoln Laboratories in experiments conducted during an inferior conjunction with Venus. A maser installed at the Millstone Hill radar site, Westford, Mass., was used. The return echoes were distinguished from the background noise using digital signal processing. The results were confirmation by other researchers, and together led to a more precise determination of the value of the astronomical unit (AU), the Earth's mean distance to the sun. A new value of the AU, 149,600,000 km was adopted at a general meeting of the International Astronomical Union in Hamburg (1964). Radar was also bounced off the Sun (7 Apr 1959). Lincoln Laboratories had been set up to conduct military rather than astronomical research.*TIS

1996 Deep Blue defeats Kasparov
In the first game of a six game match, IBM's Deep Blue chess computer defeated world champion Garry Kasparov. No computer had ever won a game against a world champion in chess. Kasparov would eventually win the series 4-2, but would lose to Deep Blue in a re-match a year later.*CHM

2012 2/10/2012 is a palindrome, and even if it's written 2/10/12. Or even in Roman numerals II/X/MMXII. What other years may be expressed as palindromes in two of these three methods (or European date style, dd/mm/yy  4/10/2014 works with or without the 20, ... 41014.  And April 20, 2024 (4202024) or (42024) does as well.

BIRTHS

1747 Aida Yasuaki (February 10, 1747 – October 26, 1817) Japanese mathematician who published about 2000 works. Aida compiled Sampo tensi shinan which appeared in 1788. It is a book of geometry problems, developing formulae for ellipses, spheres, circles etc. Aida explained the use of algebraic expressions and the construction of equations. He also worked on number theory and simplified continued fraction methods due to Seki. *SAU

1785 Claude Louis Marie Henri Navier (10 Feb 1785 in Dijon, France - 21 Aug 1836 in Paris, France) Claude-Louis Navier was a French mathematician best known for the Navier-Stokes equations describing the behaviour of a incompressible fluid. We should note, however, that Navier derived the Navier-Stokes equations despite not fully understanding the physics of the situation which he was modelling. He did not understand about shear stress in a fluid, but rather he based his work on modifying Euler's equations to take into account forces between the molecules in the fluid. Although his reasoning is unacceptable today. *SAU

1811 Jean-Laurent Palmer, a French metal worker and instrument maker ran a workshop in Paris that produced drawn wire and seamless metal tubes, and he apparently needed an instrument to measure wire diameter and the thickness of sheet stock and tube walls. In 1848, he produced the instrument illustrated in our first image: a screw micrometer. The idea for a micrometer – an instrument that measures distance or thickness by counting the turns of a screw – was 180 years old, and calipers were far older, but no one had ever combined the two into a single hand-held tool. Palmer's micrometer had two numerical scales--one to count the screw turns, and another to measure fractions of a turn. Since the threads were 1 mm apart, and since the fractional scale was divided into 20 parts, that means Palmers' instrument could measure thickness to an accuracy of .05 mm, and with a Vernier scale that could be reduced to .01 mm – one hundred-thousandth of a meter.  Impressive for such a simple instrument. *Linda Hall Org

1885 Hardy Cross (10 Feb 1885; died 11 Feb 1959 at age 73) U.S. professor of civil and structural engineering whose outstanding contribution was a method of calculating tendencies to produce motion (moments) in the members of a continuous framework, such as the skeleton of a building. By the use of Cross's technique, known as the moment distribution method, or simply the Hardy Cross method, calculation can be carried to any required degree of accuracy by successive approximations, thus avoiding the immense labour of solving simultaneous equations that contain as many variables as there are rigid joints in a frame. He also successfully applied his mathematical methods to the solution of pipe network problems that arise in municipal water supply design; these methods have been extended to gas pipelines.
*TIS

1888 Selig Brodetsky (10 February 1888 - 20 May 1954)was educated at Cambridge and Leipzig. He became a lecturer at Bristol and later lecturer and professor at Leeds. He worked on fluid flow with particular emphasis on aerodynamics. He was President of the Hebrew University of Jerusalem for a short time. *SAU

1901 Richard Dagobert Brauer (10 Feb 1901; 17 Apr 1977 at age 76) German-American mathematician and educator, a pioneer in the development of algebra theory. He worked with Weyl on several projects including a famous joint paper on spinors (published in 1935 in the American Journal of Mathematics). This work provided a background for Paul Dirac's theory of the spinning electron within the framework of quantum mechanics. With Nesbitt, Brauer introduced the theory of blocks (1937). Brauer used this to obtain results on finite groups, particularly finite simple groups, and the theory of blocks would play a big part in much of Brauer's later work. Starting with his group-theoretical characterisation of the simple groups (1951), he spent the rest of his life formulating a method to classify all finite simple groups. *TIS

