Wednesday 6 November 2024

#31 Loxodrom, Rhumb Line.....History and Etymology of Math Terms

  Loxodrome

The shortest path between two points on the surface of the Earth is along a great circle arc, but this path is often not possible for ships. One reason is that a great circle arc takes constant changes of compass heading. Because it is not much longer in the middle latitudes, ships often sail a path of constant compass heading, called a loxodrome (and sometimes a rhumb line). Loxodrome comes from the Greek roots loxos for slanted, and drome which means path or course. The word rhumb was derived from the old Spanish term rumb for room or space, and the "h" seems to have crept in over confusion with the word rhombus. The first person to study the rhumb lines, and realize that they were not the shortest path between two points on the globe, was Pedro Nunez, the Portugese mathematician. In 1537, Nunez, the Royal Cosmographer of Portugal published his studies in Tratado da Sphera. In 1541 Gerard Mercator published the first globe with rhumb lines marked on it. The Globe was also the largest globe made up to that time. Today one of the globes may be found at the National Maritime Museum in Greenwich in Great Britain. Another is at the Harvard University Map Collection. You can view selected images of the globe at this web link.

The term "loxodrome" first appears in Tiphys batavus in 1624 by the Dutch Scientist Willebrord van Roijen Snell who is also known for his optical law of refraction.

Until the middle of the 18th century, finding a ships longitude at sea was nearly impossible. This forced seamen to try to navigate along a constant direction and use their estimated speed to "dead reckon" their position. It was 1569, almost 28 years after Mercator's use of rhumb lines on a globe, that he hit upon his most marvelous creation, a flat map in a new projection that would make navigation much easier, the type of map we now call a Mercator or cylindrical projection (at right). A straight line drawn on a Mercator projection map is a loxodrome.

The word loxodrome is also sometimes used for a logarithmic spiral because it always cuts a line through the origin with the same angle. A true complete loxodromic spiral on a sphere will endlessly circle the poles without reaching them. For that reason, the loxodrome is also called a spherical spiral.One of the first to show this was true was the English Mathematician Thomas Harriot. "He exhibited the logarithmic spiral as the stereographic projection of a loxodrome on a sphere, a projection he proved to be conformal." [St Andrews Univ math history web site

On This Day in Math - November 6




I have made this letter longer than usual, because I lack the time to make it short.
~ Blaise Pascal, (my favorite Pascal Quote)


The 310th day of the year; 310 = 1234 in base six. In base 2 it repeats one period, 100,110,110

(1!)²+(2!)²+...+(310!)² is prime. *Math Year-Round ‏@MathYearRound

The four possible 3 digit permutations of 310 all use the same digits in their squares as well, 1302 = 16900, 3102 = 96100, 1032 = 10609,and 3012 = 90601. (Are there numbers with a digit greater than three for which this is true? With or without a 0.)

310 is a magnanimous number. A number (which we assume of at least 2 digits) such that the sum obtained inserting a "+" among its digit in any position gives a prime.  31+0 is prime and 3+10 is prime

EVENTS

1500 Nicholas Copernicus observes a deep (85%) partial eclipse of the Moon from Rome. *David Dickinson ‏@Astroguyz 4m:

1572, a supernova was first noted by Wolfgang Schuler of Wittenberg in the W-shaped constellation of Cassiopeia but was seen by many observers throughout Europe and in the Far East. It appeared as a new star, adjacent to the fainter star seen just northwest of the middle of the "W." Tycho Brahe first noticed this new star on 11 Nov 1572, and he began to meticulously record its appearance. Although he was not the first to see it, he gained fame from his book Stella Nova (Latin: "new star"). For two weeks it was brighter than any other star in the sky and visible in daytime. By month's end, it began to fade and change color, from bright white to yellow and orange to faint reddish light. It was visible to the naked eye for about 16 months until Mar 1574 *TIS
De Stella Nova opened to display image with the Supernova located in the foot of the serpent bearer

*Wik



1766 Lagrange welcomed, at age 30, to the Berlin Academy by Frederick the Great. “The greatest king in Europe” wished to have at his court “the greatest mathematician of Europe.” *VFR 
By March 1766 d'Alembert knew that Euler was returning to St Petersburg and wrote again to Lagrange to encourage him to accept a post in Berlin. Full details of the generous offer were sent to him by Frederick II in April, and Lagrange finally accepted. Leaving Turin in August, he visited d'Alembert in Paris, then Caraccioli in London before arriving in Berlin in October. Lagrange succeeded Euler as Director of Mathematics at the Berlin Academy on 6 November 1766.


1780 Aloisio Galvani discovers the famous "twitch" in a frog's leg. *A history of physics in its elementary branches By Florian Cajori 
During the 1780's, biologist Luigi Galvani performed experiments at the University of Bologna involving frogs. While cutting a frog’s leg, Galvani's steel scalpel touched a brass hook that was holding the leg inplace. The leg twitched. Further experiments confirmed this effect, and Galvani was convinced that he was seeing the effects of what he called animal electricity. *batteryfacts



1869 The first game of intercollegiate "football" between two colleges from the United States was an unfamiliar ancestor of today's college football, as it was played under 99-year-old soccer-style Association rules. The game was played between teams from Rutgers University and Princeton University, which was called the College of New Jersey at the time. It took place on November 6, 1869 at College Field, which is now the site of the College Avenue Gymnasium at Rutgers University in New Brunswick, New Jersey. Rutgers won by a score of 6 "runs" to Princeton's 4 *Wik

