"Big Fleas have little fleas upon their backs to bite 'em,
and little fleas have lesser fleas,
and so ad infinitum.
~Augustus De Morgan
The 301st day of the year; 301 is the sum of three consecutive primes starting at 97
\( 301 \equiv 1 Mod _b \) for every base,b, from 2 through 6 (Sixth grade version, if you divide 301 by any number 2 through 6, you get a remainder of 1)
301, like every odd number, is the difference of two consecutive squares, 151^2 - 150^2 . It is also 25^2 - 18^2 (students should expand (x+7)^2 - x^2 to see why, and when this type of relation will next be useful.
EVENTS1386 Opening of the University of Heidelberg. It is the oldest university in Germany and was the third university established in the Holy Roman Empire. *Wik
1462 Archbishop Adolph of Nassau captured the city of Maintz and allowed his soldiers to plunder the city. This forced Gutenberg and his printers to flee, but rather than nipping printing in the bud, it forced its spread to Strasburg, Cologne, Basel, Augsburg, Ulm, Nuremberg, Subiaco, and by 1470, Paris. [G. H. Putnam, Books and Their Makers During the Middle Ages (1896),
p. 372]. *VFR
1636 Harvard College founded. The only mathematical master’s thesis in the U.S. before 1700 was at Harvard. This was in 1693 when the candidate took the affirmative position on “Is the quadrature of a circle possible?”. *VFR The University web site has, "On September 8, 1636, Harvard, the first college in the American colonies, was founded. Who founded Harvard? Despite popular opinion (and a certain statue) John Harvard did not found Harvard, but he was the first major benefactor and he donated half of his estate and his library of more than 400 books to the School.(Read again, but keep in mind they had Masters candidates affirming the impossible, so math was not their best subject.)
1752 Euler writes to (?Goldbach?) to say that he only knows of seven perfect numbers, those of the form \( (2^p -1)(2^{p-1}) \) with p = 2, 3, 5, 7, 13, 17, and 19. He also says he is uncertain whether \(2^{31} - 1\) is prime (it is), and adds that if it has a factor , it will be of the form 64n+1. Numbers of the form \( 2^p -1|\) are called Mersenne primes, and as of Jan 2020, there were only 51 known. *L E Dickson, History of the Theory of Numbers *GIMPS (On Oct 21, 2024 the addition of a new largest known Mersenne prime brings the total known to 52. The new (and surely only temporary) largest known Mersenne Prime is
2136,279,841 − 1.
1752 Euler publishes a paper listing the 161 numbers less than 15,000 for which \( n^2+1 \) is a prime. He also listed eight numbers for which \( n^4 + 1 \) is a prime; {1, 2, 4, 6, 16, 20, 24, and 34}.
He had described to Goldbach as early as July 9, 1743 a manor by which numbers of this form might be divisible. *L. E. Dickson, History of the Theory of Numbers
1886 The Statue of Liberty was dedicated on Bedloe’s Island in New York Harbor. The sculptur Bartholin was present. The statue had almost been moved to another city when there was not enough interest in New York to pay the cost of building the pedestal. Joseph Pulitzer, publisher of the World, a New York newspaper, announced a drive to raise $100,000 (the equivalent of $2.3 million today). Pulitzer pledged to print the name of every contributor, no matter how small the amount given.The drive captured the imagination of New Yorkers, especially when Pulitzer began publishing the notes he received from contributors. "A young girl alone in the world" donated "60 cents, the result of self denial." As the donations flooded in, the committee resumed work on the pedestal. After five months of daily calls to donate to the statue fund, on August 11, 1885, the World announced that $102,000 had been raised from 120,000 donors, and that 80 percent of the total had been received in sums of less than one dollar. *Wik
In this period when we need to remember that all Americans are immigrants, perhaps the second half of the plaque from Emma Lazarus's "The New Colossus"
"Keep, ancient lands, your storied pomp!" cries she
With silent lips. "Give me your tired, your poor,
Your huddled masses yearning to breathe free,
The wretched refuse of your teeming shore.
Send these, the homeless, tempest-tost to me,
I lift my lamp beside the golden door!"
