Wednesday, 11 March 2026

Fifteen Peg Puzzle Solution is Prime

From 2012


The puzzle shown above, often called a triangular peg solitaire game is so common you may have last seen it on your table at Cracker Barrel Restaurants.
Below I will give a solution to a common form of the puzzle, so don't look too far below if you want to test out your skills without clues or a solution. If you want to play the online version of the game, try your luck here




If you get really interested, you can try games removing any one of the pegs instead of a corner (which is NOT the easiest possible solution).    If you get frustrated, here are some good hints about the game from an excellent page by George Bell.





Note the symmetry of the triangular board: there are three corner holes (red), three interior holes (green), and three holes at the midpoint of each edge (blue), plus six "other" holes (yellow).
The following rules of thumb are based on a mathematical analysis of the game and should help you solve the puzzle


  1. Avoid jumping into a corner. Of course, in some situations (such as beginning without a corner peg) this is the only jump possible.
  2. Avoid any jump which starts from one of the green interior holes. Such a move is almost always a dead end (none of the solutions on the next page include this jump).
  3. The easiest place to begin the game is with the missing peg (hole) at one of the blue midpoint locations. The hardest place to begin is with the missing peg at one of the green interior holes. 


Complete solution below:::


The truth is, there are thousands of possible solutions to the game. The solution I just came across is for the case in which you start with the top corner (the one hole) empty, and finish with a single peg in that hole (which I just learned is called a single vacancy complement solution). If you number the holes starting at an apex of the triangle with one, then two and three on the next row, and continue with 11 through 15 on the bottom row, then moves can be described with (x,y) coordinates where the term (x,y) means move the peg in hole x to hole y.
A winning solution to the 15-hole triangular peg solitaire game using this method is: (4,1), (6,4), (15,6), (3,10), (13,6), (11,13), (14,12), (12,5), (10,3), (7,2), (1,4), (4,6), (6,1).

Not only does this solution leave the final peg in the original empty hole, but the sum of all the x,y hole numbers in the solution is prime (179) and if I time this right it should be first posted on the 179th day of the year 2012. By the way, if you only sum the values of the landing holes, that's prime also (73).

I first came across this curious little fact at the Prime Curios page.

Haven't pursued it yet, but since there are thousands of solutions to this puzzle, I assume that there would be other sequences which produced a prime also.

Good luck, and share the ones that you find with me.



On This Day in Math - March 11

  

*Wik


If scientific reasoning were limited to the logical processes of arithmetic, we should not get very far in our understanding of the physical world. One might as well attempt to grasp the game of poker entirely by the use of the mathematics of probability.
~Vannevar Bush


The 70th day of the year; 70 is the smallest "Weird" number. In number theory, a weird number is a natural number that is abundant but not semiperfect. In other words, the sum of the proper divisors (divisors including 1 but not itself) of the number is greater than the number, but no subset of those divisors sums to the number itself.

270 = 1180591620717411303424. The sum of the digits is 70, and if you reverse the order, 424303114717026195081,  it is a prime #.


All the primes in the 70's, are emirps, primes that are still prime when you reverse the order of the digits, 71----17 etc.

\( 1^2 + 2^2 + 3^2 + \cdots + 24^2 = 70^2 \)

Several languages, especially ones with vigesimal(base 20) number systems, do not have a specific word for 70: for example, French soixante-dix "sixty-ten"; Danish halvfjerds, short for halvfjerdsindstyve "three and a half score". (For French, this is true only in France; other French-speaking regions such as Belgium, Switzerland, Aosta Valley and Jersey use septante.) *Wik 


70 is the second smallest number where the sum of its divisors is a perfect square.  \(1 + 2 + 5 + 7 + 10 + 14 + 35 + 70= 12^2 = 144\)  There are only three year dates (to my knowledge)  for which the sum of the divisors is a square.  



EVENTS

1574 By means of an equinoctial armillary which he constructed on the facade of the church of Santa Maria Novella, Egnatio Danti observed that the vernal equinox occurred eleven days earlier than it should have according to the Julian Calendar. This is one of the many events which led to the Gregorian calendar reform of 1584. *VFR

*Renaissance Mathematicus

 

1582 At noon the sun shone in through the mouth of the South Wind, a mural on one wall, and crossed the meridional sundial line in the Meridian Room in the Tower of Winds in Rome. This should have happened on March 21, so Pope Gregory VIII was (supposedly) convinced of the need for calendar reform. *Sky and Telescope, 64(1982), 530–533