1936 Problem number 153 was entered into the Scottish Book by Stanislaw Mazur. The problem asked (although not in these words) about the existence of Schauder bases in separable Banach spaces. As with many of the problems in the Scottish Book the proposer would offer a prize for their solution. Prizes offered included wine, spirits, or a meal in Cambridge but Mazur offered a live goose as the prize for this particular problem. Per Enflo showed in 1972 that the problem had a negative solution and, while in Warsaw lecturing on his solution, Mazur presented him with his prize, the live goose! The ceremony was broadcast throughout Poland. *SAU





1960 The New York Times picked up an Associated Press story about a Catholic Church near Cologne, Germany which had decided to put a modern touch to the new church bell, so they ordered Einstein's famous equation to be engraved on the bell. Unfortunately, someone miss engraved the bell, replacing the C with an R. Unfortunately, when the story ran in the press, another adjustment to the Professor's great equation had occurred... read it for yourself.
*J F PTAK

1980 Microsoft signs a contract with IBM to create an operating system for the new IBM PC. The PC ignited the personal computer market, making home computers popular among more than just hobbyists. Microsoft cofounders Bill Gates and Paul Allen developed the Microsoft Disk Operating System, commonly known as MS-DOS, using existing software from a Seattle company as a foundation. *CHM



2002 A group of Australian scientists published a paper in Applied Ergonomics with the title, "An Analysis of the Forces Required to Drag Sheep over Various Surfaces." *sciencedirect abstract


BIRTHS

1638 James Gregory (6 Nov 1638; Oct 1675) Scottish mathematician, astronomer and inventor of a type of reflecting telescope, born in Aberdeen. He was the first to investigate converging number series, which have an infinite number of terms but a finite sum.
 Gregory published Vera Circuli et Hyperbolae Quadratura (1667) in which he approximated the areas of the circle and hyperbola with convergent series:

[James Gregory] cannot be denied the authorship of many curious theorems on the relation of the circle to inscribed and circumscribed polygons, and their relation to each other. By means of these theorems he gives with infinitely less trouble than by the usual calculations, … the measure of the circle and hyperbola (and consequently the construction of logarithms) to more than twenty decimal places. Following the example of Huygens, he also gave constructions of straight lines equal to the arcs of the circle, and whose error is still less.
"The first proof of the fundamental theorem of calculus and the discovery of the Taylor series can both be attributed to him.
 He made important contributions to the development of the calculus, although some of his best work remained virtually unknown until long after his death. In 1660 he published his Optica Promota, in which he described the first practical reflecting ("Gregorian") telescope. Light reflected from a concave elliptical secondary mirror is brought to a focus just behind a hole in the primary mirror. It was superceded by the Newtonian and Cassegrain telescopes. Gregory also introduced estimation of stellar distances by photometric methods. *TIS  (For more on the origin of reflecting telescopes see this blog by the Renaissance Mathematicus.)

*Wik



1781 Giovanni Antonio Amedeo Plana (6 November 1781 – 20 January 1864) was an Italian astronomer and mathematician. In 1800 he entered the École Polytechnique, and was one of the students of Joseph Lagrange. Jean Fourier, impressed by Plana's abilities, managed to have him appointed to the chair of mathematics in a school of artillery in Piedmont in 1803, which came under the control of the French in 1805. In 1811 he was appointed to the chair of astronomy at the University of Turin thanks to the influence of Lagrange. He spent the remainder of his life teaching at that institution.
His contributions included work on the motions of the Moon, as well as integrals, elliptic functions, heat, electrostatics, and geodesy. In 1820 he was one of the winners of a prize awarded by the Académie des Sciences in Paris based on the construction of lunar tables using the law of gravity. In 1832 he published the Théorie du mouvement de la lune. In 1834 he was awarded with the Copley Medal by the Royal Society for his studies on lunar motion. He became astronomer royal, and then in 1844 a Baron. At the age of 80 he was granted membership in the prestigious Académie des Sciences. He died in Turin. He is considered one of the premiere Italian scientists of his age. *Wik



1906 Emma Markovna Lehmer (née Trotskaia) (November 6, 1906 – May 7, 2007) was a mathematician known for her work on reciprocity laws in algebraic number theory. She preferred to deal with complex number fields and integers, rather than the more abstract aspects of the theory. At UC Berkeley, she started out in engineering in 1924, but found her niche in mathematics. One of her professors was Derrick N. Lehmer, the number theorist well known for his work on prime number tables and factorizations. While working for him at Berkeley finding pseudosquares, she met her future husband Derrick H. Lehmer. Upon her graduation summa cum laude with a B.A. in Mathematics (1928), Emma married the younger Lehmer. They moved to Brown University, where Emma received her M.Sc., and Derrick his Ph.D., both in 1930. Emma did not obtain a Ph.D. herself. Most universities had nepotism rules which prevented husband and wife from both holding teaching positions, although Emma claimed there were many advantages to not holding a Ph.D.
The Lehmers had two children, Laura (1932) and Donald (1934). Emma did independent mathematical work, including a translation from Russian to English of Pontryagin's book Topological Groups. She worked closely with her husband on many projects; 21 of her 60-some publications were joint work with him. Her publications were mainly in number theory and computation, with emphasis on reciprocity laws, special primes, and congruences. *Wik
Photo by Paul Halmos
*SAU