(Hard to imagine some politicians today reading these words, sad. )
1899 Robert Goddard has a "Cherry Tree Dream" of space flight. He will forever remember this as his "anniversary day.:
He became interested in space when he read H. G. Wells' science fiction classic The War of the Worlds when he was 16 years old. His dedication to pursuing space flight became fixed on October 19, 1899. The 17-year-old Goddard climbed a cherry tree to cut off dead limbs. He was transfixed by the sky, and his imagination grew. He later wrote:
On this day I climbed a tall cherry tree at the back of the barn … and as I looked toward the fields at the east, I imagined how wonderful it would be to make some device which had even the possibility of ascending to Mars, and how it would look on a small scale, if sent up from the meadow at my feet. I have several photographs of the tree, taken since, with the little ladder I made to climb it, leaning against it.
It seemed to me then that a weight whirling around a horizontal shaft, moving more rapidly above than below, could furnish lift by virtue of the greater centrifugal force at the top of the path.
I was a different boy when I descended the tree from when I ascended. Existence at last seemed very purposive.
For the rest of his life he observed October 19 as "Anniversary Day", a private commemoration of the day of his greatest inspiration. *Wik
1938 The Indianapolis Star newspaper carried a story of a new proof of the Pythagorean Theorem by Ann Condit, a Junior at Central High School in South Bend, Ind. Her proof is unique in that it used the midpoint of the hypotenuse is the origin of all auxiliary lines and triangles.
In less than two years her proof would appear in Elisha Scott Loomis' 2nd edition of his The Pythagorean Proposition, expanded to 344 proofs from the 230 proofs in his first edition. *David Acheson, The Wonder Book of Geometry
I believe this is her construction:
On this day in 1952, Charles Coulson delivered his inaugural lecture as Rouse Ball Professor of Mathematics at the University of Oxford on The spirit of applied mathematics.
The Rouse Ball Professorship of Mathematics is one of the senior chairs in the Mathematics Departments at the University of Cambridge and the University of Oxford. The two positions were founded in 1927 by a bequest from the mathematician W. W. Rouse Ball. At Cambridge, this bequest was made with the "hope (but not making it in any way a condition) that it might be found practicable for such Professor or Reader to include in his or her lectures and treatment historical and philosophical aspects of the subject.
The current holders of the position (2023) are Wendelin Werner[ at Cambridge and Luis Fernando Alday at Oxford
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| *Walter William Rouse Ball | 14 August 1850 |
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1957 Only three weeks after Sputnik went into space, young Denis Cox in Victoria, Australia sent a design for a spaceship addressed, "TO A TOP SCIENTIST AT Woomera ROCKET RANGE South Australia." His design included locations for Australian Insignia, four Rolls Royce Engines, guided missiles, etc, but advised the scientists, "YOU PUT IN OTHER DETAILS". The
letter can be seen here at the Letters of Note web site Edited by Shaun Usher.
On September 24, 2009, an article on ABC Australia's web page indicated that "The Defence Science Technology Organisation is now finally organising a letter from rocket scientists in response to the letter."
In 1965, the Gateway Arch (630' (190m) high) was completed in St. Louis, Missouri. This graceful sweeping tapered curve of stainless steel is the tallest memorial in the U.S. The architect of the catenary curve arch (correct children, it is NOT a parabola) was Eero Saarinen who won the design competition in 1947. It was constructed 1961-66 in the Jefferson National Expansion Memorial Park, established on the banks of the Mississippi River, on 21 Dec 1935, to commemorate the westward growth of the United States between 1803 and 1890. Cost for the $30 million national monument was shared by the federal government and the City of St. Louis. The memorial arch has an observation room at the top for visitors reached by trams running inside the legs of the arch.*TIS
The connection between Thomas Jefferson as the president who made the Louisiana Purchase and who created the English term Catenary should not go un-noted.
BIRTHS1703 Antoine Deparcieux (28 Oct 1703 in Clotet-de-Cessous, France - 2 Sept 1768 in Paris, France) was a French mathematician who is best known for an early work on annuities and mortality.*SAU
1804 Pierre François Verhulst (28 October 1804, Brussels, Belgium – 15 February 1849, Brussels, Belgium) was a mathematician and a doctor in number theory from the University of Ghent in 1825. Verhulst published in 1838 the equation:
\( \frac{dN}{dt} = r N (1-\frac{N}{k}) \)
when N(t) represents number of individuals at time t, r the intrinsic growth rate and k is the carrying capacity, or the maximum number of individuals that the environment can support. In a paper published in 1845 he called the solution to this the logistic function, and the equation is now called the logistic equation. This model was rediscovered in 1920 by Raymond Pearl and Lowell Reed, who promoted its wide and indiscriminate use.*Wik
1845 Ulisse Dini (14 Nov 1845 in Pisa, Italy - 28 Oct 1918 in Pisa, Italy) Dini looked at infinite series and generalised results such as a theorem of Kummer and one of Riemann, the ideas for which had first emerged in work of Dirichlet. He discovered a condition, now known as the Dini condition, ensuring the convergence of a Fourier series in terms of the convergence of a definite integral. As well as trigonometric series, Dini studied results on potential theory. *SAU
1880 Michele Cipolla (born 28 October 1880 in Palermo; died 7 September 1947 in Palermo) was an Italian mathematician, mainly specializing in number theory.