1672 Robert Hooke FRS started writing his ‘Memoranda’, as he called his daily entries, on 10 March 1672. There’s no clear statement about why he started this project, just the terse entry ‘Memoranda begun’, followed by some characteristically abrupt notes about the weather and so on. It’s worth reproducing the whole of his first entry here:
Sun. 10 [mercury] fell from 170 to 185. most part of ye Day cleer but cold & somewhat windy at the South. [I was this morning better with my cold then I had been 3 months before] [moon] apogeum. It grew cloudy about 4. [mercury] falling still.
I told Cox how to make Reflex glasses by Silver and hinted to him making them by printing. Hewet brought me £10 from Brother John Hooke. News of 3 empty Dutch ships taken by ye montacu frigat
*Robert Hooke's London
1680 Portrait of a Mathematician by Mary Beale, conjectured to be of Hooke but also conjectured to be of Isaac Barrow




1702  The UK’s first daily newspaper hit the streets on this day. Called The Daily Courant, it owed its appearance to the fact that control of the Press by the Government had been abandoned some five years earlier. The Courant also owed its existence to a remarkable and determined woman – Elizabeth Mallet, the newspaper’s first proprietor and editor.




1711 Robert Simson, who had no formal training in mathematics, was elected to the chair of mathematics at the University of Glasgow on the condition that “he give satisfactory proof of his skill in mathematics previous to his admission.” *VFR He must have proved his skill as he held the position until 1761. The pedal line is often called the Simson line.





1782 Euler writes to accept membership in the American Academy of Arts and Sciences. He was the first foreign member. 

1794 At the instigation of Monge the Ecole Polytechnique was founded. *VFR The Polytechnique was established during the French Revolution, it became a military school under Napoleon in 1804. It is still under the control of French Ministry of Defense today.

In 1811, the Luddite riots began in Nottingham, England. There was poverty and misery, made worse by the new inventions - machinery which could do jobs better and faster than people. In those days of low wages and the ever-present threat of actual starvation should those wages stop for any reason, these innovations must have made the prospect even more gloomy. There were food shortages resulting from the Napoleonic Wars, and high unemployment. A group of laborers attacked a factory, breaking up 63 stocking and lace manufacturing frames, the machines which they feared would replace them. During the next three weeks gangs of upwards of fifty men, armed with pistols, guns and heavy hammers broke two hundred more frames. *TIS
Nottingham’s textile workers claimed to be following the orders of a mysterious “General Ludd.” Merchants received threatening letters addressed from “Ned Ludd’s office, Sherwood Forest.” Newspapers reported that Ludd had been a framework knitting apprentice who had been whipped at the behest of his master and took his revenge by demolishing his master’s machine with a hammer.

Ned Ludd, however, was likely no more real than another legendary denizen of Sherwood Forest who fought against injustice, Robin Hood. Mythic though he may have been, Ned Ludd became a folk hero in parts of Nottingham and inspired verses such as:

Chant no more your old rhymes about bold Robin Hood

His feats I but little admire

I will sing the Achievements of General Ludd

Now the Hero of Nottinghamshire  *History





1878 Shortly after Edison developed his phonograph, the French Academy of Sciences had it demonstrated by the Count du Moncel.  Edison's French licensee was represented by a man named Puskas who set in front of the committee and spoke into the phonograph, then fitted a large horn to the device for amplification and to the astonishment of all they heard the phonograph express its pleasure at being presented to the Academy in Puskas' nasal American-French.  
Some were more astonished than others.  Physician Jean Bouillard, 82, confronted Puskas for his Parlor trick as no machine could produce accents.  To calm, and convince the doctor, Moncel himself set down and spoke into the machine, "We thank Mr Edison for having sent us his phonograph." When du Moncel's words were reproduced in his Parisian French accent, the Doctor was convinced.  




BIRTHS

1780 August Leopold Crelle (11 Mar 1780; died 6 Oct 1855 at age 75). Although always interested in mathematics he lacked the money to enroll at a university and so became an engineer instead. In 1826, when he had the money, he founded the Journal f¨ur die rein und angewandte Mathematik and edited fifty two volumes. Although not a great mathematician he had a gift for recognizing the abilities of such men as Abel, Jacobi, Steiner, Dirichlet, Pl¨ucker, M¨obius, Eisenstein, Kummer, and Weierstrass and offered to publish their papers in his journal. *VFR As a civil engineer in the service of the Prussian Government and worked on the construction and planning of roads and the first railway in Germany (completed in 1838). He founded (1826) the world's oldest mathematical periodical still in existence, Journal für die reine und angewandte Mathematik ("Journal for Pure and Applied Mathematics"), now known as Crelle's Journal,and edited it for the rest of his life. *TIS





