## Thursday 30 November 2023

### On This Day in Math - November 30

Gilbert shall live, till Load-stones cease to draw,
Or British Fleets the boundless Ocean awe.
— John Dryden

The 334th day of the year
; 334 is an even semi-prime, and together with 335 they form a semi-prime pair. (There will be one more day this year that is part of a semi-prime pair, can you find it?)

D. R. Kaprekar  created the name "self number" for numbers that can not be made up as the sum of any number n and the sum of its digits. They are also called Colombian numbers or Devlali numbers. 1, 3, 5, 7, 9, 20, 31, are some of the smaller self-numbers, and of course, 334 is a self number.

334 in base three looks more like a binary number, its 110101. Students might explore other numbers in base three (or four or five) that look binary (ie only made up of zeros and ones).

EVENTS

3340 BC Our ancient Irish ancestors were expert astronomers, who carved images of an eclipse on ancient stone megaliths over 5000 years ago. November 30th 3340 BC: The world's oldest known solar eclipse was recorded in stone.
Substantially older than the recordings made in 2800 BC by the Chinese astronomers, it is situated at Loughcrew in Co Meath. The Irish Neolithic astronomer priests at this site recorded events on 3 stones relating to the eclipse, as seen from that location.
This is the only eclipse that fits these petroglyphs out of 92 solar eclipses tracked by the discoverer, Irish archaeoastronomer Paul Griffin. With none of the technology available to modern mankind, the Neolithic Irish constructed complex structures in stone which not only endured for five millennia, but were built so accurately that they still perform their astronomical functions today. Many historians believe the Celts created a “festival of light” to welcome an eclipse, which they were capable of predicting. *newgrange.com

1504 Leonardo Da Vinci, having descended into an obsession with squaring the cirle, perhaps as a result of his work on the geometric images for Pacioli's De Divina Proportione’ (around 1492-1494), writes a note alongside some of his geometric sketches, "The night of St Andrews Day I came to the end with the squaring of the circle: and it was the end of the light and the end of the night, and the paper on which I was writing."  It is not clear if he had given up his search, forever, or for the night, or mistakenly thought he had solved it.  While he didn't find anything new mathematically, he did rediscover a Pythagorean relation about lunes discovered by Alhazen in the 10th century, *David Richeson, Tales of Impossibility
The Lunes of Alhazen is an extension of an ancient Greek attempt to square the circle. Prove that the sum of areas of lunes AC and BC is equal to the area of the triangle ABC as shown below.

1536 Lodovico Ferrari arrived at Cardan's house on 30 November, a fourteen year old boy ready to take over his cousin Luke's position and become a servant. Cardan, upon the discovery that the lad could read and write, exempted him from menial tasks and appointed the youngster as his secretary. *SAU (Cardano gives this date as 14 November, and writes that Ludovico ("Luigi") and his brother (Luke?)arrived together. He noted that a magpie chirped in the courtyard so long they knew someone must be arriving. *Tales of Mathematicians and Physicists By Simon Gindikin)

In 1609, the modern face of the moon first emerged when Galileo Galilei in Padua turned his telescope toward the moon, noted the irregularities of the crescent face, and made a drawing to record his discoveries. He made at least five more drawings of the moon over the next eighteen days, prepared six careful watercolor sketches from these drawings, and then selected four of these to be engraved for his revolutionary Starry Messenger, which appeared the following March. Galileo's treatise announced to an astonished public that the moon was a cratered chunk of elements - a world - and not some globe of quintessential perfection. It was a new land, to be explored, charted, and named. *TIS  English mathematician Thomas Harriot had studied the moon four months earlier, but only saw a "strange spottednesse")
 *Wikipedia

1703 Newton made president of the Royal Society, an office he held until his death.*VFR

1710 John Machin was elected a Fellow of the Royal Society. *SAU

1712 William Jones elected fellow of the Royal Society. In 1706 he introduced the Greek letter π for the ratio of the circumfrence of a circle to a diameter in his book Synopsis palmariarum matheseos (1706). This title is hard to translate. Literally it means a synopsis of the palm leaves of mathematics. Thus it is a compendium of the most praisworthy parts of mathematics. Earlier William Oughtred (1647) and Isaac Barrow (1669) used the same symbol for twice the number. The symbol was not generally used in our sense until Euler, who adopted it in 1737, popularixed π in his Introductio in analysin inﬁnitorum of 1748. See DSB 7, 163, and “The ubiquitous π ” by Dario Castellanos, Mathematics Magazine 61(1988), 67–98, especially p. 91. A nice post by Thony Christie, at The Renaissance Mathematicus discusses Jones part in preserving John Collins Library.
The modern notation for 3.14159 .... was introduced in 1706. It was in that year that William Jones made himself noted, without being aware that he was doing anything noteworthy, through his designation of the ratio of the length of the circle to its diameter by the letter π. He took this step without ostentation. No lengthy introduction prepares the reader for the bringing upon the stage of mathematical history this distinguished visitor from the field of Greek letters. It simply came, unheralded, in the following prosaic statement (p. 263):

