## Thursday 4 July 2024

### On This Day in Math - July 4

Things that people learn purely out of curiosity
can have a revolutionary effect on human affairs

~Frederick Seitz - born 100+ years ago today

The 185th day of the year; the decimal expansion of the first 185 digits of Euler's constant is prime. *Prime Curios

185 is the sum of two square numbers in two different ways: $13^2+ 4^2$ and $11^2 + 8^2$  I'm not sure it is commonly known that this implies that these pairs can be used as the opposite sides of a quadrilateral forcing the diagonals to be perpendicular(if the sides of a quadrilateral are 13, 11, 4, 8; then the quadrilateral has perpendicular diagonals.)

That also means that 185 is the hypotenuse of four Pythagorean Triangles,
(60, 75, 185) (111, 148, 1854)(57, 176, 185) (104,153,185)

185 =the sum of five squares, 100+64+16+4+1

185 is a palindrome in base 6(505) 5*6^2 + 5.

Like all odd numbers, 185 is the difference of the squares of consecutive integers, 93^2 - 92^2 = 185, because it ends in five, it is the difference of two squares of integers that are five apart; 21^2 - 16^2 = 185

and from Jim Wilder @wilderlab An equation for July 4th: 7⁴ = 2401 = (2 + 4 + 0 + 1)⁴   And a followup from World Observer@WKryst2011 points out that there are only two other such year dates. (student's should find both)

See more Math Facts for every year date here.

EVENTS

1054 The Crab Nebula supernova is recorded in China and Japan. *VFR The Crab Nebula (catalogue designations M1, NGC 1952, Taurus A) is a supernova remnant and pulsar wind nebula in the constellation of Taurus. Corresponding to a bright supernova recorded by Chinese astronomers in 1054, the nebula was observed later by John Bevis in 1731. *Wik

1662 “By and by comes Mr. Cooper ... of whom I entend to learn Mathematiques; and so begin with him today ... . After an hour’s being with him at Arithmetique, my ﬁrst attempt being to learn the Multiplication table, then we parted till tomorrow.” Samuel Pepys, in his diary....At the time he was something like a modern Secretary of the Navy. *VFR

He was an English diarist and naval administrator. He served as administrator of the Royal Navy and Member of Parliament, but is most remembered today for the diary he kept for almost a decade. Though he had no maritime experience, Pepys rose to be the Chief Secretary to the Admiralty under both King Charles II and King James II through patronage, diligence, and his talent for administration. His influence and reforms at the Admiralty were important in the early professionalization of the Royal Navy. *Wik

1744 Euler wrote Christian Goldbach that he has ﬁnished his book Introductio in analysin inﬁnitorum (Lausanne 1748). In this work the trigonometric and logarithmic functions were ﬁrst treated in their modern form. *VFR

 Thanks to Alan Leaver

1802 The United States Military Academy at West Point established by act of congress earlier in the year opened on July 4. This school was the ﬁrst engineering school in the U.S. Charles Davies, a noted textbook writer, taught there.*VFR Before 1812 it was conducted as an apprentice school for military engineers and, in effect, as the first U.S. school of engineering.

1819 William Herschel writes to his sister, Caroline, "Lina, there is a great comet. I want you to come and assist me. Come to dine and spend the day here.... we shall have time to prepare maps and telescopes. I saw it's situation last night, it has a long tail." He was eighty years old at the time, and he was still at work when he died, two years later. *Timothy Ferris, Coming of Age in the Milky Way

After her brother died in 1822, Caroline was grief-stricken and moved back to Hanover, Germany, continuing her astronomical studies to verify and confirm William's findings and producing a catalogue of nebulae to assist her nephew John Herschel in his work. [36] Her nephew thought highly of her, in fact he was quoted in 1832 as saying “She runs about the town with me and skips up her two flights of stairs as wonderfully fresh at least as some folks I could name who are not a fourth of her age… In the morning till eleven or twelve she is dull and weary, but as the day advances she gains life, and is quite ‘fresh and funny’ at ten or eleven p.m. and sings old rhymes, nay, even dances to the great delight of all who see her." John Herschel spent long periods with his aunt during the vacations and was greatly influenced by Caroline. She saw him educated at Cambridge, make a name for himself as a mathematician, become elected to the Royal Society, join his father in research in astronomy and be awarded the Copley Medal of the Royal Society for his achievements. Caroline continued to assist William with his observations but her status had greatly improved from the housekeeper she had been in her young days. She was the guest of Maskelyne at the Royal Observatory in 1799 and a guest of members of the Royal Family at various times in 1816, 1817 and 1818. However, her observations were hampered by the architecture in Hanover, and she spent most of her time working on the catalogue.[13] In 1828 the Royal Astronomical Society presented her with their Gold Medal for this work—no woman would be awarded it again until Vera Rubin in 1996. *Wik