1811 Urbain-Jean-Joseph Le Verrier (11 Mar 1811; 23 Sep 1877 at age 66) French astronomer who predicted by mathematical means the existence of the planet Neptune. He switched from his first subject of chemistry to to teach astronomy at the Ecole Polytechnique in 1837 and worked at the Paris Observatory for most of his life. His main activity was in celestial mechanics. Independently of Adams, Le Verrier calculated the position of Neptune from irregularities in Uranus's orbit. As one of his colleagues said, " ... he discovered a star with the tip of his pen, without any instruments other than the strength of his calculations alone. In 1856, the German astronomer Johan G. Galle discovered Neptune after only an hour of searching, within one degree of the position that had been computed by Le Verrier, who had asked him to look for it there. In this way Le Verrier gave the most striking confirmation of the theory of gravitation propounded by Newton. Le Verrier also initiated the meteorological service for France, especially the weather warnings for seaports. Incorrectly, he predicted a planet, Vulcan, or asteroid belt, within the orbit of Mercury to account for an observed discrepancy (1855) in the motion in the perihelion of Mercury. *TIS (A nice blog about Le Verrier is at the Renaissance Mathematicus blog.)
I was reminded that as much as we appreciate his work in discovering Neptune, we should not overlook that his very first paper on astronomy submitted to The Academy of sciences was on 

Statue of Le Verrier at the Paris Observatory was On the Secular Variations of the Orbits of the Planets.  It was in this paper , presented on September 16, 1839 that he became the first person to compute the eigen vectors of a matrix. *Hat Tip to Alain Juhel






1822 Joseph-Louis-François Bertrand (11 Mar 1822; 5 Apr 1900 at age 78) was a French mathematician and educator and educator remembered for his elegant applications of differential equations to analytical mechanics, particularly in thermodynamics, and for his work on statistical probability and the theory of curves and surfaces. In 1845 Bertrand conjectured that there is at least one prime between n and (2n-2) for every n greater than 3, as proved five years later by Chebyshev. It is not clear to me if he was the one who suggested the jingle
I've told you once and I'll tell you again
There's always a prime between n and 2n.
In 1855 he translated Gauss's work on the theory of errors and the method of least squares into French. He wrote a number of notes on the reduction of data from observations. *TIS At age 11 he started to attend classes at the Ecole Polytechnique, where his Uncle Duhamel was a well-known professor of mathematics. At 17 he received his doctor of science degree. *VFR
In combinatorics, Bertrand's ballot problem is the question: "In an election where candidate A receives p votes and candidate B receives q votes with greater than q, what is the probability that A will be strictly ahead of B throughout the count?" which Bertrand asked, and proved in 1887 in Comptes Rendus de l'Académie des Sciences.
The answer is   \frac{p-q}{p+q}.




1832  Mary Everest Boole (11 March 1832 in Wickwar, Gloucestershire – 17 May 1916 in Middlesex, England) was a self-taught mathematician who is best known as an author of didactic works on mathematics, such as Philosophy and Fun of Algebra, and as the wife of fellow mathematician George Boole. Her progressive ideas on education, as expounded in The Preparation of the Child for Science, included encouraging children to explore mathematics through playful activities such as curve stitching. Her life is of interest to feminists as an example of how women made careers in an academic system that did not welcome them.
Mary Everest was born in England, the daughter of Reverend Thomas Roupell Everest, Rector of Wickwar, and Mary nee Ryall. Her uncle was George Everest, the surveyor and geographer after whom Mount Everest was named. She spent the first part of her life in France where she received an education in mathematics from a private tutor. On returning to England at the age of 11, she continued to pursue her interest in mathematics through self-instruction. Self-taught mathematician George Boole tutored her, and she visited him in Ireland where he held the position of professor of mathematics at Queen's College Cork. Upon the death of her father in 1855, they married and she moved to Cork. Mary greatly contributed as an editor to Boole's The Laws of Thought, a work on algebraic logic. She had five daughters with him. *Wik
For more about Mary Boole and her incredible offspring see, Those Amazing Boole Girls.
From left to right, from top to bottom:
 Margaret Taylor, Ethel L. Voynich, Alicia Boole Stott, Lucy E. Boole, Mary E. Hinton,
Julian Taylor, Mary Stott, Mary Everest Boole, George Hinton,
 Geoffrey Ingram Taylor, Leonard Stott.



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




1853 Salvatore Pincherle (11 March 1853 in Trieste, Austria (now Italy)-10 July 1936 in Bologna, Italy) worked on functional equations and functional analysis. Together with Volterra, he can claim to be one of the founders of functional analysis. Pincherle contributed to the development and dissemination of Weierstrass's development of a theory of analytic functions. He wrote an expository paper in 1880 which was published in the Giornale di Matematiche which was inspired by the lectures of Weierstrass. This work is important both in the development of analysis and in particular the progress of mathematics in Italy. *SAU

He contributed significantly to (and arguably helped to found) the field of functional analysis, established the Italian Mathematical Union (Italian: "Unione Matematica Italiana"), and was president of the Third International Congress of Mathematicians. The Pincherle derivative is named after him.