"There are various other ways of finding the Lengths or Areas of particular Curve Lines, or Planes, which may very much facilitate the Practice; as for instance, in the Circle, the Diameter is to the Circumference as 1 to , &c. = 3.14159, &c. = π. This series (among others for the same purpose, and drawn from the same Principle) I received from the Excellent Analyst, and my much esteem'd Friend Mr. John Machin; and by means thereof, Van Ceulen's Number, or that in Art. 64.38 may be Examin'd with all desirable Ease and Dispatch."

1720  María Andresa Casamayor (30 November 1720 , 23 October 1780) was the first Spanish woman to publish a science book. In March 1738, when only 17 years old, she published the arithmetic text Tyrocinio arithmético designed to facilitate the learning of basic arithmetic: addition, subtraction, multiplication and division.
She states on the title page that she is a "disciple of the Escuela Pía" and dedicates the Tyrocinio  to the same "Escuela Pía del Colegio de Santo Tomás de Zaragoza". One might ask how María Andresa can be a disciple of the Escuela Pía when their school only educated boys? Well, she does not admit to being a girl on the title page since the author of the book appears with a male name as Casandro Mamés de La Marca y Araioa. Those good at anagrams will see that in fact Casandro Mamés de La Marca y Araioa is simply an anagram of María Andresa Casamayor de La Coma.
In 2009, the City Council of Saragossa renamed a street in her honor  *SAU

============================================================================
1753 Benjamin Franklin received the Copley Medal, the highest honor of the Royal Society of London, for his “curious experiments and observations on electricity.” He was the ﬁrst American to receive the Copley Medal. Three years later he was elected a member of the Royal Society. *VFR
The Copley Medal is the Society’s oldest and most prestigious award. The medal is awarded for sustained, outstanding achievements in any field of science.

First awarded in 1731 following donations from Godfrey Copley FRS (PDF), it was initially awarded for the most important scientific discovery or for the greatest contribution made by experiment. The Copley Medal is thought to be the world's oldest scientific prize and it was awarded 170 years before the first Nobel Prize. Notable winners include Benjamin Franklin, Dorothy Hodgkin, Albert Einstein and Charles Darwin. The medal is of silver gilt, is awarded annually, alternating between the physical and biological sciences (odd and even years respectively), and is accompanied by a a gift of £25,000.

In 1784, American physician and scientist John Jeffries recorded the first scientific data for free air, to a height of 9,309-ft, during a balloon flight in London, England, including twelve observations of temperature, pressure, and humidity. Jeffries' values agree closely with modern determinations. Jeffries had provided himself with thermometer, barometer, electrometer, hygrometer and timepiece. He also took air samples at different elevations for Cavendish, who subsequently made a chemical analysis of the air. This was the first of two balloon flights Jeffries financed. He flew with Frenchman Jean Pierre Blanchard, who had experience in balloon flight. On 7 Jan 1785, they made the first balloon crossing of the English Channel.*TIS

1877 Luigi Bianchi received his degree in mathematics. His work on metric diﬀerential geometry found application in Einstein’s studies on relativity.*VFR

In 1904, the first electron tube, a diode thermionic valve, was invented by John Ambrose Fleming. The valve consists of a carbon or tungsten filament lamp, to which is added a metal plate (insulated from the filament), and a connecting wire brought through the glass wall of the bulb to a third terminal outside. When battery current is applied to the filament making it incandescent, the space between the filament and the insulated plate will be found to conduct electrons in only one direction. That means if the valve is connected in a circuit in with an oscillating current, its one-way conductivity will convert the oscillating current into a unidirectional current capable of actuating a telephone receiver. He notified Marconi in a 30 Nov 1904 letter.*TIS

1917 Bose Institute founded. Bose Institute is a research institute in the fields of Physics, Chemistry, Plant biology, Microbiology, Biochemistry, Biophysics, Animal physiology, Immunotechnology and Environmental science. The institute was established in 1917 by Acharya Jagdish Chandra Bose, who was the founder of modern scientific research in India. Bose Institute pioneered the concept of inter-disciplinary research in India in synch with global trends. Its alumni have achieved renown in India and the world.
Acharya Jagadish Chandra Bose founded the Institute on 30'th November 1917 with the following opening speech:
“I dedicate today this Institute as not merely a laboratory but a temple .... In the pursuit of my investigations I was unconsciously led into the border region of physics and physiology. To my amazement, I found boundary lines vanishing, and points of contact emerging, between the realms of the living and the non-living .... The lectures given here will not be mere repetitions of second-hand knowledge. They will announce new discoveries, demonstrated for the first time in these halls. Through regular publication of the work of the Institute, these Indian contributions will reach the whole world. They will become public property. No patents will ever be taken. The spirit of our national culture demands that we should forever be free from the desecration of utilizing knowledge only for personal gain."
*Wik