1960 Amir D. Aczel (November 6, 1950 – November 26, 2015) was an Israeli-born American lecturer in mathematics and the history of mathematics and science, and an author of popular books on mathematics and science.
Aczel was born in Haifa, Israel. Aczel's father was the captain of a passenger ship that sailed primarily in the Mediterranean Sea. When he was ten, Aczel's father taught his son how to steer a ship and navigate. This inspired Aczel's book The Riddle of the Compass.
When Aczel was 21 he studied at the University of California, Berkeley. He graduated with a BA in mathematics in 1975, and received a Master of Science in 1976. Several years later Aczel earned a Ph.D. in statistics from the University of Oregon.
Aczel taught mathematics at universities in California, Alaska, Massachusetts, Italy, and Greece. He married his wife Debra in 1984 and has one daughter, Miriam, and one stepdaughter. He accepted a professorship at Bentley College in Massachusetts where he taught classes on the history of science and the history of mathematics. While teaching at Bentley, Aczel wrote several non-technical books on mathematics and science, as well as two textbooks. His book, Fermat's Last Theorem (ISBN 978-1-56858-077-7), was a United States bestseller and was nominated for a Los Angeles Times Book Prize. Aczel appeared on CNN, CNBC, The History Channel, and Nightline. Aczel was a 2004 Fellow of the John Simon Guggenheim Memorial Foundation and Visiting Scholar in the History of Science at Harvard University (2007). In 2003 he became a research fellow at the Boston University Center for Philosophy and History of Science, and in Fall 2011 was teaching mathematics courses at University of Massachusetts Boston.
He died of cancer on Nov. 26, 2015 in Nîmes, in the south of France. He was 65. *Wik, *Obit
His most recent book was Finding Zero: A Mathematician's Odyssey to Uncover the Origins of Numbers




1966 Laurent Lafforgue (born 6 November 1966, in Antony, Hauts-de-Seine) is a French mathematician.
He won 2 silver medals at International Mathematical Olympiad (IMO) in 1984 and 1985. He entered the École Normale Supérieure in 1986. In 1994 he received his Ph.D. under the direction of Gérard Laumon in the Arithmetic and Algebraic Geometry team at the Université de Paris-Sud. Currently he is a research director of CNRS, detached as permanent professor of mathematics at the Institut des Hautes Études Scientifiques (I.H.E.S.) in Bures-sur-Yvette, France.
In 2002 at the 24th International Congress of Mathematicians in Beijing, China he received the Fields Medal together with Vladimir Voevodsky. Lafforgue made outstanding contributions to Langlands' program in the fields of number theory and analysis, and in particular proved the Langlands conjectures for GLn of a function field. The crucial contribution by Lafforgue to solve this question is the construction of compactifications of certain moduli stacks of shtukas. The monumental proof is the result of more than six years of concentrated efforts.
He received the Clay Research Award in 2000. His younger brother Vincent Lafforgue is also a notable mathematician.*Wik





DEATHS

1656 Jean-Baptiste Morin (February 23, 1583 – November 6, 1656) was a French astrologer and astronomer who attempted to solve the longitude problem using lunar observations. He was certainly not the first to propose the method but he did add one important new piece of understanding, namely he took lunar parallax into account.
Since Morin put forward his method for a longitude prize, a committee was set up by Cardinal Richelieu​ to evaluate it. Étienne Pascal, Mydorge, Beaugrand, Hérigone, J C Boulenger and L de la Porte served on the committee and they were in dispute with Morin for the five years after he made his proposal.
Morin realized that instruments had to be improved, improved methods of solving spherical triangles had to be found and better lunar tables were needed. He made some advances in these areas but his method, although theoretically sound, could not achieve either the computational or observational accuracy to succeed. Morin refused to listen to objections to his proposal.
Even while the dispute was going on, in 1638, Morin attacked Descartes saying that he had realized as soon as they met how bad his philosophy was. These disputes alienated Morin from the scientific community. He was to spend the latter part of his life isolated from other scientists although Cardinal Richelieu's successor Cardinal Mazarin did award him a pension for his work on the longitude in 1645. *SAU



1790 James Bowdoin (7 Aug 1726, 6 Nov 1790) American founder and first president of the American Academy of Arts and Sciences (1780). He was a scientist prominent in physics and astronomy, and wrote several papers including one on electricity with Benjamin Franklin, a close friend. In one of his letters to Franklin, Bowdoin suggested the theory, since generally accepted, that the phosphorescence of the sea, under certain conditions, is due to the presence of minute animals. Bowdoin was also a political leader in Massachusetts during the American revolution (1775-83), and governor of Massachusetts (1785-87). His remarkable library of 1,200 volumes, ranged from science and math to philosophy, religion, poetry, and fiction. He left it in his will to the Academy.*TIS
Among his bequests was a gift to Harvard College for awards that are now known as the Bowdoin Prizes. His son James III donated lands from the family estate in Brunswick, Maine, as well as funds and books, to establish Bowdoin College in his honor.







1880 Giusto Bellavitis (22 Nov 1803 in Bassano, Vicenza, Italy - 6 Nov 1880 in Tezze (near Bassano) Italy ) Bellavitis solved various mechanical problems by original methods, among them Hamilton's quaternions. He developed very personal critical observations about the calculus of probabilities and the theory of errors. He also explored physics, especially optics and electrology, and chemistry. As a young man, Bellavitis weighted the problem of a universal scientific language and published a paper on this subject in 1863. He also devoted time to the history of mathematics and, among other things, he vindicated Cataldi by attributing the invention of continued fractions to him. *SAU
Bellavitis anticipated the idea of a Euclidean vector with his notion of equipollence. Two line segments AB and CD are equipollent if they are parallel and have the same length and direction. The relation is denoted  In modern terminology, this relation between line segments is an example of an equivalence relation. The concept of vector addition was written by Bellavitis as: According to Laissant, Bellavitis published works in "arithmetic, algebra, geometry, infinitesimal calculus, probability, mechanics, physics, astronomy, chemistry, mineralogy, geodesy, geography, telegraphy, social science, philosophy, and literature.   *Wik