1870 Louis Jean-Baptiste Alphonse Bachelier (March 11, 1870 – April 28, 1946) was a French mathematician at the turn of the 20th century. He is credited with being the first person to model the stochastic process now called Brownian motion, which was part of his PhD thesis The Theory of Speculation, (published 1900).
His thesis, which discussed the use of Brownian motion to evaluate stock options, is historically the first paper to use advanced mathematics in the study of finance. Thus, Bachelier is considered a pioneer in the study of financial mathematics and stochastic processes. *Wik Bachelier is now recognised internationally as the father of financial mathematics, but this fame, which he so justly deserved, was a long time coming. The Bachelier Society, named in his honour, is the world-wide financial mathematics society and mathematical finance is now a scientific discipline of its own. The Society held its first World Congress on 2000 in Paris on the hundredth anniversary of Bachelier's celebrated PhD Thesis, Théorie de la Spéculation *SAU




1888 William Edward Hodgson Berwick (11 March 1888 in Dudley Hill, Bradford – 13 May 1944 in Bangor, Gwynedd) was a British mathematician, specializing in algebra, who worked on the problem of computing an integral basis for the algebraic integers in a simple algebraic extension of the rationals.*Wik


1890 Birthdate of Vannevar Bush (11 Mar 1890; 28 Jun 1974 at age 84), the electrical engineer who developed the differential analyzer in the 1930s. This was an analogue device for integrating second order differential equations. It provides a nice simple model of the definite integral. *VFR Pre-World-War II computer pioneer Vannevar (pronounced "Van-ee-ver") Bush, who also was deeply involved with wartime computer projects, invented an electromechanical differential analyzer that used mechanical integrators to help solve differential equations. Bush was a co-founder of Raytheon, a military contractor. He also became very interested in information retrieval, which led him to imagine a machine he called "memex" -- an electronic extension of an individual's mind and memory base -- that mimicked human associative linking of information, and anticipated hypertext research. *CHM
Reminded by a tweet from Chris Stokes, "@Nisaccom" that Bush drove a Stanley Steamer in his youth I found this nice anecdote.
He drove a steam car, a Stanley Steamer, for many years and came to an easy understanding of its workings. He mastered the art of coaxing it up icy hills to see his future wife and of avoiding major fires. One day when it flooded and caught fire he sat by the side of the road waiting for it to go out but a traffic cop turned up and complained that if he wanted to burn his car there was a municipal dump just up the road. He explained that it was only a matter of time but the traffic cop wasn't convinced. When the fire eventually went out he drove away on the full head of steam that had built up leaving behind a bewildered traffic cop.
*iprogrammer info web page  

Differential analyzer in use at the Cambridge University Mathematics Laboratory, 1938





1915 Joseph Carl Robnett Licklider (March 11, 1915 – June 26, 1990), known simply as J.C.R. or "Lick" was an American computer scientist, considered one of the most important figures in computer science and general computing history. He is particularly remembered for being one of the first to foresee modern-style interactive computing, and its application to all manner of activities; and also as an Internet pioneer, with an early vision of a world-wide computer network long before it was built. He did much to actually initiate all that through his funding of research which led to a great deal of it, including today's canonical graphical user interface, and the ARPANET, the direct predecessor to the Internet.*Wik



1920  Nicolaas Bloembergen (March 11, 1920 – September 5, 2017) Dutch-American physicist who shared (with Arthur L. Schawlow of the United States and Kai M. Siegbahn of Sweden) the 1981 Nobel Prize for Physics for their revolutionary spectroscopic studies of the interaction of electromagnetic radiation with matter. Bloembergen made a pioneering use of lasers in these investigations and developed three-level pumps used in both masers and lasers.*TIS




1921 Frank Harary (March 11, 1921 – January 4, 2005) was an American mathematician, who specialized in graph theory. He was widely recognized as one of the "fathers" of modern graph theory. Harary was a master of clear exposition and, together with his many doctoral students, he standardized the terminology of graphs. He broadened the reach of this field to include physics, psychology, sociology, and even anthropology. Gifted with a keen sense of humor, Harary challenged and entertained audiences at all levels of mathematical sophistication. A particular trick he employed was to turn theorems into games—for instance, students would try to add red edges to a graph on six vertices in order to create a red triangle, while another group of students tried to add edges to create a blue triangle (and each edge of the graph had to be either blue or red). Because of the theorem on friends and strangers, one team or the other would have to win.*Wik