1847 lithograph of Caroline Herschel around 97 years of age

1826 Thomas Jefferson , principal author of the Declaration of Independence dies on U.S. Independence day. (See Date under Deaths)  He was buried at his home, Monticello. He wrote his own epitaph: “Here was buried Thomas Jefferson, author of the Declaration of Independence, of the statute of Virginia for religious freedom, and father of the University of Virginia.” *VFR I find it striking that when he lists his accomplishments, being President of the US did not make his top three.

1843 Liouville began an address to the Academy of Sciences with the words: “I hope to interest the Academy in announcing [that in] the papers of Evariste Galois I have found a solution, as precise as it is profound, of this beautiful problem: whether or not it [the general equation of ﬁfth degree] is solvable by radicals.” This work of Galois was published in 1846. *VFR

1862 Charles Lutwidge Dodgson, mathematics teacher at Oxford, went boating on the Isis, a tributary of the Thames, with the three daughters of Henry George Liddell, dean of Christ Church, Oxford. He was especially fond of Alice Liddell, then ten, and it was mainly for her that he began the story of another Alice’s tumble down a rabbit hole. The work was published exactly three years later as Alice’s Adventures under Ground under the pseudonym Lewis Carroll, with the famous illustrations by John Tenniel (see note). This work is a favorite of mathematicians, so if you haven’t read it recently, you should. See 26 November 1864. [Note: "When Charles Dodgson – more widely known as Lewis Carroll – made drawings in the early 1960s for his book Alice’s Adventures in Wonderland, he was disappointed with the results. He employed cartoonist John Tenniel to create the now-famous illustrations, while his original ideas were consigned to the archive of Christ Church College, Oxford, where he worked as a lecturer in mathematics until his death in 1898. TATE ETC. sent a cultural historian to view Dodgson’s rarely seen drawings which feature in Tate Liverpool’s ‘Alice in Wonderland’ exhibition. " *Tate ETC] From Nov 2011 to Jan 2012 the Tate Liverpool was showing these original works as part of the "Alice in Wonderland" exhibit. You can see some of them at the web page where I found the notes above.)

1874  The Eads Bridge is a combined road and railway bridge over the Mississippi River connecting the cities of St. Louis, Missouri and East St. Louis, Illinois. It is located on the St. Louis riverfront between Laclede's Landing, to the north, and the grounds of the Gateway Arch, to the south. The bridge is named for its designer and builder, James Buchanan Eads. Work on the bridge began in 1867.

The Eads Bridge, a  was ready to be opened after seven years of construction on July 4, 1874. The celebration included a fifteen-car train filled with 500 dignitaries pulled by three locomotives that departed from the St. Louis, Vandalia, and Terre Haute Railroad station in East St. Louis. Locomotives were provided by the Illinois Central Railroad and the Vandalia line (a Pennsylvania Railroad subsidiary). The route crossed the Eads Bridge and traveled through the tunnel to Mill Creek Valley and then returned.

Locomotive smoke is a concern in tunnels, especially passenger tunnels. Specially designed coke-burning “smoke-consuming engines” from the Baldwin Locomotive Works had yet to be ordered. News reports tell of passengers coughing and gasping for breath. Construction of the tunnel was not yet complete. Only one of the two tracks was available and ventilation was not yet arranged.

The Bridge is now the oldest bridge crossing the Mississippi river.

 *LibraryofCongress

1934 Leo Szilard patented the chain-reaction design for the atomic bomb.

1943 The 1943 Gibraltar Liberator AL523 crash was an aircraft crash that resulted in the death of General Władysław Sikorski, the commander-in-chief of the Polish Army and Prime Minister of the Polish government-in-exile. Sikorski's Liberator II crashed off Gibraltar almost immediately after takeoff on 4 July 1943. An estimated sixteen people died, including many other senior Polish military leaders. The plane's pilot was the only survivor. Included in the casulties was Zofia Lesniowka, the first commandant of the Polish Women's Auxiliary Service, the General's Daughter.
The crash was ruled to have been an accident, but Sikorski's death remains an unsolved mystery. The crash marked a turning point for Polish influence on their Anglo-American allies in World War II.