In 1954, in Sylacauga, Alabama, USA, Ann Hodges, 32, was bruised on the arm and hip by a meteorite that fell through the roof of her house into her living room. It smashed the case of her wooden radio and struck her as she lay resting on her sofa. The 9-lb (4-kg), 6 in (15 cm) diameter fragment came from a larger, likely more than 150-lb, chondrite meteorite that exploded over central Alabama about 2 pm, according to reports from people in several states that saw a bright flash across the sky. This remains (2006) the only recorded instance of a person being hit by a meteorite. She donated it in 1956 to the Alabama Museum of Natural History, and it is known by her name as the Hodges Meteorite.*TIS
I imagine Ms Hodges never heard "Stars Fell on Alabama" in quite the same way again.

1959 The first two IBM 7090 computers are delivered. Along with the faster version, which IBM released three years later, the series was a popular family of transistorized mainframes. Designed for scientific research and large-scale technological application, the computers were used in such projects as the Mercury and Gemini space flights and the Ballistic Missile Early Warning System. *CHM

1967 Ireland issued two stamps to commemorate the tercentenary of the birth of Jonathan Swift, author of Gulliver’s Travels. If you have read this book, then you know why this entry is included here; if you haven’t, then you should, and then you would. [Scott #240-241]. *VFR

BIRTHS

1549 Sir Henry Savile (30 Nov 1549 in Bradley (near Halifax), Yorkshire, England - 19 Feb 1622 in Eton, Berkshire, England) Savile was an English mathematician who founded professorships of geometry and astronomy at Oxford. It is interesting to read Savile's comments in these lectures on why he felt that mathematics at that time was not flourishing. Students did not understand the importance of the subject, Savile wrote, there were no teachers to explain the difficult points, the texts written by the leading mathematicians of the day were not studied, and no overall approach to the teaching of mathematics had been formulated. Of course, as we shall see below, fifty years later Savile tried to rectify these shortcomings by setting up two chairs at the University of Oxford. *SAU

1602 Otto von Guericke (originally spelled Gericke) (November 20, 1602 – May 11, 1686 (Julian calendar); November 30, 1602 – May 21, 1686 (Gregorian calendar)) was a German scientist, inventor, and politician. He is best remembered for his invention of the Magdeburg hemispheres, popularized in the writings of Caspar Schott. His major scientific achievements were the establishment of the physics of vacuums, the discovery of an experimental method for clearly demonstrating electrostatic repulsion, and his advocacy of the reality of "action at a distance" and of "absolute space". *Wik

1711 Ebenezer Kinnersley (30 Nov 1711; 4 Jul 1778) English-born American experimenter and inventor who investigated electricity. In 1748 Kinnersley demonstrated that the electric fluid actually passed through water, using a 10-ft long trough of water. In 1751, as one of the earliest popularizers of science, he began delivering lectures on "The Newly Discovered Electrical Fire." His experiments discovered the difference between the electricity that was produced by the glass and sulphur globes, which he communicated to Benjamin Franklin at Philadelphia, since they showed beyond a doubt that the positive and negative theory was correct. He also sought ways to protect buildings from lightning, invented an electric thermometer (c. 1755), and demonstrated that electricity can produce heat.*TIS

1756 Ernst Florens Friedrich Chladni (30 Nov 1756; 3 Apr 1827) German physicist, known as the "father of acoustics" for his mathematical investigations of sound waves. Chladni figures, seen when thin plates covered in sand at set in vibration, are complex patterns of vibration with nodal lines that remain stationary and retain sand. He demonstrated these to an audience of scientists in 1809. He measured the speed of sound in various gases by determining the pitch of the note of an organ pipe filled with different gases. To determine the speed of sound in solids, Chladni, used analysis of the nodal pattern in standing-wave vibrations in long rods. He performed on the euphonium, an instrument he invented, made of glass and steel bars vibrated by rubbing with a moistened finger. He also investigated meteorites.*TIS

1869 Nils Dalén (30 Nov 1869; 9 Dec 1837)Swedish engineer who won the Nobel Prize for Physics in 1912 for his invention of the automatic sun valve, or Solventil, which regulates a gaslight source by the action of sunlight, turning it off at dawn and on at dusk or at other periods of darkness. It rapidly came into worldwide use for buoys and unmanned lighthouses. While recovering from an accident, convalescing at home, he noticed how much time his wife spent caring for their wood-burning stove. He decided to invent a more efficient and cost-effective stove. In 1922, Dalen's Amalgamated Gas Accumulator Co. patented his design and put the first AGA stoves into production. These stoves produced a radiant heat that kept the kitchen warm. The AGA remains popular today.*TIS (My wife's favorite entry. Her first experience with an AGA was to turn materials for a pie into pure carbonized dust.)