 Richard and Ilse Brauer in 1970 *Wik

1907 Agnes Mary Clerke (10 Feb 1842, 20 Jan 1907) Irish astronomical writer who was a diligent compiler of facts rather than a practicing scientist. Nevertheless, by 1885, her exhaustive treatise, A Popular History of Astronomy in the Nineteenth Century gained international recognition as an authoritative work. In 1903, with Lady Huggins, she was elected an honorary member of the Royal Astronomical Society, a rank previously held only by two other women, Caroline Herschel and Mary Somerville. Her publications included several books and 55 pieces in the Edinburgh Review. She contributed some astronomer biographies to the Dictionary of National Biography and some astronomical entries in the Encyclopaedia Britannica. *TIS More detail about her here

DEATHS

1576 Wilhelm Xylander (born Wilhelm Holtzman, graecized to Xylander) (December 26, 1532 – February 10, 1576) was a German classical scholar and humanist.
Xylander was the author of a number of important works. He translated the first six books of Euclid into German with notes, the Arithmetica of Diophantus, and the De quattuor mathematicis scientiis of Michael Psellus into Latin. *Wik

1865 Heinrich Friedrich Emil Lenz (24 Feb 1804, 10 Feb 1865 at age 61) was the Russian physicist who framed Lenz's Law to describe the direction of flow of electric current generated by a wire moving through a magnetic field. Lenz worked on electrical conduction and electromagnetism. In 1833 he reported investigations into the way electrical resistance changes with temperature, showing that an increase in temperature increases the resistance (for a metal). He is best-known for Lenz's law, which he discovered in 1834 while investigating magnetic induction. It states that the current induced by a change flows so as to oppose the effect producing the change. Lenz's law is a consequence of the, more general, law of conservation of energy. *TIS

1868 Sir David Brewster (11 Dec 1781; 10 Feb 1868) Scottish physicist noted for his experimental work in optics and polarized light (light in which all waves lie in the same plane.) He is known for Brewster's Law, which relates the refractive index of a material to its polarizing angle (which is the incident angle at which reflected light becomes completely polarized. He patented the kaleidoscope in 1817. Later, he used lenses to improve three-dimensional images viewed with a stereoscope. Brewster also recommended the use of the lightweight, flat Fresnel lens in lighthouses.*TIS

The first biography of Newton was written by John Conduit, his step-nephew-in-law, if that is a viable term. Conduit inherited all of Newton's papers that the other heirs did not want, but if he used them to write his biography, it does not show, for the Newton who emerges from his pages is brilliant, devout, humble, friendly, caring, and devoted to physics and God. However, in the early 19th century, some of Newton’s correspondence was brought to light by a French physicist, Jean-Baptiste Biot, who published a short biography of Newton in 1822, in which he revealed that Newton had gone mad in 1693, suffering a mental breakdown from which he never recovered. Biot maintained that after his psychotic episode, Newton could no longer do physics, and that is when he found religion. His Christian faith, in other words, developed only when his mind had weakened and could no longer handle more important matters.

When Biot’s account was translated into English in 1829, British scientists, who worshipped Newton as the greatest genius of all time, got quite a jolt. The British had little use for the French, who had recently inflicted Napoleon on the world, but this was going too far. It was Brewster who took it upon himself to defend his countryman from Gallic slurs, and he published his own short biography, The Life of Isaac Newton in 1831 (first image). Brewster was not a historian, and he did not have access to Newton's papers (they were owned by the Portsmouth family, who refused all requests for access), and so Brewster’s Newton was a reincarnation of Conduit's, a perfect human being in nearly every way, and the psychotic episode of 1693 was treated as just a minor event, the kind of thing that happens to geniuses now and then, when they have to deal with ordinary mortals. Newton had been restored to the ranks of the superhuman.*Linda Hall Org

1891 Sonya Kovalevsky (Sofya Vasilyevna Kovalevskaya) (15 Jan 1850; 10 Feb 1891) professor of mathematics at Stockholm. In her youth, her bedroom was wallpapered with the pages of a text from her father’s schooldays, namely, Ostrogradsky’s lithographed lecture notes on the calculus. Study of the novel wallpaper introduced her to the calculus at age 11. She became the greatest woman mathematician prior to the twentieth century. *VFR a Russian mathematician and novelist who made valuable contributions to the theory of differential equations.*TIS She died of influenza in 1891 at age forty-one, after returning from a pleasure trip to Genoa. She is buried in Solna(Stockholm suburb), Sweden, at Norra begravningsplatsen (Northern Cemetery). Alfred Nobel is buried in the same cemetery.