*Wik, *Jenny Grant@SilenceinPolish

1956 MIT's Whirlwind Allows Keyboard Input to the Machine
Direct keyboard input on computers debuted on MIT's Whirlwind, which had been completed five years earlier. The now-common method of input was revolutionary at a time when programmers offered instructions to machines by inserting punched cards and changing dials and switches.
The Whirlwind also helped bring in a new form of memory for computers: core memory, which was installed in 1953.  *CHM

 *CHM

1963 The San Francisco Chronicle carried a report entitled, “A Milestone in Math—Professor’s New Concept,” by David Perlman. This popular account of Paul J. Cohen’s proof of the independence of the axiom of choice was probably the ﬁrst published. *VFR

1971 Michael S. Hart posts the first e-book, a copy of the United States Declaration of Independence, on the University of Illinois at Urbana–Champaign's mainframe computer, the origin of Project Gutenberg. *wik

1994 Replica of Hubble space telescope is dedicated in Edwin Hubble's hometown, on the west side of the Webster County Courthouse in Marshfield, Mo.
The Hubble telescope is named after astronomer Edwin Hubble and is one of NASA's Great Observatories.

1997 Mars Pathfinder lands on the surface of Mars. Launched on December 4, 1996 by NASA aboard a Delta II booster a month after the Mars Global Surveyor was launched, it landed on July 4, 1997 on Mars's Ares Vallis, in a region called Chryse Planitia in the Oxia Palus quadrangle. The lander then opened, exposing the rover which conducted many experiments on the Martian surface. *Wik

2014 U S Independence day occurs on Friday. In what year will it next appear on a Friday? And the time after that?

BIRTHS

1790 Sir George Everest, (4 July 1790 – 1 December 1866) British military engineer and geodesist, born in Gwernvale, Powys, Wales, UK. He worked on the trigonometrical survey of India (1818-43), providing the accurate mapping of the subcontinent. For more than twenty-five years and despite numerous hardships, he surveyed the longest arc of the meridian ever accomplished at the time. Everest was relentless in his pursuit of accuracy. He made countless adaptations to the surveying equipment, methods, and mathematics in order to minimize problems specific to the Great Survey: immense size and scope, the terrain, weather conditions, and the desired accuracy. Mount Everest, formerly called Peak XV, was renamed in his honour in 1865. *TIS Mathematically, he was the uncle of Mary Everest Boole, the wife of George Boole, and a mathematician in her own right who is remembered for encouraging children to explore mathematics through playful activities such as 'curve stitching'. (string-art) *Wik  The Preparation of the Child for Science

1868 Henrietta Swan Leavitt (July 4, 1868 – December 12, 1921) American astronomer known for her discovery of the relationship between period and luminosity in Cepheid variables, pulsating stars that vary regularly in brightness in periods ranging from a few days to several months. Leavitt's greatest discovery came from her study of 1777 variable stars in the Magellanic Clouds. She determined the periods of 25 Cepheid variables and in 1912 announced what has since become known as the famous Period-Luminosity relation: "since the variables are probably nearly the same distance from the earth, their periods are apparently associated with their actual emission of light, as determined by their mass, density, and surface brightness." Today the Period-Luminosity relation is used to calculate the distances of galaxies.*TIS

 *Wik

1906 Dan Rutherford (4 July 1906 in Stirling, Scotland - 9 Nov 1966 in St Andrews, Fife, Scotland)studied at St Andrews and Amsterdam. He spent most of his career in St Andrews becoming Gregory Professor of Applied Mathematics. In spite of this title most of his research was in pure mathematics and in particular in algebra. He became President of the EMS in 1940 and 1963. *SAU
Rutherford's dissertation was published in 1932 as Modular Invariants in the Cambridge Tracts. He became an assistant lecturer at the University of Edinburgh and then an assistant lecturer at the University of St Andrews, where he in 1934 was promoted to "Lecturer in Mathematics and Applied Mathematics" and given the task of building up the department in applied mathematics. At St Andrews, he received in 1949 a D.Sc. and then became in 1952 a reader and in 1964 a professor in the Gregory Chair of Applied Mathematics. His research specialty was algebra and in particular the representation theory of symmetric groups. His most famous book, Substitutional Analysis (1948), presents his research on the Young tableaux of Alfred Young. Rutherford published some research on numerical methods in fluid dynamics. He was the author of 3 books on pure mathematics and 3 books on applied mathematics and also the coauthor of a textbook on elementary abstract algebra.