He was a professor of Algebraic Analysis at the University of Catania and, later, the University of Palermo. He developed (among other things) a theory for sequences of sets and Cipolla's algorithm for finding square roots modulo a prime number. He also solved the problem of binomial congruence.*Wik
1937 Dr. Marcian Edward (Ted) Hoff, Jr. was born October 28, 1937 at Rochester, New York. He received a BEE (1958) from Rensselear Polytechnic Institute in Troy, NY. During the summers away from college he worked for General Railway Signal Company in Rochester where he made developments that produced his first two patents. He attended Stanford as a National Science Foundation Fellow and received a MS (1959) and Ph.D. (1962) in electrical engineering. He joined Intel in 1962. In 1980, he was named the first Intel Fellow, the highest technical position in the company. He spent a brief time as VP for Technology with Atari in the early 1980s and is currently VP and Chief Technical Officer with Teklicon, Inc. Other honors include the Stuart Ballantine Medal from the Franklin Institute.*CHM
1955 Bill Gates, cofounder and CEO of Microsoft Corporation, was born. Gates developed a version of BASIC for the Altair 8800 while being a student at Harvard. With the success of BASIC, he and co-developer Paul Allen founded Microsoft, which delivered an operating system for the IBM PC, the Microsoft Word word processing program, the Window system software, and other programs. *CHM
DEATHS1703 John Wallis (23 Nov 1616, 28 Oct 1703) British mathematician who introduced the infinity math symbol. Wallis was skilled in cryptography and decoded Royalist messages for the Parliamentarians during the Civil War. Subsequently, he was appointed to the Savilian Chair of geometry at Oxford in 1649, a position he held until his death more than 50 years later. Wallis was part of a group interested in natural and experimental science which became the Royal Society, so Wallis is a founder member of the Royal Society and one of its first Fellows. Wallis contributed substantially to the origins of calculus and was the most influential English mathematician before Newton. *TISBetween 1643 and 1689 he served as chief cryptographer for Parliament and, later, the royal court. He is credited with introducing the symbol ∞ to represent the concept of infinity.
1916 Cleveland Abbe (3 Dec 1838, 28 Oct 1916) U.S. astronomer and first meteorologist, born in New York City, the "father of the U.S. Weather Bureau," which was later renamed the National Weather Service. Abbe inaugurated a private weather reporting and warning service at Cincinnati. His weather reports or bulletins began to be issued on Sept. 1, 1869. The Weather Service of the United States was authorized by Congress on 9 Feb 1870, and placed under the direction of the Signal Service. Abbe was the only person in the country who was already experienced in drawing weather maps from telegraphic reports and forecasting from them. Naturally, he was offered an important position in this new service which he accepted, beginning 3 Jan 1871, and was often the official forecaster of the weather.*TIS
1918 Edward Bouchet (15 Sept 1852, New Haven, Conn – 28 Oct 1918, New Haven, Conn) was the first African-American to earn a Ph.D. in Physics from an American university and the first African-American to graduate from Yale University in 1874. He completed his dissertation in Yale's Ph.D. program in 1876 becoming the first African-American to receive a Ph.D. (in any subject). His area of study was Physics. Bouchet was also the first African-American to be elected to Phi Beta Kappa.
Bouchet was also among 20 Americans (of any race) to receive a Ph.D. in physics and was the sixth to earn a Ph. D. in physics from Yale.
When Bouchet was born there were only three schools in New Haven open to black children. Bouchet was enrolled in the Artisan Street Colored School with only one teacher, who nurtured Bouchet's academic abilities. He attended the New Haven High School from 1866–1868 and then Hopkins School from 1868-1870 where he was named valedictorian (after graduating first in his class).
Bouchet was unable to find a university teaching position after college, most likely due racial discrimination. Bouchet moved to Philadelphia in 1876 and took a position at the Institute for Colored Youth (ICY). He taught physics and chemistry at the ICY for 26 years. The ICY was later renamed Cheyney University. He resigned in 1902 at the height of the W. E. B. Du Bois-Booker T. Washington controversy over the need for an industrial vs. collegiate education for blacks.