Kovalevskaya at 18 years

 *Wik

1923 Wilhelm Conrad Röntgen (27 Mar 1845 - 10 Feb 1923 at age 77) was a German physicist who discovered the highly penetrating form of radiation that became known as X-rays on 8 Nov 1895. He received the first Nobel Prize for Physics (1901), “in recognition of the extraordinary services he has rendered by the discovery of the remarkable rays subsequently named after him.” This high-energy radiation, though first called Röngen rays, became known as X-rays. His discovery initiated revolutionary improvements in making medical diagnoses and enabled many new advances in modern physics. *TIS "In 1901 he became the ﬁrst physicist to receive a Nobel prize." *VFR

 Rontgen Family Grave, Giessen

1927 Alfred George Greenhill (29 Nov 1847 in London, England - 10 Feb 1927 in London, England) graduated from Cambridge and became Professor of Mathematics at the Royal Military Academy at Woolwich. His main work was on Elliptic Functions but he published widely on applications of mathematics to practical problems. He became an honorary member of the EMS in 1908. *SAU

1936 Eleanor Mildred (Balfour) Sidgwick, (11 March 1845 – 10 February 1936) was an activist for the higher education of women, Principal of Newnham College of the University of Cambridge and a leading figure in the Society for Psychical Research.
She was born in East Lothian, daughter of James Maitland Balfour and Lady Blanche Harriet. She was born into perhaps the most prominent political clan in nineteenth-century Britain, the 'Hotel Cecil': her brother Arthur would eventually himself become prime minister. Another brother, Frank, a biologist, died young in a climbing accident.
One of the first students at Newnham College in Cambridge, in 1876 she married (and became converted to feminism by) the philosopher Henry Sidgwick. In 1880 she became Vice-Principal of Newnham under the founding Principal Anne Clough, succeeding as Principal on Miss Clough's death in 1892. She and her husband resided there until 1900, the year of Henry Sidgwick's death. In 1894 Mrs Sidgwick was one of the first three women to serve on a royal commission, the Bryce commission on Secondary Education.
As a young woman, Eleanor had helped (John William Strutt, who was married to her sister, Evelyn) Lord Rayleigh improve the accuracy of experimental measurement of electrical resistance. She conducted several experiments in electricity and with him published three papers in the Philosophical Transactions of the Royal Society.
She subsequently turned her careful experimental mind to the question of testing the veracity of claims for psychical phenomena. She was elected President of the Society for Psychical Research in 1908 and named 'president of honour' in 1932. Her Husband, Henry, her brother and future Prime Minister, Arthur, and Lord Rayleigh all were also Presidents of the Society.)
She was a member of the Ladies Dining Society in Cambridge, with 11 other members.
In 1916 Mrs Sidgwick left Cambridge to live with one of her brothers near Woking; she remained there until her death in 1936.
She was awarded honorary degrees by the universities of Manchester, Edinburgh, St Andrews and Birmingham.Most of her writings related to Psychical Research, and are contained in the Proceedings of the Society for Psychical Research. However, some related to educational matters, and a couple of essays dealt with the morality of international affairs. *Wik & encyclopedia com

 Portrait of Eleanor Mildred Sidgwick painted by Sir James Jebusa Shannon, 1889 *Wik

1951 George Abram Miller (31 July 1863 – 10 February 1951) was an early group theorist whose many papers and texts were considered important by his contemporaries, but are now mostly considered only of historical importance.
Miller was born in Lynnville, Lehigh County, Pennsylvania, and died in Urbana, Illinois.*Wik

1994 Fritz John (14 June 1910 – 10 February 1994) was a German-born mathematician specialising in partial differential equations and ill-posed problems. His early work was on the Radon transform and he is remembered for John's equation.*Wik

1997 Jerome Namias (19 Mar 1910, 10 Feb 1997 at age 86) American meteorological researcher most noted for having pioneered the development of extended weather forecasts and who also studied the Dust Bowl of the 1930s and the El Niño phenomenon. *TIS In 1971 he joined the Scripps Institution and established the first Experimental Climate Research Center. His prognosis of warm weather during the Arab oil embargo of 1973 greatly aided domestic policy response.*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