Harrary and Frank Harary (left) and Klaus Wagner in Oberwolfach, 1972








DEATHS


1849 Louis Paul Emile Richard (31 March 1795 in Rennes, France - 11 March 1849 in Paris, France) Richard perhaps attained his greatest fame as the teacher of Galois and his report on him which stated, "This student works only in the highest realms of mathematics.... "
It is well known. However, he also taught several other mathematicians whose biographies are included in this archive including Le Verrier, Serret and Hermite. He fully realised the significance of Galois' work and so, fifteen years after he left the college, he gave Galois' student exercises to Hermite so that a record of his school-work might be preserved. It is probably fair to say that Richard chose to give them to Hermite since in many ways he saw him as being similar to Galois. Under Richard's guidance, Hermite read papers by Euler, Gauss and Lagrange rather than work for his formal examinations, and he published two mathematics papers while a student at Louis-le-Grand.
Despite being encouraged by his friends to publish books based on the material that he taught so successfully, Richard did not wish to do so and so published nothing. This is indeed rather unfortunate since it would now be very interesting to read textbooks written by the teacher of so many world-class mathematicians.*SAU
Four of his students   




1895 Daniel Friedrich Ernst Meissel (31 July 1826 in Neustadt-Eberswalde, Brandenburg, Prussia - 11 March 1895 in Kiel, Herzogtum Holstein, Prussia) Ernst Meissel's mathematical work covers number theory, work on Möbius inversion and the theory of partitions as well as work on Bessel functions, asymptotic analysis, refraction of light and the three body problem. *SAU



1924 Niels Fabian Helge von Koch (Stockholm, January 25, 1870 – ibidem, March 11, 1924) was a Swedish mathematician who gave his name to the famous fractal known as the Koch snowflake, one of the earliest fractal curves to be described. Von Koch wrote several papers on number theory. One of his results was a 1901 theorem proving that the Riemann hypothesis is equivalent to a stronger form of the prime number theorem. He described the Koch curve in a 1904 paper entitled "On a continuous curve without tangents constructible from elementary geometry" (original French title: "Sur une courbe continue sans tangente, obtenue par une construction géométrique élémentaire"). *Wik






1967 Walter Andrew Shewhart (March 18, 1891 - March 11, 1967) was an American physicist, engineer and statistician, sometimes known as the father of statistical quality control.
W. Edwards Deming said of him, "As a statistician, he was, like so many of the rest of us, self-taught, on a good background of physics and mathematics. "
His more conventional work led him to formulate the statistical idea of tolerance intervals and to propose his data presentation rules, which are listed below:

Data have no meaning apart from their context.
Data contain both signal and noise. To be able to extract information, one must separate the signal from the noise within the data.
Walter Shewhart visited India in 1947-48 under the sponsorship of P. C. Mahalanobis of the Indian Statistical Institute. Shewhart toured the country, held conferences and stimulated interest in statistical quality control among Indian industrialists
*SAU




1971  Philo Taylor Farnsworth (August 19, 1906 – March 11, 1971) American pioneer in the development of electronic television, taking all of the moving parts out of television inventions. Farnsworth was a 15-year-old high school student when he designed his first television system. Six years later he obtained his first patent. In 1935 he demonstrated his complete television system. Farnsworth's basic television patents covered scanning, focusing, synchronizing, contrast, controls, and power. He also invented the first cold cathode ray tubes and the first simple electronic microscope. The Philco TV manufacturing was named after him. 



1974 Hidegorō Nakano ( 16 May 1909 – 11 March 1974) is a Japanese mathematician, after whom Nakano Spaces are named.
After graduating from National First High School, a preparatory school for the Imperial University of Tokyo, he progressed to study mathematics in Tokyo Imperial University and graduated with a Bachelor of Science in 1933. Then he entered Graduate School at the same university under the supervision of Takuji Yoshie, and attained his doctoral degree in 1935. At that time, a doctorate was more commonly awarded to people over 50 years old.

Nakano started teaching in The National First High School in 1935. At the same year he married Sumiko Yamamura (11 December 1913, Tokyo - 5 March 1999, Detroit). Then he held academic positions (1938-1952) in Tokyo Imperial University, before moving to Hokkaido University and being appointed as a professor.