1913 Sir William Henry Preece (15 Feb 1834, 6 Nov 1913) Welsh electrical engineer who was a major figure in the development and introduction of wireless telegraphy and the telephone in Great Britain. Preece's interest in applied electricity and telegraphic engineering was developed as a graduate student under Michael Faraday. For 29 years, from 1870, he was an engineer with the Post Office telegraphic system and contributed many inventions and improvements, including a railroad signaling system that increased railway safety. An early pioneer in wireless telegraphy, he originated his own system in 1892. He encouraged Guglielmo Marconi by obtaining assistance from the Post Office for his work. Preece also introduced into Great Britain the first Bell telephones. Preece was knighted in 1899. *TIS



1946 Dunham Jackson (July 24, 1888, Bridgewater, Massachusetts – November 6, 1946) was a mathematician who worked within approximation theory, notably with trigonometrical and orthogonal polynomials. He is known for Jackson's inequality. He was awarded the Chauvenet Prize in 1935. His book Fourier Series and Orthogonal Polynomials (dated 1941) was reprinted in 2004.
Harold Bacon recalls that Jackson was an inspired writer of limericks. When Bacon purchased Jackson's "The Theory of Approximations" he took it to Jackson's office and requested he sign it, suggesting a limerick. Without any visible prethought Jackson wrote on the flyleaf:
There was a young fellow named Bacon
Whose judgement of books was mistaken
In a moment too rash
He relinquished some cash
And his faith in the Author was shaken
*Steven Krantz, Mathematical Apocrypha Redux
*Wik




1966 Frieda Nugel (18 June 1884 in Cottbus, Brandenburg, Germany
- 6 Nov 1966 in Bad Godesberg, Bonn, Germany) was a German mathematician who was one of the first women to receive a doctorate in Germany. *SAU



1975  Samuel Stephens Kistler (March 26, 1900  – November 6, 1975) was an American scientist and chemical engineer, best known as the inventor of aerogels, one of the lightest known solid materials.
The exact circumstances of the creation of the first aerogels are not well recorded. A popular story is that they resulted from a competition between Kistler and one Charles Learned "to see if they could replace the liquid inside of a jelly jar without causing any shrinkage". Whether these experiments were performed at the College of the Pacific, still with limited facilities following the move in 1923 to the new Stockton campus, or at Stanford, where Kistler began pursuing a doctorate in 1927, is a source of some confusion. Either way, in 1931 Kistler published a paper in Nature (vol. 127, p. 741) titled "Coherent Expanded Aerogels and Jellies".
He died in Salt Lake City in November 1975, shortly before the resurgence of interest in aerogels caused by the discovery of a less time-consuming method of manufacture by researchers led by Stanislaus Teichner in France.



1979 Alexander Weinstein (21 Jan 1897 in Saratov, Russia
- 6 Nov 1979 in Washington DC, USA)Weinstein's research covered a wide range of topics. He is famed for solving a variety of boundary value problems. For example he solved Helmholtz's problem for jets, giving the first uniqueness and existence theorems for free jets in a series of papers from 1923 to 1929. He examined boundary problems in an infinite strip, giving hydrodynamic and electromagnetic applications.
Weinstein's method was developed to give accurate bounds for eigenvalues of plates and membranes. In examining singular partial differential equations he introduced a new branch of potential theory and applied the results to many different situations including flow about a wedge, flow around lenses and flow around spindles. *SAU



2021 Laszlo Belady,( April 29, 1928 in Budapest - November 6, 2021) creator of the Belady algorithm (used in optimizing the performance of computers), is born. Belady worked at IBM for 23 years in software engineering before joining the Mitsubishi Electronics Research Laboratory in the mid-1980s. He wins numerous awards, including the J.D. Warnier Prize for Excellence in Information and an IEEE fellowship. *CHM







Credits
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*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

Tuesday 5 November 2024

Political Polls and Margins of Error????

 This was written just before the election in 2008, and most of the polls had settled into a 53-45 spread for Obama, which, for all my nay-saying in this blog, was very close.  




Well, we are almost to the election, which means an end, finally, to the interminable projection polls. Ok, I actually like statistics, but I'm not sure I accept that political polls are not playing a little fast and loose with the assumptions that are needed to compute confidence intervals. I love it when the election goes the wrong way and they have to come up with scenarios for WHY they blew it. Of course with so many of them out there making 95% confidence intervals, about five percent of the ones you hear SHOULD be wrong... but I think there is more to the problem than just that.

I came across a blog from Iowahawk ( I didn't provide a link because my students come here and some of his language is not the sort of thing I display for my students..they know all the words anyway, but they won't hear them from me) that had a nice expression of what I felt, so I stole parts of it shamelessly...


Statisticians love balls and urns. A typical Stats 101 midterm, for example, usually includes a question along these lines:

"You take a simple random sample of 1000 balls from an urn containing 120,000,000 red and blue balls, and your sample shows 450 red balls and 550 blue balls. Construct a 95% confidence interval for the true proportion of blue balls in the urn."
From this the typical Intro stats student can deduce that they are 95% certain the real proportion of blue balls in that urn is 55%, plus or minus 3.1% .

"This is, for all intents and purposes, how political pollsters compute the mysterious "margin of error," which has everything to do (and only to do) with pure mathematical sampling error. If you look at the formula above and round it just a smidge, you get a simple rule of thumb for the margin of error of a sampled probability:
Margin of Error = 1 / sqrt(n)

So if the sample size is 400, the margin of error is 1/20 = 5%; if the sample size is 625 the margin of error is 1/25 = 4%; if the sample size is 1000, it's about 3%.