1891 Edward Lindsay Ince (30 Nov 1891 in Amblecote, Staffordshire, England
- 16 March 1941 in Edinburgh, Scotland) Ince graduated from Edinburgh and researched at Edinburgh and Cambridge. He worked at universities in Leeds, Liverpool, Cairo, Edinburgh and Imperial College London before moving back to Edinburgh as Head of Technical Mathematics. He worked on Special Functions. *SAU

1910 Franz Leopold Alt (November 30, 1910 – July 21, 2011) was an Austrian-born American mathematician who made major contributions to computer science in its early days. He was best known as one of the founders of the Association for Computing Machinery, and served as its president from 1950 to 1952. *Wik

1936 Dmitri Victorovich Anosov (November 30, 1936 in Moscow,-Aug 5, 2014 ) is a Soviet and Russian mathematician, known for his contributions to dynamical systems theory.
He is a full member of the Russian Academy of Sciences and a laureate of the USSR State Prize (1976). He was a student of Lev Pontryagin.*Wik

DEATHS

1603 William Gilbert (24 May 1544, 30 Nov 1603) English scientist, the "father of electrical studies" and a pioneer researcher into magnetism, who spent years investigating magnetic and electrical attractions. Gilbert coined the names of electric attraction, electric force, and magnetic pole. He became the most distinguished man of science in England during the reign of Queen Elizabeth I. Noting that a compass needle not only points north and south, but also dips downward, he thought the Earth acts like a bar magnet. Like Copernicus, he believed the Earth rotates on its axis, and that the fixed stars were not all at the same distance from the earth. Gilbert thought it was a form of magnetism that held planets in their orbits. *TIS

# on Electricity to Queen Elizabeth I and her Court, 19th century

1647 (Francesco) Bonaventura Cavalieri (1598, 30 Nov 1647) Italian mathematician who made developments in geometry that were precursors to integral calculus. Cavalieri's theory of indivisibles, presented in his Geometria indivisibilis continuorum nova (1635) was a development of Archimedes' method of exhaustion incorporating Kepler's theory of infinitesimally small geometric quantities. The area and volume of various geometric figures can easily be found with this method. He was largely responsible for introducing logarithms as a computational tool in Italy through his book Directorium Generale Uranometricum, including logarithms of trigonometric functions for astronomers. He also wrote on optics and astronomy. Galileo thought highly of his writing, and corresponded with him. *TIS  (One of my persona; favorites)

1720 Pierre Jartoux (c1670; Embrun, France.- 30 Nov, 1720, Manchuria) known in China as Du Demei, Jartoux was a Jesuit Priest who went to live and work in China. His knowledge came to the attention of the Emperor and he was called to Peking (Beijing) to work in the calendar bureau. The emperor took notice of his skills in theoretical mathematics as well as with clocks and other mechanical devices. When not occupied at court, Jartoux ministered to Christians in the capital. In 1708 he assisted two Jesuit confreres, Joachim Bouvet and Jean-Baptiste Regis, in the first stages of making a map of the Chinese empire. His travels took him to the Great Wall north of the capital and throughout Manchuria, where he also ministered to the Christians. Illness forced him to return to Peking, where he began to collate the maps of the provinces in preparation for a general atlas. The final version was presented to the emperor one year after Jartoux died in Manchuria.
He is remembered here for his influence on the introduction of some Western mathematical ideas into the mathematical culture of China and Japan. In China his influence on shows in the 1759 work of Mei Juecheng, the Chishui yizhen (Pearls recovered from the Red River). This contained the infinite series expansion for sin(x) which was discovered by James Gregory and Isaac Newton. In fact it was Jartoux who introduced the infinite series for the sine into China in 1701 and it was known there by the name 'formula of Master Du'. In fact Pearls recovered from the Red River was one of two chapters that Mei Juecheng appended to the works of Mei Wending that he was editing and republishing. Mei Juecheng's study of the motion of the moon to provide improved predictions of eclipses of the moon used the best of European and Chinese astronomical data, and surpassed both cultures work.
In Japan, he was probably the source of the critical equation in the "yenri" (Circle Principle) presented by Takebe. His use of a "Wallis-like" infinite series was accompanied by a very unsatisfactory explanation of his development of the series. D. E. Smith and Mikami believe that he acquired the formula from Jartoux, who had passed on the same series (along with five others) to Mei Juecheng who added three to it in the above mentioned Chinese work. * SAU, Smith/Mikami "A History of Japanese Mathematics"