In 1960, he left Japan and took a visit to Queen's University in Canada for a year, under the invitation of Canadian Mathematical Congress. He then took up professorship in Wayne State University, Detroit, US, in 1961, and continued working there until his death in 1974. 
Nakano is known for his research in Functional Analysis, [original research especially in vector lattice and operator theory in Hilbert spaces. He mainly made his name in his contribution to several mathematical subjects around modulars, Riesz spaces, Orlicz-Nakano spaces and Nakano space.*Wik






Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell

Tuesday, 10 March 2026

Some History Notes about Alphametic Puzzles (and some early versions of a Topology Gem)

   

*Pinterest.com

They go by various names, Verbal arithmetic, alphametics, cryptarithmetic, crypt-arithmetic, cryptarithms, but you remember seeing them in school, probably as far back as elementary school. All of the terms are much newer than the puzzle. The name "cryptarithmie" was coined by puzzlist Minos (pseudonym of Simon Vatriquant) in the May 1931 issue of Sphinx, a Belgian magazine of recreational mathematics, and was translated as "cryptarithmetic" by Maurice Kraitchik in 1942. In 1955, J. A. H. Hunter introduced the word "alphametic" (my personal favorite) to designate cryptarithms, such as Dudeney's, whose letters form meaningful words or phrases

The almost certainly most well known version, published in the July 1924 issue of Strand Magazine by Henry Dudeney, is:

\(\begin{matrix} & & \text{S} & \text{E} & \text{N} & \text{D} \\ + & & \text{M} & \text{O} & \text{R} & \text{E} \\ \hline = & \text{M} & \text{O} & \text{N} & \text{E} & \text{Y} \\ \end{matrix}\)

The problems existed for at least sixty years before that, and almost any place on the internet you can find that , "Verbal arithmetic puzzles are quite old and their inventor is not known. An 1864 example in The American Agriculturist disproves the popular notion that it was invented by Sam Loyd." (As with many things popularly known to have been invented by Sam Loyd, it was he who popularized the notion that he had invented them.) But not one of the dozens of sites I found this exact statement on, had the original problem. Finally I dug deep into Google Books, and at last ladies and gentlemen, after a period of perhaps 150 years, the first known verbal arithmetic problem ever published:



Yikes, Ten different letters for a 4 digit by 6 digit multiplication......... This can NOT be the first such problem. Recreational problems start out with simple ideas that people stumble across and find curious, and then expand to more and more complexity.

For a modern, but challenging version, here is one I got from Dave Radcliffe@daveinstpaul in early 2016. No solution is offered, although he said he did it first by computer, and warned that "It wasn't so easy."


If that sounds too tough, Dave says  "I was inspired by HALF+HALF=WHOLE, which I saw on FB"
 -It has more than one answer, so if you find one too quickly, try to figure out how many it has in all. (collect the whole set, send them in the comments ) If you have trouble with Dave's problem, you can look to the bottom of the blog.... or you can visit this site which is set up to solve these types of problems for you .

Benjamin Vitale ‏@BenVitale came up with this one which has two solutions with the same total, NOT + IN + THE = MOOD

A little while later he did a second post with this somewhat unusual version:
(x, y, z)   are positive integers in arithmetic sequence such that
x \; < \; y \; < \; z,
z^3 \; - \; y^3 \; = \; TWO     and     y^3 \; - \; x^3 \; = \; TOW
Find   (x, \; y, \; z) And along the way, O, T, and W



While looking for the answer to the earliest alphametic, which I never found, I came across an early version of a common, "bet you can't do this" problem many students run into:

The problem is generally called the "five rooms" problem, and the object of the puzzle is to draw a continuous path through the walls of all 5 rooms, without going through any wall twice, and without crossing any path. At least that is the modern version of the problem, (and not too modern at that, as this was the version I encountered as a student a very long time ago.)..
But the earliest versions of the problem ask for it to be drawn with "three strokes of the pencil, without erasing any lines, or going over the same line twice.  This is the same version Henry E. Dudeney used in his 1917 "Amusements in Mathematics", problem 239.  I was surprised to see that Gardner's "Entertaining Mathematical Puzzles", 1961 also had this version under the title "Five Bricks" on page 77. In his "My Best Mathematical and Logic Puzzles" on pages 6 and 7 he calls it "Cross the Network" and it takes the form of the five rooms problem.





Here is a slightly blown up copy for you to try.



There are a number of these types of puzzles. Martin Gardner described them as one of the oldest of topological puzzles but gives no clear details on origin. I could find no references to the type of problem in David Singmaster's Chronology or Recreational Mathematics, but maybe it slipped my eye.
Lewis Carroll (Charles Dodgson) like to give one that is possible to his young friends according to an old article in the Strand Magazine, 1908. Although it is sometimes attributed to Carroll, the author of the article says he "saw it in a little book published in 1835. He then contrasts the easy solution of Carroll's problem with what he calls "the old circle and square" problem, I assume because he believes it is older.


If you have information about this problem in either form I would love information, links, or digital copies.

Sometimes you come across things in old puzzle magazines that leave you stumped, as I di in this problem. An interesting, and probably challenging question for people in the US, A question in one of the 1860 editions asked, "What four US coins can be used to make a total of 51 cents... If you get stuck, I will post this answer a little lower down the post..