"It works pretty well if you're interested in hypothetical colored balls in hypothetical urns, or survival rates of plants in a controlled experiment, or defects in a batch of factory products. It may even work well if you're interested in blind cola taste tests. But what if the thing you are studying doesn't quite fit the balls & urns template?"



What if 40% of the balls have personally chosen to live in an urn that you legally can't stick your hand into?

What if 50% of the balls who live in the legal urn explicitly refuse to let you select them?

What if the balls inside the urn are constantly interacting and talking and arguing with each other, and can decide to change their color on a whim?

What if you have to rely on the balls to report their own color, and some unknown number are probably lying to you?

What if you've been hired to count balls by a company who has endorsed blue as their favorite color?

What if you have outsourced the urn-ball counting to part-time temp balls, most of whom happen to be blue?

What if the balls inside the urn are listening to you counting out there, and it affects whether they want to be counted, and/or which color they want to be?

If one or more of the above statements are true, then the formula for margin of error simplifies to

Margin of Error = Who the heck knows?

On This Day in Math - November 5

 

Bonfire night in my old area in East Anglia

I hope you enjoy the absence of pupils ... the total oblivion of them for definite intervals is a necessary condition for doing them justice at the proper time.
~James Clerk Maxwell (every teacher knows how true this statement is.)

The 309th day of the year; 3095= 2,817,036,000,549. It is the smallest number whose fifth power contains all the digits 0 to 9. (Students, is there a smaller number that contains all the digits for some other power?)

  is prime  *Prime Curios

309 = 155^2 - 154^2 = 53^2-50^2

And 309 is the number of primes less than 2^11 = 2058, and the number of fractions in a Farey Sequence with a largest denominator of 31   See A Curious Property of Vulgar Fractions 

309 is 303 plus the sum of digits of 303, and also 294 plus the sum of digits of 294.



EVENTS
1603 Edmund Bruce, a Scot traveling in Italy, in a letter to Kepler put forward some ideas based on Bruno’s cosmology. He maintained that the Sun, at the center of the planetary orbits, turns on its axis and thereby drives the planets around in their orbits, the more distant more slowly than those closer to the Sun. The light of the stars, he went on, is due to their motion, not their matter.


In 1662, Robert Hooke was appointed Curator of Experiments to the Royal Society, London. The position was established as a provision of the Royal Charter given by King Charles II (passed by the Great Seal on 15 July 1662) to incorporate the Royal Society. The Society was the successor of the Society for the Promoting of Physico-Mathematical Experimental Learning formed by at a meeting of a dozen scientist on 28 Nov 1660 at Gresham College. Hooke was required to demonstrate three or four experiments at every meeting of the Society, starting without recompense until 1664 when the Society was in a position to do so. Hooke's genius produced a wealth of original ideas over the following 15 years.*TIS
The Curious Life of Robert Hooke: The Man Who Measured London



1666 Leibniz received his doctor’s degree at age 20 for his essay on a new method (the historical) of teaching law from the University of Altdorf near Nuremberg. He had studied law at his home town University of Leipzig, entering at 15, but left at 20 when he was denied his doctorate, officially on account of his youth. Altdorf offered him a professorship in law, but he declined. [Bell, Men of Mathematics, 122] *VFR

In 1824, the Rensselaer School was founded in Troy, N.Y., by Stephen van Rensselaer becoming the first engineering college in the U.S. It opened on 3 Jan 1825, with the purpose of instructing persons, who may choose to apply themselves, in the application of science to the common purposes of life." The first class of 10 students graduated on 26 Apr 1826. The first director and senior professor was Amos Eaton who served from Nov 1824 - 10 May 1842. The name of Renssalaer Institute was adopted on 26 Apr 1832, and Renssalaer Polytechnic Institute on 8 Apr 1861.*TIS
*From Little Acorns, Great Oaks Grow


1828 Augustus DeMorgan, age 22, gave his introductory lecture, “On the study of mathematics,” at London University (UCL). It described the position which mathematics held in a person’s education. DeMorgan was the first to hold the university’s chair in mathematics, being chosen from 32 candidates, even though he was by far the youngest. See the chapter on DeMorgan in A History of Mathematics Education in England (1982), by. A. G. Howson [p. 82].*VFR
Among the students in his classes was fourteen year old James Joseph Sylvester. Sylvester had to be interviewed by the instructor to determine his knowledge of mathematics to determine his placement. He must have impressed DeMorgan who placed him in his highest senior class. *James Joseph Sylvester: Jewish Mathematician in a Victorian World By Karen Hunger Parshall




1859 Benjamin Peirce suggests variations on modern paper-clip as symbols for pi and  e. *J. D. Runkle's Mathematical Monthly


1884 Evelyn Lamb's research seems to indicate that the first review for E A Abbott's "Flatland" was on this date. I can't find that review, but 3 days later this one appeared

The Academy (November 8, 1884), p. 302.
"Flatland is a world inhabited by beings whose experience of space is limited to two dimensions. In this book a native of this strange region has undertaken to describe its peculiarities to us dwellers in `Spaceland.' It seems the male Flatlanders are plane rectilineal figures, varying in shape according to their position in the social scale, or, what in Flatland is the same thing, to their degree of intellectual development; the lowest class being isosceles triangles, and the highest class, or priesthood, being polygons which have so many sides that they are accounted circles. The Flatland women, being deplorably lacking in intellect, are not figures at all, but merely straight lines. Of course, the inhabitants of two-dimensional space cannot see each other as figures, but only as straight lines. For the means by which they can infer one another's true shape, and for the manners and institutions of Flatland, the reader must be referred to the book itself. The historian of Flatland is by rank and figure `a square,' and he has a grandson, a clever hexagon, who one day startles him with a suggestion that space may have a third dimension, and that beings may exist who are capable of seeing the inside of a closed figure. The notion is angrily rejected as absurd; but the `Square' afterwards undergoes a miraculous experience that introduces him to the threefold space which he was previously unable to imagine. Guided by the analogy of his own experience, he ventures to suggest to the inhabitants of `Spaceland' that a fourth dimension may have real existence, though it is to them as inconceivable as the third dimension once was to himself. The `Square' has forgotten to tell us by what means he has managed to make himself intelligible to tri-dimensional mankind, and one or two other weak points might easily be found in his story; but, on the whole, the idea is very cleverly worked out, with many happy satiric touches, and the book is much more entertaining than this account of it will lead the reader to suppose."