1761 John Dollond (10 Jun 1706, 30 Nov 1761) British maker of optical and astronomical instruments who developed (1758) and patented an achromatic (non- colour- distorting) refracting telescope and a practical heliometer, a telescope used to measure the Sun's diameter and the angles between celestial bodies. In the 1730's, Chester More Hall, an attorney with an interest in telescopes, first discovered that flint glass appeared to have a greater color dispersion than crown glass did at the same magnifications. Hall reasoned that if he cemented the concave face of a flint glass lens to the convex face of a crown glass lens, he could remove the dispersion properties (and thus, chromatic aberration) from both lenses simultaneously. Dollond learned of the technique in the 1750's and developed it.*TIS

Dollond patented the achromatic doublet, which combines crown glass and flint glass.

1836 Pierre-Simon Girard (Caen, 4 November 1765 – Paris, 30 November 1836) was a French mathematician and engineer, who worked on fluids.
A prodigy who invented a water turbine at age 10, Girard worked as an engineer at the École Nationale des Ponts et Chaussées. He was in charge of planning and construction of the Amiens canal and the Ourcq canal. He collaborated with Gaspard de Prony on the Dictionnaire des Ponts et Chaussées (Dictionary of Bridges and Highways). He wrote works on fluids and on the strength of materials.*Wik
 *Linda Hall Org

1850 Germain Henri Hess (7 Aug 1802, 30 Nov 1850) Swiss-born Russian chemist whose studies of heat in chemical reactions formed the foundation of thermochemistry. He formulated an empirical law, Hess's law of constant heat summation (1840), which states that the heat evolved or absorbed in a chemical process is the same whether the process takes place in one or in several steps. It is explained by thermodynamic theory, which holds that enthalpy is a state function. Chemists have made great use of the law of Hess in establishing the heats of formation of compounds which are not easily formed from their constituent elements. His early investigations concerned minerals and the natural gas found near Baku, and he also discovered the oxidation of sugars to yield saccharic acid.*TIS

1921 Hermann Amandus Schwarz (25 Jan 1843 in Hermsdorf, Silesia (now Poland)
- 30 Nov 1921 in Berlin, Germany) Schwarz worked on the conformal mapping of polyhedral surfaces onto the spherical surface and on a problem of the calculus of variation, namely surfaces of least area. In 1870 he produced work related to the Riemann mapping theorem. Although Riemann had given a proof of the theorem that any simply connected region of the plane can be mapped conformally onto a disc, his proof involved using the Dirichlet problem. Weierstrass had shown that Dirichlet's solution to this was not rigorous, see for details. Schwarz's gave a method to conformally map polygonal regions to the circle. Then, by approximating an arbitrary simply connected region by polygons he was able to give a rigorous proof of the Riemann mapping theorem. Schwarz also gave the alternating method for solving the Dirichlet problem which soon became a standard technique.
His most important work is a Festschrift for Weierstrass's 70th birthday. Schwarz answered the question of whether a given minimal surface really yields a minimal area. An idea from this work, in which he constructed a function using successive approximations, led Émile Picard to his existence proof for solutions of differential equations. It also contains the inequality for integrals now known as the 'Schwarz inequality', *SAU

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

## Wednesday 29 November 2023

### Too Nice to Ignore, Gravity and Bernoulli's Lemniscate

 *Wik
Two stories intersect here, one a famous event from the history of calculus that most folks are familiar with, and one that seems not to make it much into classrooms and that I only learned about today.
Almost every student of mathematics will sooner or later come across the beautiful problem of the Brachistochrone, which in Greek means "shortest time." It is the path that will carry a point-like body from one place to another in the least amount of time under the force of constant gravity. Given two points A and B, with A not lower than B, only one upside down cycloid passes through both points, has a vertical tangent line at A, and has no maximum points between A and B: the brachistochrone curve. The curve does not depend on the body's mass or on the strength of the gravitational constant.

The story goes that Johann Bernoulli posed the problem to readers of Acta Eruditorum in June, 1696. He published his solution along with four other solutions from Newton, Jakob Bernoulli, Gottfried Leibniz, and Ehrenfried Walther von Tschirnhaus. ( l'Hôpital also seems to have had a correct solution, but it was not published).

Newton historians claim that Newton received the problem in the mail one afternoon after returning from his job at the mint (so this would be after he was older). The story goes that he solved it overnight, and posted it the next morning. Since it took weeks for some of the others to solve it, we may assume that Newton was still a pretty good mathematician well after his known prime.