The solution of the problem of the four coins to make 51 cents was two quarters and two 1/2 cent pieces. The 1/2 cent coins were produced in the United States from 1793 to 1857. The half-cent piece was made of 100% copper and was valued at five milles, or one two-hundredth of a dollar.

The solution to Dave's alphametic is A=7 E=5 F=1 H=6 I=4 L=0 N=3 O=8 T=2 W=9

On This Day in Math - March 10

  

Rings of Uranus from Voyager 2, *astronomynotes.com



A rule of thumb for any good math talk is that it should have one proof and one joke
and they should not be the same.

~Ron Graham

The 69th day of the year; the square and the cube of 69 together contain all ten numerals.
692 = 4761, 693 =328509

1069+69 is prime and;
10069-69 is prime

On Many scientific calculators, 69! is the largest factorial that can be calculated, with an overflow error for larger numbers. 69! is appx 1.711 (1098)

Don S. McDonald ‏@McDONewt pointed out that \( \binom{69}{5}\) = 11238513, 7 Fibonacci #'s almost in order.

The first squared square to be found was a square filled with 69 smaller squares. ( electrical network theory was used to make the discovery, previously most mathematicians felt that there were not likely to be any squared squares see Jan 21).. (I have since found out that this was not the first. In 1938 Roland Sprague found a solution using several copies of various squared rectangles and produced a squared square with 55 squares, and side lengths of 4205)

A "simple" squared square is one where no subset of more than one of the squares forms a rectangle or square, otherwise it is "compound".

Lowest-order perfect squared square *Wik


The Sprague Square





EVENTS

Coptic ostrakon noting an eclipse of the sun which had occurred at midday on 10 March 601 CE, Egypt.* @HistAstro



1615 Henry Briggs was completely engaged in the study of logarithms by this date for he wrote “Neper, lord of Markinston, hath set my head and hands a work with his new and admirable logarithms. I hope to see him this summer, if it please God, for I never saw a book, which pleased me better, and made me more wonder.” *VFR


1625 Henry Briggs writes to Kepler that work was underway to edit Thomas Harriot’s papers, “since we may expect and hope for a posthumous book from that author any day”. *Thomas Harriot’s Doctrine of Triangular Numbers, Beery & Stedall, pg 28

Thomas Harriot (1560–1621) was a mathematician and astronomer who founded the English school of algebra. He is known not only for his work in algebra and geometry but also as a prolific writer with wide-ranging interests in ballistics, navigation, and optics. (He discovered the sine law of refraction now known as Snell's law.)

By about 1614, Harriot had developed finite difference interpolation methods for navigational tables. In 1618 (or slightly later) he composed a treatise entitled ‘De numeris triangularibus et inde de progressionibus arithmeticis, Magisteria magna', in which he derived symbolic interpolation formulae and showed how to use them. This treatise was never published.  

The ideas in the ‘Magisteria' were spread primarily through personal communication and unpublished manuscripts, and so, quite apart from their intrinsic mathematical interest, their survival in England during the seventeenth century provides an important case study in the dissemination of mathematics through informal networks of friends and acquaintances. Harriot's method was not superseded until Newton, apparently independently, made a similar discovery in the 1660s.




1672 From Hooke's Journal: Hooke’s first weather report was for Sunday 10 March 1672"[mercury] fell from 170 to 185. most part of ye Day cleer but cold & somewhat windy at the South–[I was this morning better with my cold then I had been 3 months before] [moon] apogeum–It grew cloudy about 4. [mercury] falling still"
Instead of writing the words ‘mercury’ and ‘moon’ (transcribed in square brackets here), Hooke depicted them with their astrological symbols ☿ and ☽ as a kind of shorthand. *felicityhen, Hooke's London.com



1695 John Evelyn writes in his journal of a visit to the Earl of Sunderland, who had acquired one of the best math libraries in Europe from the estate of Charles Scarborough; "My Lord showed me his library, now again improved by many books bought at the sale of Sir Charles Scarborough, an eminent physician, which was the very best collection, especially of mathematical books, that was I believe in Europe" *John Evelyn's Diary  *AMS





1763 Euler's E812. Read before the Academy of Berlin 10 March 1763 but only published posthumously in 1862. "Reflexions sur une espese singulier de loterie nommée loterie genoise." Opera postuma I, 1862, p. 319–335. The paper determined the probability that a particular number be drawn in a lottery.
Euler's interest in lotteries began at the latest in 1749 when he was commissioned by Frederick the Great to render an opinion on a proposed lottery. The first of two letters began 15 September 1749. A second series began on 17 August 1763. *Ed Sandifer, How Euler Did It




1773 Laplace introduces inverse probability.  Stephen Stigler called it the most influential paper published in probability to appear before 1800.  *Springer’s 1985 Statistics Calendar

In probability theory, inverse probability is an old term for the probability distribution of an unobserved variable.