In 1934 Rutherford was elected a member of the Royal Society of Edinburgh. His proposers were Herbert Turnbull, Sir Edmund Taylor Whittaker, Edward Copson and Geoffrey Timms.[2] He won the Society's Keith Medal in 1953. In 1966 he (posthumously) won the Makdougall Brisbane Prize. He was survived by his widow and two daughters.*Wik

1911 Frederick Seitz (July 4, 1911 – March 2, 2008) American physicist who made fundamental contributions to the theory of solids, nuclear physics, fluorescence, and crystals. As Eugene Wigner's first doctoral student, late in 1932, Seitz developed the cellular method of deriving solid-state wave functions. The widespread application of this Wigner-Seitz method to the understanding of metals is regarded as the catalyst for the formation of the field of solid-state physics in the U.S. His subsequent research focused on the theory and properties of crystals. He studied dislocations and imperfections in crystal structures, the effect of irradiation on crystals, and the process of diffusion (the movement of atoms or particles caused by random collision) in crystalline materials.*TIS

1936 Birthday of Guy Otttewel, writer of the eclipse book Understanding Eclipses and many other astronomical publications. *NSEC

1945 John Allen Paulos (July 4, 1945 - )born in Denver, Colorado. Currently a professor at Temple University, he is the author of the popular book Innumeracy. *VFR American mathematician and author of books encouraging people to make sense of the statistics and figures that inform their lives. He represents that mathematics as a subject that is easy to learn and understand. Paulos argues that ignorance of basic mathematical concepts discourages critical thinking and results in costly mistakes and misguided decisions by both political leaders and ordinary people in their everyday lives.*TIS

DEATHS

1742 Luigi Guido Grandi (1 October 1671 – 4 July 1742) was an Italian Jesuit who worked on geometry and hydraulics.Grandi was the author of a number of works on geometry in which he considered the analogies of the circle and equilateral hyperbola. He also considered curves of double curvature on the sphere and the quadrature of parts of a spherical surface.
In 1701 Grandi discussed the conical loxodrome, the curve that cuts the generators of a cone of revolution in a constant angle. He studied the curve the Witch of Agnesi in 1703. In fact his work of 1703 is important in introducing Leibniz's calculus into Italy.
In 1728 Grandi published Flores geometrici a work in which he defines the clelie curve. He named the curve after Countess Clelia Borromeo and dedicated his book to her. If the longitude and colatitude of a point P on a sphere is denoted by θ and φ and if P moves so that θ = m φ, where m is a constant, then the locus of P is a clelie. Grandi also applied the term "clelies" to the curves determined by certain trigonometric equations involving the sine function
a sin θ = b sin mφ
a sin θ = a - b sin mφ
Grandi also worked on hydraulics and was involved with a number of projects such as ones to drain the Chiana Valley and the Pontine Marshes. He also published a number of works on mechanics and astronomy. His practical work on mechanics included experimenting with a steam engine. *SAU
He is noted for the roses that he introduced. His idea was to ﬁnd a geometrical deﬁnition of curves which resemble ﬂowers. These curves are still part of our calculus courses, except now we use polar coordinates to deﬁne them.*VFR

1826 Thomas Jefferson (13 Apr 1743, 4 Jul 1826 at age 83) U.S. president who was throughout his lifetime an extraordinarily learned man, including interests in mathematics and natural sciences. He corresponded with such men as Joseph Priestley, and sometimes contributed time and money to progress in these fields. He was one of the first to use graph paper in the US, which he purchased a large quantity in France.  He collected and classified fossils. He was interested in the experiments being made in balloons and submarines. While visiting Europe, he sent home various mechanical and scientific gadgets produced including a polygraph and phosphorus matches. At his Monticello estate, he practiced scientific farming, and was always on the lookout for a significant new plant or seed. Jefferson died shortly before 1pm. His old friend, John Adams, died a few hours later.*TIS