A footnote to this story, in the epic novel Moby Dick, "Ishmael thinks about them while cleaning the try-pots (giant cauldrons in which whale blubber is rendered) on the deck of the Pequod.  It was in the ...trypot with the soapstone diligently circling around me, that I was first struck by the remarkable fact, that in geometry all bodies gliding along the cycloid, ...,will descend from any point in precisely the same time."
How would Melville's modest education bring him this incredible math fact.  A possible answer.....Joseph Henry, you know, the guy for whom the unit of inductance is named.
It is almost certain that the limited public school education of Melville would not include this fact.  Most high school students today would never be introduced to it.  But in Melville's brief time at the Albany Academy it was said that Herman excelled in "ciphering" and won the school prize.  Perhaps his interest in geometry and such was inspired by an outstanding teacher, and former alumni of the Albany Academy, young Joseph Henry.

(Once Upon A Prime by Sarah Hart)

Ok, so that's the one everybody knows about. But I was just fixing up some notes on the life of Gian Francesco Malfatti, whose date of death was, well, today, in 1807. Now Malfetti did some nice stuff, too. He did some really important work on fifth degree equations; but he is best known for a geometry problem about three mutually tangent circles inscribed in a triangle. He posed the problem of as how to
,
 *Mathworld
carve three circular columns out of a triangular block of marble, using as much of the marble as possible. He thought the solution was described by the triangle problem. The Geometry problem of constructing three circles each tangent to each other and two sides of the triangle is now generally known as Malfatti's problem, even though he didn't do it first, Japanese geometer Chokuen Ajima beat him too it.  (Both the earliest solutions, I'm told, used a combination of geometry and algebra, but it seems Steiner did show how to do it with pure geometric methods). What's worse is that it wasn't even the solution to the physical problem of the columns he was trying to show. Around 1930 someone proved that it wasn't always the best solution, and then in the 60's, M. Goldberg showed it was NEVER the best solution.

Then while checking some dates on his Wikipedia entry, I noticed something else he had done, the something I had never heard of, and this time he was right. He was working with the lemniscate (it means ribbon) first described in 1694 by Jakob Bernoulli, and he noticed an interesting gravitational relationship about it. If you draw a chord (pick a chord, any chord... ok; sorry) through the center and any other point on the lemniscate, then a point acting under the influence of gravity will reach that point of intersection at the same moment, whether it travels down the chord, or around the lemniscate. Now that just seems to nice to have ignored in math and calculus classrooms. If you are a teacher, maybe the next time you talk about the brachistochrone, (or maybe tomorrow when they need a diversion) you should point out this little beauty, also.

### On This Day in Math - November 29

I did try to make things clear, first to myself and then to my students,
and somehow to make these dry bones live.
~Horace Lamb

The 333rd day of the year; There are 333 possible hexagonal polyominoes with seven cells.

333 is a base ten palindrome, and also a palindrome in base 8,

If you add the smallest primes containing each of the digits 0 to 9, the sum is 333. 101 + 11 + 2 + 3 + 41 + 5 + 61 + 7 + 83 + 19=333

Of course you know that 32 + 42 = 52, but did you know that 332 + 442= 552 and  3332 + 4442 = 5552.... and the magic doesn't end there.

EVENTS

1114 An Earthquake devastated the town of Antioch in Turkey. In the suburb of Mamistra, the young mathematician, Adelard of Bath, freshly to the Middle East to study the wisdom of the Arabs, clung to a stone bridge in fear for his life. *Jonathan Lyons, The House of Wisdom: How the Arabs Transformed Western Civilization

1813 Iodine was discovered on this date. The discovery was made during the process of producing potassium nitrate for gunpowder and was made public in a meeting of the Imperial Institute of France. Its name is derived from the Greek 'iodes' meaning violet. *.rsc.org

Iodine is a chemical element; it has symbol I and atomic number 53. The heaviest of the stable halogens, it exists at standard conditions as a semi-lustrous, non-metallic solid that melts to form a deep violet liquid at 114 °C (237 °F), and boils to a violet gas at 184 °C (363 °F). The element was discovered by the French chemist Bernard Courtois in 1811 and was named two years later by Joseph Louis Gay-Lussac
 *Wik

1877 It was on this day, November 29, 1877, that Thomas Edison demonstrated his hand-cranked phonograph. *Thomas Robb
Charles Cros, a French poet and amateur scientist, is the first person known to have made the conceptual leap from recording sound as a traced line to the theoretical possibility of reproducing the sound from the tracing and then to devising a definite method for accomplishing the reproduction. On April 30, 1877, he deposited a sealed envelope containing a summary of his ideas with the French Academy of Sciences, a standard procedure used by scientists and inventors to establish priority of conception of unpublished ideas in the event of any later dispute. #Wik