John A Adam commented, "It's a wonderful little book, and the movies, Flatland and Sphereland, are excellent. Also, there's a book, Sphereland, by Dionysus Burger written in the same spirit as Flatland."

 

*http://www.math.brown.edu/~banchoff




In 1891, Marie Curie enrolled in the Sorbonne, two days before her 24th birthday. She has been out of school for 5 years, is now in a foreign country (France instead of her homeland of Poland), has barely enough money to survive, and even faints from hunger on at least one occasion in the classroom. Yet she eventually graduated at the top of her class. Then on this same day in 1906, (see below) she delivered her first lecture at the Sorbonne as the first female physics teacher in the school's history.*TIS



1895  George B. Selden is granted the first U.S. patent for an automobile. *the painter flynn
He filed for a patent on May 8, 1879 with a witness who  was a local bank-teller, George Eastman, later to become famous for the Kodak camera. His application included not only the engine but its use in a 4-wheeled car. He then filed a series of amendments to his application which stretched out the legal process resulting in a delay of 16 years before the patent.  *Wik

In the small town of Memphis, Michigan there is a roadside marker for another, and perhaps the earliest self-propelled four-wheeler in this great automobile state. It reads, "The Thing" was a self-propelled vehicle, powered by a steam engine, built in 1884-1885 by Thomas and John Clegg (father and son) in their Memphis machine shop. The historical marker states that The Thing was "the first recorded self-propelled vehicle in Michigan (and perhaps the country)" and that "It ran about 500 miles before Clegg dismantled it and sold the engine to a creamery."

*Wikipedia



In 1906, at 1:30 pm, Marie Curie gave her inaugural lecture as the first woman lecturer at the Sorbonne. She explained the theory of ions in gases and her treatise on radioactivity to 120 students, public and press. Following the accidental death of her husband, Pierre Curie, she had been invited to occupy the Physics chair at the Sorbonne that he had held. Madame Curie, by now a Nobel prize winner and authority on radioactivity, continued the work she started with her husband.*TIS





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1955 Doc Emmett Brown conceives of the Flux Capacitor which would power the time traveling DeLorean and the following Jules Verne Train in the "Back to the Future" movies. Brown came up with the idea of the flux capacitor after slipping and bumping his head while standing on his toilet to hang a clock. The idea came to him in a vision he had after being knocked out. He drew an inverted Y-shape with wires and stated "flux compression". He also performed some mild calculations on the paper. *Wik (HT to Colin@icecolbeveridge & @arbesman for the heads up on this one)  The flux capacitor can be seen lit up behind Marty just before temporal displacement.

1965 climate scientists summarized the risks associated with rising carbon pollution in a report for Lyndon Baines Johnson. "a section on atmospheric carbon dioxide and climate change, written by prominent climate scientists Roger Revelle, Wallace Broecker, Charles Keeling, Harmon Craig, and J Smagorisnky. Reviewing the document today, one can’t help but be struck by how well these scientists understood the mechanisms of Earth’s climate change 50 years ago." *theguardian.com

In 1992, the discovery of chemical evidence of 5000-year-old beer found at Godin Tepe in the Zagros mountains of Iran was reported in the journal Nature. Beer was the preferred fermented beverage of the ancient Sumerians. Chemical evidence was found from an organic residue inside a pottery vessel that had apparently been used for beer fermentation or storage. Some grooves were found inside the double-handled jar which contained a pale yellowish residue that gave a positive test for oxalate ion. Calcium oxalate, only slightly water-soluble is a principal component of sediment that settles from barley beer. In 1991, evidence for the earliest grape wine of had been found in the same area, and to be of similar age, about 3500 - 3100 BC. *TIS
Beer Receipt,  Alulu beer receipt recording a purchase of "best" beer from a brewer, c. 2050 BC, from the Sumerian city of Umma in ancient Iraq.  (Make it Lite, I'm trying to lose weight!)




2018  A second earth made vehicle has passed the boundaries of the heliosphere into the space between stars.  Seven years after Voyager 1 crossed the same boundary, Voyager 2 passed the heliopause with loads of new equipment to measure the physical nature of the space outside the heliosphere.  Light from our sun that reaches Earth in about 8 minutes, will need another 16+ hours to reach Voyager 2.  Path viewed from above the Solar System