1901 Peter Guthrie Tait (28 April 1831 – 4 July 1901) Scottish physicist and mathematician who helped develop quaternions, an advanced algebra that gave rise to vector analysis and was instrumental in the development of modern mathematical physics.*TIS Tait was a fellow-pupil of Maxwell at Edinburgh Academy and both of them went on to study at Edinburgh University and Cambridge. Tait became Professor of Mathematics at Queen's College Belfast and then moved to the Chair of Natural Philosophy at Edinburgh which he occupied for more than 40 years. With his collaborations with Maxwell, Thomson (Lord Kelvin) and Hamilton he made important contributions in both mathematics and physics. He became one of the first honorary members of the EMS in 1883. *SAU

1910 Giovanni Virginio Schiaparelli, (14 March 1835 - 4 July 1910) Italian astronomer who is remembered for his observations of Mars over seven oppositions and named the "seas" and "continents". In 1877, he saw on the surface of the planet Mars the markings that he called canali (channels), later misinterpreted as "canals." He made extensive studies, both observational and theoretical, of comets, determining from the shapes of their tails that there was a repulsive force from the sun. He showed that meteor swarms travel through space in cometary orbits. He explained the regular meteor showers as the result of the dissolution of comets and proved it for the Perseids. He suggested that Mercury and Venus rotate on their axes, discovered the asteroid Hesperia (1861) and was a major observer of double stars.*TIS

1934 Marie Marja Sklodowska Curie (7 November 1867 – 4 July 1934) was a Polish-born French chemist and physicist. In 1898, her celebrated experiments on uranium minerals led to discovery of two new elements. First she separated polonium, and then radium a few months later. The quantity of radon in radioactive equilibrium with a gram of radium was named a curie (subsequently redefined as the emission of 3.7 x 1010 alpha particles per sec.) With Henri Becquerel and her husband, Pierre Curie, she was awarded the 1903 Nobel Prize for Physics. She was then sole winner of a second Nobel Prize in 1911, this time in Chemistry. Her family won five Nobel awards in two generations. She died of radiation poisoning from her pioneering work before the need for protection was known.*TIS

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

1986 Oscar Zariski's (April 24, 1899 – July 4, 1986) work was on foundations of algebraic geometry using algebraic methods. He worked on the theory of normal varieties, local uniformisation and the reduction of singularities of algebraic varieties.*SAU
Zariski emigrated to the United States in 1927 supported by Solomon Lefschetz. He had a position at Johns Hopkins University where he became professor in 1937. During this period, he wrote Algebraic Surfaces as a summation of the work of the Italian school. The book was published in 1935 and reissued 36 years later, with detailed notes by Zariski's students that illustrated how the field of algebraic geometry had changed. It is still an important reference.
After spending a year 1946–1947 at the University of Illinois at Urbana–Champaign, Zariski became professor at Harvard University in 1947 where he remained until his retirement in 1969. In 1945, he fruitfully discussed foundational matters for algebraic geometry with André Weil. Weil's interest was in putting an abstract variety theory in place, to support the use of the Jacobian variety in his proof of the Riemann hypothesis for curves over finite fields, a direction rather oblique to Zariski's interests. The two sets of foundations weren't reconciled at that point.

At Harvard, Zariski's students included Shreeram Abhyankar, Heisuke Hironaka, David Mumford, Michael Artin and Steven Kleiman—thus spanning the main areas of advance in singularity theory, moduli theory and cohomology in the next generation. Zariski himself worked on equisingularity theory. Some of his major results, Zariski's main theorem and the Zariski theorem on holomorphic functions, were amongst the results generalized and included in the programme of Alexander Grothendieck that ultimately unified algebraic geometry.

Zariski proposed the first example of a Zariski surface in 1958.*Wik

1987 Bengt Strömgren (21 Jan 1908; 4 Jul 1987) Bengt (Georg Daniel) Strömgren was a Danish astrophysicist who pioneered the present-day knowledge of the gas clouds in space. Researching for his theory of the ionized gas clouds around hot stars, he found relations between the gas density, the luminosity of the star, and the size of the "Strömgren sphere" of ionized hydrogen around it. He surveyed such H II regions in the Galaxy, and he also did important work on stellar atmospheres and ionization in stars. *TIS

2002 Laurent-Moïse Schwartz (5 March 1915 in Paris – 4 July 2002 in Paris) was a French mathematician. He pioneered the theory of distributions, which gives a well-defined meaning to objects such as the Dirac delta function. He was awarded the Fields medal in 1950 for his work (developing the theory of distributions, a new notion of generalized functions motivated by the Dirac delta-function of theoretical physics). He was the first French mathematician to receive the Fields medal. For a long time he taught at the École polytechnique. *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