1907 Florence Nightingale was presented with the Order of Merit. *@EnglishHeritage (Thony Christie ‏@rmathematicus advised me that, "One is not presented with the Order of Merit one is appointed to it; it's a membership." )

In 1932, a U.S. patent was issued for the first card game table with an automatic dealing device, to Laurens Hammond of Chicago, Ill. (No. 1,889,729), who later invented the Hammond organ. When cards were played in a recessed tray, four shuffled 13-card bridge hands were delivered to the players. A rotary mechanism built within the square game table had an arm with a rubber tip to pick up and carry cards from the deck to the player. The destination hand was controlled by a serrated wheel with varied notch depths in 52 positions. A deal took about one minute. Marketed for a few years from 1932, the invention was an attempt to diversify Hammond's declining clock business during the depression-era, but sold poorly.*TIS

1960 Digital Equipment Company (DEC) announces the PDP-1, the ﬁrst computer with a video display terminal. *VFR
The PDP-1 is the original hardware for playing history's first game on a minicomputer, Steve Russell's Spacewar!

PDP-1 exhibit at the Computer History Museum in Mountain View, California
 *CHM

1972 Atari Corporation announces Pong, an early video game popular both at home and at video arcades. In Pong, players were represented by paddles that could move up and down to try to deflect a ball and keep it from passing into their goal. Despite simplistic graphics, Pong started a craze. Atari, founded by Nolan Bushnell, sold video games as well as computers on which to play the games. (Oh for the days of REAL video games!")*TIS

BIRTHS

1803 Christian Doppler (29 Nov 1803; 17 Mar 1853) Austrian physicist who first described how the observed frequency of light and sound waves is affected by the relative motion of the source and the detector, known as the Doppler effect. In 1845, to test his hypothesis, Doppler used two sets of trumpeters: one set stationary at a train station and one set moving on an open train car, all holding the same note. As the train passed the station, it was obvious that the frequency of the notes from the two groups didn't match. Sound waves would have a higher frequency if the source was moving toward the observer and a lower frequency if the source was moving away from the observer. Edwin Hubble used the Doppler effect of light from distant stars to determine that the universe is expanding.*TIS

Experiment by Buys Ballot (1845) depicted on a wall in Utrecht (2019)

1849 Sir John Ambrose Fleming (29 Nov 1849; 18 Apr 1945) English engineer who made numerous contributions to electronics, photometry, electric measurements, and wireless telegraphy. In 1904, he discovered the one directional current effect between a positively biassed electrode, which he called the anode, and the heated filament in an evacuated glass tube; the electrons flowed from filament to anode only. Fleming called the device a diode because it contained two electrodes, the anode and the heated filament. He noted that when an alternating current was applied, only the positive halves of the waves were passed - that is, the wave was rectified (from a.c. to d.c.). It would also take a radio frequency wave and produce d.c.corresponding to the on and off of the Morse code transmitted signals.*TIS

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

1849 Horace Lamb (29 Nov 1849 in Stockport, England - 4 Dec 1934 in Cambridge, England) wrote important texts and made important contributions to applied mathematics, in particular to acoustics and fluid dynamics. Describing his own teaching at the celebrations for his eightieth birthday, Lamb said, "I did try to make things clear, first to myself (an important point) and then to my students, and somehow to make these dry bones live." *SAU

1866 Ernest (William) Brown (29 Nov 1866; 22 July 1938) was a British astronomer who devoted his career to the theory of the Moon's motion and constructing accurate lunar tables. His theory took account of "the gravitational action of every particle of matter which can have a sensible effect on the Moon's motion," some 1500 terms. He then determined the numerical values of the constants by analyzing 150 years of Greenwich observations, and computed tables accurate to 0.01 arcsec. After 30 years of work, Brown published his lunar tables Tables of the Motion of the Moon in 1919. In 1926 Brown published a paper in which he ascribed fluctuations in the Moon's motion to irregular changes in the Earth's period of rotation, which has subsequently proved correct.*TIS

1879 Nikolai Mitrofanovich Krylov (29 Nov 1879 in St Petersburg, Russia - 11 May 1955 in Moscow, USSR) was a Russian mathematician who published over 200 papers on analysis and mathematical physics. *SAU

1892 Dr. Gustav Doetsch (November 29, 1892 – June 9, 1977) was a German mathematician, aviation researcher, decorated war veteran, and became a enthusiastic Nazi supporter. The modern formation and permanent structure of the Laplace transform is found in Doetsch's 1937 work Theorie und Anwendung der Laplace-Transformation, which was well-received internationally. He dedicated most of his research and scientific activity to the Laplace transform, and his books on the subject became standard texts throughout the world, translated into several languages. His texts were the first to apply the Laplace transform to engineering. *Wik