BIRTHS

1846 Edward Singleton Holden (November 5, 1846 – March 16, 1914) was an American astronomer. Born in St. Louis, Missouri in 1846 to Jeremiah and Sarah Holden. From 1862-66, he attended Washington University in St. Louis, where he obtained a B.S. degree. He later trained at West Point in the class of 1870.In 1873 he became professor of mathematics at the US Naval Observatory, where he made a favorable impression on Simon Newcomb. He was director of Washburn Observatory at the University of Wisconsin–Madison from 1881 to 1885. He was elected a member of the American National Academy of Sciences in 1885.
On August 28, 1877, a few days after Asaph Hall discovered the moons of Mars Deimos and Phobos, he claimed to have found a third satellite of Mars. Further analysis showed large mistakes in his observations.
He was president of the University of California from 1885 until 1888, and the first director of the Lick Observatory from 1888 until the end of 1897. Meanwhile in 1893 while at the observatory he published a book on Mughal Emperors, The Mogul emperors of Hindustan, A.D. 1398- A.D. 1707. He resigned as a result of internal dissent over his management among his subordinates. While at the Lick Observatory, he was the founder of the Astronomical Society of the Pacific and its first President (1889–1891).
In 1901 he became the librarian of the United States Military Academy at West Point, where he remained until his death.
His cousin, George Phillips Bond, was director of Harvard College Observatory.
He discovered a total of 22 NGC objects during his work at Washburn Observatory.
He wrote many books on popular science (and on other subjects, such as flags and heraldry), including science books intended for children. For example the book Real Things In Nature. A Reading Book of Science for American Boys and Girls published in 1916.*Wik



1848 James Whitbread Lee Glaisher (5 November 1848 – 7 December 1928) son of James Glaisher, the meteorologist, was a prolific English mathematician. He was educated at St Paul's School and Trinity College, Cambridge, where he was second wrangler in 1871. Influential in his time on teaching at the University of Cambridge, he is now remembered mostly for work in number theory that anticipated later interest in the detailed properties of modular forms. He published widely over other fields of mathematics. He was the editor-in-chief of Messenger of Mathematics. *TIS



1866 Alfred Tauber (5 Nov 1866 in Pressburg, now Bratislava, Slovakia , 1942 in Theresienstadt, Germany now Terezin, Czech Republic) Tauber's research was on function theory and potential theory. He obtained important results on divergent series and the name 'Tauberian Theorems' was coined by Hardy and Littlewood. This all came out of his work on Abel's limit theorem which dated back to 1826. The conditions which Tauber gave to allow him to prove the converse of Abel's limit theorem on power series are now known as 'Tauberian conditions' and appeared in Ein Satz aus der Theorie der unendlichen Reihen (1897). This is by far his most significant piece of work. Further major results in this area were obtained by Norbert Wiener. Of lesser importance is Tauber's work on differential equations and the gamma function, but let us give the title of one of his papers on this latter topic, namely über die unvollständigen Gammafunktionen (1906). The date of his death is unknown. He was sent by the Nazis to Theresienstadt concentration camp on June 28 1942. Just after Tauber arrived the entire non-Jewish population of 3,700 of Theresienstadt was evacuated and he was one of 53,000 inhabitants of the camp. *SAU



1906 Fred Lawrence Whipple (5 Nov 1906; 30 Aug 2004) was an American astronomer who proposed the "dirty snowball" model for comet nuclei. In the 1930s, using a new, two-station method of photography, he determined meteor trajectories and found that nearly all visible meteors are made up of fragile material from comets, and that none come from beyond the solar system. Whipple suggested (1950) that comets have icy cores inside thin insulating layers of dirt, and that jets of material ejected as a result of solar heating were the cause of orbital changes. This model was confirmed in 1986 when spacecraft flew past comet Halley. Whipple’s work on tracking artificial satellites led to improved knowledge of the shape of the earth and greatly improved positions on earth. *TIS




1930 John Frank Adams (5 Nov 1930 in Woolwich, London, England - 7 Jan 1989 Near Brampton, Huntingdonshire, England) was an English algebraic topologist who pioneered methods for calculating the homotopy of spheres *SAU



1952 Robert Wayne Thomason (5 Nov 1952 Tulsa, Oklahoma, USA – Nov 1995 Paris, France) was an American mathematician who worked on algebraic K-theory. His results include a proof that all infinite loop space machines are in some sense equivalent, and his work on the Quillen–Lichtenbaum conjecture.*Wik



DEATHS

1526 Scipione del Ferro (6 February 1465 – 5 November 1526) was an Italian mathematician who first discovered a method to solve the depressed cubic equation. There are no surviving scripts from del Ferro. This is in large part due to his resistance to communicating his works. Instead of publishing his ideas, he would only show them to a small, select group of friends and students. It is suspected that this is due to the practice of mathematicians at the time of publicly challenging one another. When a mathematician accepted another's challenge, each mathematician needed to solve the other's problems. The loser in a challenge often lost funding or his university position. Del Ferro was fearful of being challenged and likely kept his greatest work secret so that he could use it to defend himself in the event of a challenge.
Despite this secrecy, he had a notebook where he recorded all his important discoveries. After his death in 1526, this notebook was inherited by his son-in-law Hannival Nave, who was married to del Ferro's daughter, Filippa. Nave was also a mathematician and a former student of del Ferro's, and he replaced del Ferro at the University of Bologna after his death. In 1543, Gerolamo Cardano and Ludovico Ferrari (one of Cardano's students) traveled to Bologna to meet Nave and learn about his late father-in-law's notebook, where the solution to the depressed cubic equation appeared.
Del Ferro also made other important contributions to the rationalization of fractions with denominators containing sums of cube roots.
He also investigated geometry problems with a compass set at a fixed angle, but little is known about his work in this area. *Wik



1800 Jesse Ramsden (6 Oct 1735, 5 Nov 1800) British pioneer in the design of precision tools. At 23, Ramsden chose to apprentice to a maker of mathematical instruments. By age 27 he had his own business in London and was known as the most skillful designer of mathematical, astronomical, surveying and navigational instruments in the 18th Century. He is best known for the design of a telescope and microscope eyepiece (ocular) still commonly used today and bearing his name. The French scientist N. Cassegrain proposed a design of a reflecting telescope in 1672. It was Ramsden, however, 100 years later, who found that this design reduces blurring of the image caused by the sphericity of the lenses or mirrors. He also built lathes, barometers, manometers and assay balances.
Sextant, brass, by Jesse Ramsden, c. 1770. In the Adler Planetarium and Astronomy Museum, Chicago. 37 × 38.5 × 10 cm, with a radius of 31 cm.