Bouchet spent the next 14 years holding a variety of jobs around the country. Between 1905 and 1908, Bouchet was director of academics at St. Paul's Normal and Industrial School in Lawrenceville, Virginia (presently, St. Paul's College). He was then principal and teacher at Lincoln High School in Gallipolis, Ohio from 1908 to 1913. He joined the faculty of Bishop College in Marshall, Texas in 1913. Illness finally forced him to retire in 1916 and he moved back to New Haven. He died there, in his childhood home, in 1918, at age of 66. He had never married and had no children.*Wik
1924 John Backus (3 Dec 1924, 28 Oct 1988) American computer scientist who invented the FORTRAN (FORmula TRANslation) programming language in the mid 1950s. He had previously developed an assembly language for IBM's 701 computer when he suggested the development of a compiler and higher level language for the IBM 704. As the first high-level computer programming language, FORTRAN was able to convert standard mathematical formulas and expressions into the binary code used by computers. Thus a non-specialist could write a program in familiar words and symbols, and different computers could use programs generated in the same language. This paved the way for other computer languages such as COBOL, ALGOL and BASIC. *TIS
1965 Luther Pfahler Eisenhart (13 January 1876 – 28 October 1965) was an American mathematician, best known today for his contributions to semi-Riemannian geometry.*Wik
1983 Pol(idore) Swings, (24 Sep 1906; 28 Oct, 1983) Belgian astrophysicist, made spectroscopic studies to identify elements and structure of stars and comets. He discovered the first interstellar molecule, the CH radical (1937). In comet atmospheres he studied the "Swings bands" - certain carbon emission lines. In 1941, with a slit spectrograph he identified a "Swings effect" in the violet CN bands (3875 A) - a fluorescence partly due to solar radiation that shows emmission line excitation differences dependant on the Doppler shift caused by a comet's motion relative to the Sun. He co-authored an Atlas of Cometary Spectra with Leo Haser in 1956. *TIS
1986 Irving Reiner (February 8, 1924, Brooklyn, New York – October 28, 1986) mathematician at the University of Illinois who worked on representation theory. He solved the problem of finding which abelian groups have a finite number of indecomposable modules. His book with Charles W. Curtis, (Curtis & Reiner 1962), was for many years the standard text on representation theory.*Wik
1935 Louise Schmir Hay (June 14, 1935 – October 28, 1989) was a French-born American mathematician. Her work focused on recursively enumerable sets and computational complexity theory, which was influential with both Soviet and US mathematicians in the 1970s. When she was appointed head of the mathematics department at the University of Illinois at Chicago, she was the only woman to head a math department at a major research university in her era.
Her work was influential with both Soviet and US mathematicians of the period. She co-founded the Association for Women in Mathematics (AWM) in an effort to provide support to other working mothers. In 1978, she won a Fulbright Scholarship, as did her husband, and they spent the year studying in the Philippines. In 1979, Hay was named the acting head of the University of Illinois' mathematics department. n 1980, she was appointed to the executive board of the AWM and remained in that post until 1987. She was also named as secretary of the Association for Symbolic Logic in 1982.
2003 Marie Maynard Daly (April 16, 1921 – October 28, 2003) American biochemist who was the first African-American woman to receive a Ph.D. in Chemistry (1947). Her postdoctoral research at the Rockefeller Institute included studying the composition and metabolism of components of cell nuclei, determining the base composition of deoxypentose nucleic acids, and calculating the rate of uptake of labeled glycine by components of cell nuclei. Seven years later, she took a university position. She taught biochemistry and researched the metabolism of the arterial wall and its relationship to aging, hypertension, and atherosclerosis. Later, she studied the uptake, synthesis, and distribution of creatine in cell cultures and tissues. She retired in 1986. *TIS
In 1953, Watson and Crick described the structure of DNA. Accepting the Nobel Prize for this work in 1962, Watson cited one of Daly's papers on "The role of ribonucleoprotein in protein synthesis" as contributing to his work. *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
where dLat and dLong are the differences in the latitudes and longitudes. Tables for Navigation contained both Hav(x) and its inverse invHav(x) and the logs of these values to assist in prosthaphaeresis . To find the distances on the earth, the answer would be multiplied by the radius of the earth. According to Jeff Miller's web site, the word first appeared in the third edition of Navigation and Nautical Astronomy for the use of British Seamen.