1952 John David Barrow FRS (29 November 1952 – 26 September 2020) is an English cosmologist, theoretical physicist, and mathematician. Hewas  Research Professor of Mathematical Sciences at the University of Cambridge. Barrow is also a writer of popular science and an amateur playwright.
In 1981 he joined the University of Sussex and rose to the rank of Professor and Director of the Astronomy Centre. In 1999, he became Professor in the Department of Applied Mathematics and Theoretical Physics and a fellow in Clare Hall at Cambridge University. He is Director of the Millennium Mathematics Project. From 2003–2007 he was Gresham Professor of Astronomy at Gresham College, London, and he has been appointed as Gresham Professor of Geometry from 2008–2011; only one person has previously held two different Gresham chairs. In 2008, the Royal Society awarded him the Faraday Prize.
Barrow died on 27 September 2020 from  colon cancer at the age of 67.  *Wik

1959 Richard Ewen Borcherds (29 Nov 1959, ) British mathematician who won the Fields Medal in 1998 for his for his work in the fields of algebra and geometry, in particular for his proof of the so-called Moonshine conjecture. This conjecture had been formulated at the end of the '70s by the British mathematicians John Conway and Simon Norton and presents two mathematical structures in such an unexpected relationship that the experts gave it the name "Moonshine." In 1989, Borcherds was able to cast some more light on the mathematical background of this topic and to produce a proof for the conjecture. The Moonshine conjecture provides an interrelationship between the so-called "monster group" and elliptic functions. *TIS

DEATHS

1687 Nicolaus(I) Bernoulli (21 Oct 1687 in Basel, Switzerland - 29 Nov 1759 in Basel) Nicolaus Bernoulli was one of the famous Swiss family of mathematicians. He is most important for his correspondence with other mathematicians including Euler and Leibniz. *SAU (Can't tell your Bernoulli's without a scorecard? Check out "A Confusion of Bernoulli's" by the Renaissance Mathematicus.

1872 Mary Fairfax Greig Somerville (26 Dec 1780 in Jedburgh, Roxburghshire, Scotland
- 28/29 Nov 1872 in Naples, Italy) Somerville wrote many works which influenced Maxwell. Her discussion of a hypothetical planet perturbing Uranus led Adams to his investigation. Mary Somerville was a strong supporter of women's education and women's suffrage. When John Stuart Mill, the British philosopher and economist, organised a massive petition to parliament to give women the right to vote, he had Mary put her signature first on the petition.Somerville College in Oxford was named after her.*SAU

1920 Thomas Bond Sprague (29 March 1830 in London, England - 29 Nov 1920 in Edinburgh, Scotland) studied at Cambridge and went on to become the most important actuary of the late 19th Century. He wrote more than 100 papers including many in the Proceedings of the EMS. *SAU

1953 Ernest Barnes (1 April 1874 in Birmingham, England - 29 Nov 1953 in Sussex, England) In all, Barnes wrote 29 mathematical papers during the years 1897-1910. His early work was concerned with various aspects of the gamma function, including generalisations of this function given by the so-called Barnes G-function, which satisfies the equation G(z+1)=G(z)Γ(z) and to the double gamma function. Barnes next turned his attention to the theory of integral functions, where, in a series of papers, he investigated their asymptotic structure. He also considered second-order linear difference equations connected with the hypergeometric functions. In the last five of his papers dealing with the hypergeometric functions, Barnes made extensive use of the integrals studied by Mellin in which the integral. *SAU
He was bracketed Second Wrangler in 1896 and was placed in the first division of the first class in Part II of the Mathematical Tripos in 1897. In the following year he was awarded the first Smith's Prize and was duly elected to a Trinity Fellowship.
He was an uncompromising pacifist,[12] and spoke out against British participation in the Second World War. He also expressed eugenic views.[13] Though a member of the Eugenic Society from 1924 until his death in 1953, it was not until after the Second World War that he openly argued in favour of voluntary sterilisation as a means to overcome the apparent prevalence of "mental deficiency" in society.

1992 Jean Dieudonné (1 Jul 1906, 29 Nov 1992) French mathematician and educator known for his writings on abstract algebra, functional analysis, topology, and his theory of Lie groups. Dieudonné was one of the two main contributors to the Bourbaki series of texts. He began his mathematical career working on the analysis of polynomials. He worked in a wide variety of mathematical areas including general topology, topological vector spaces, algebraic geometry, invariant theory and the classical groups. *TIS

*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