1857 Edmund Davy FRS (1785 – 5 November 1857) was a professor of Chemistry at the Royal Cork Institution from 1813 and professor of chemistry at the Royal Dublin Society from 1826. He discovered acetylene, as it was later named by Marcellin Berthelot. He was also an original member of the Chemical Society, and a member of the Royal Irish Academy. He was a cousin of Humphry Davy, and spent eight years as operator and assistant to Humphry Davy in the Royal Institution laboratory. (Humphry Davy's younger brother, Dr. John Davy, (24 May 1790 - 24 Jan 1868) also was a chemist who spent some time (1808–1811) assisting Humphry in his chemistry research at the Royal Institution. John was the first to prepare and name phosgene gas.) *Wik



1879 James Clerk Maxwell (13 Jun 1831, 5 Nov 1879)Scottish physicist and mathematician. Maxwell's researches united electricity and magnetism into the concept of the electro-magnetic field. In London, around 1862, Maxwell calculated that the speed of propagation of an electromagnetic field is approximately that of the speed of light. He proposed that the phenomenon of light is therefore an electromagnetic phenomenon. The four partial differential equations, now known as Maxwell's equations, first appeared in fully developed form in Electricity and Magnetism (1873). He died relatively young; some of the theories he advanced in physics were only conclusively proved long after his death. Maxwell's ideas also paved the way for Einstein's special theory of relativity and the quantum theory. *TIS



1934 Walther Franz Anton von Dyck (6 Dec 1856 in Munich, Germany - 5 Nov 1934 in Munich, Germany) Von Dyck made important contributions to function theory, group theory (where a fundamental result on group presentations is named after him), topology (where he was influenced by the work of Riemann), and to potential theory. He made significant contributions to the Gauss-Bonnet theorem.
Another important project which von Dyck undertook was one to publish the complete works of Kepler, including all Kepler's letters. He undertook this in his role as class secretary of the Bayerische Akademie der Wissenschaften in 1906. This project has extended well beyond von Dyck's lifetime with Volume 7 appearing in 1953, and Volume 8 in 1963. *SAU



1981 Stanisław Mazur (born 1 January 1905, Lviv - 5 November 1981, Warsaw) was a Polish mathematician and a member of the Polish Academy of Sciences. He made important contributions to geometrical methods in linear and nonlinear functional analysis and to the study of Banach algebras. Mazur was also interested in summability theory, infinite games and computable functions.
Mazur was a student of Stefan Banach at University of Lwów. His doctorate, under Banach's supervision, was awarded in 1935.
Mazur was a close collaborator with Banach at Lwów and was a member of the Lwów School of Mathematics, where he participated in the mathematical activities at the Scottish Café. On 6 November 1936, Mazur posed the "basis problem" of determining whether every Banach space has a Schauder basis, with Mazur promising a "live goose" as a reward: Thirty-seven years later, a live goose was awarded by Mazur to Per Enflo in a ceremony that was broadcast throughout Poland.*Wik





1992 Jan Hendrik Oort (28 Apr 1900, 5 Nov 1992) was a Dutch physicist and astronomer, one of the most important figures in 20th-century efforts to understand the nature of the Milky Way Galaxy, who measured the rotation of the earth's galaxy and hypothesized an "Oort Cloud." In 1927 Oort analyzed motions of distant stars, found evidence for differential rotation and founded the mathematical theory of galactic structure. After World War II, he led the Dutch group which used the 21-cm line to map hydrogen gas in the Galaxy. They found the large-scale spiral structure, the galactic center, and gas cloud motions. In 1950 Oort proposed the now generally accepted model for the origin of comets. He continued researching galaxies until shortly before his death at 92. *TIS



2005 Arthur Taylor Winfree (May 15, 1942 – November 5, 2002) was a theoretical biologist at the University of Arizona. He was born in St. Petersburg, Florida, United States.
Winfree was noted for his work on the mathematical modeling of biological phenomena: from cardiac arrhythmia and circadian rhythms to the self-organization of slime mold colonies and the Belousov–Zhabotinsky reaction. Winfree was a MacArthur Fellow from 1984 to 1989 and shared the 2000 Norbert Wiener Prize in Applied Mathematics with Alexandre Chorin. *Wik
Among numerous awards he was a Westinghouse Science Talent Search Finalist in 1960, a John Simon Guggenheim Memorial Fellowship awardee in 1982, and shared the AMS-SIAM Norbert Wiener Prize in Applied Mathematics with A. Chorin in 2000. His obituary in Siam began: "When Art Winfree died in Tucson on November 5, 2002, at the age of 60, the world lost one of its most creative scientists. I think he would have liked that simple description: scientist. After all, he made it nearly impossible to categorize him any more precisely than that. He started out as an engineering physics major at Cornell (1965), but then swerved into biology, receiving his PhD from Princeton in 1970. Later, he held faculty positions in theoretical biology (Chicago, 1969-72), in the biological sciences (Purdue, 1972-1986), and in ecology and evolutionary biology (University of Arizona, from 1986 until his death). " *SIAM
He was the father of Erik Winfree, another MacArthur Fellow and currently a professor at the California Institute of Technology, and Rachael Winfree, currently an Assistant Professor in the Department of Entomology at Rutgers University.




*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