The term "inverse probability" appears in an 1837 paper of De Morgan, in reference to Laplace's method of probability




1797 The surveyor Caspar Wessel presented his one and only mathematics paper to the Danish Academy of Sciences. It established his priority in publishing a geometrical representation of complex numbers. The paper was essentially unknown until 1895 when Christian Juel pointed out its significance. *VFR (this paper introduced what are now often called Argand Diagrams) He represented complex numbers as points in a Cartesian plane, with the real portion of the number on the x axis and the imaginary part on the y axis. This was also independently devised a few years later, by Jean-Robert Argand, an amateur mathematician who self-published his ideas in an anomymous monograph (1806). Through publicity generated when Argand came forward and identified himself as the author, it was his name that has the lasting association with the Argand diagram


1797 Thomas Jefferson (1743-1826) presented a paper on the megalonyx to the American Philosophical Society. It was published as "A Memoir on the Discovery of Certain Bones of a Quadruped of the Clawed Kind in the Western Parts of Virginia," Transactions of American Philosophical Society 4:255-256, along with an account by Caspar Wistar (1761-1818). This is arguably the first American publication in paleontology, but the only paleontology paper written by Jefferson. In 1822, this huge extinct sloth was named Megalonyx jeffersoni by a French naturalist. (Megalonyx Gr. large claw). It was a bear-sized ground sloth, over 2 meters tall, widespread in North America during the last Ice Age.



1812 Jean Jacques Bret became docteur d´es sciences, having previously been professor of transcen-dental mathematics at the lyc´ee in Grenoble. Later he was involved in a prolonged polemic with J. B. E. Dubourguet concerning the fundamental theorem of algebra. *VFR



1820
 Founding of the Royal Astronomical Society of England. Charles Babbage was one of the founding members. *Goldstine, The Computer from Pascal to von Neumann, p. 10 *VFR.
  The 'Astronomical Society of London' was conceived on 12 January 1820 when 14 gentlemen sat down to dinner at the Freemason's Tavern, in Lincoln's Inn Fields, London. After an unusually short gestation the new Society was born on 10 March 1820 with the first meeting of the Council and the Society as a whole. An early setback, when Sir Joseph Banks induced the Duke of Somerset to withdraw his agreement to be the first President, was overcome when Sir William Herschel agreed to be the titular first President, though he never actually took the Chair at a meeting. *Royal Astronomical Society


1876  Alexander Graham Bell and his assistant, Thomas A Watson,  talked by telephone over a two-mile wire stretched between Boston and Cambridge Massachusetts. The message was a simple statement, "Mr Watson, come here, I want to see you."  The common story is that he had invented the device by accident and would not have one in his home because he saw it as a distraction.  

Whatever his objections, years later on January 25 of 1915, he place another call to his former assistant, between Bell in New York and Watson in San Francisco, and they repeated the exact same dialogue as their first message.  The call was a public relations stunt by A T & T to demonstrate their ability to make transcontinental calls, a 3,400 mile communication.  The call was timed to agree with the opening of the 1915 Panama–Pacific International Exposition in San Francisco which would open on Feb 20. A telephone line was also established to New York City so people across the continent could hear the Pacific Ocean. 

The transcontinental line was completed on June 17, of 1914 and successfully voice tested in July. A postage stamp commemorating the completion was released in 1914 also.







1897 Schering in Gottingen in response to a note from Fuchs that he had found materials related to Guass' Disquisitiones Arithmetica in the papers of Dirichlet describes a story that he had shared with Kronecker a decade before,
"The piece of Guass's Disquisitiones Arithmeticiae, which is found among Dirichlet's papers, is probably that portion which, as Dirichlet told me himself, he saved from the hand of Gauss when the latter lit his pipe with his manuscript of the Disquisitiones Arithmeticae on the day of his doctoral jubilee."
On 28 April of the same year, Dedekind expressed skepticism of the tale since he reasoned, if Gauss had saved the paper for fifty years he obviously valued it, and that if the anecdote were true, Dirichlet surely would have shared it with him as well. *Uta Merzbach, An Early Version of Gauss's Disquisitiones Arithmeticae, Mathematical Perspectives, 1981




*Wik
1926 Amazing Stories was the first magazine devoted solely to science fiction. Before Amazing, science fiction stories had made regular appearances in other magazines, including some published by Gernsback, but Amazing helped define and launch a new genre of pulp fiction.The first issue appeared on 10 March 1926, with a cover date of April 1926. *Wik












1977 Rings of Planet Uranus discovered. The rings of Uranus were discovered by James L. Elliot, Edward W. Dunham, and Douglas J. Mink. More than 200 years ago, William Herschel also reported observing rings (in 1789); some modern astronomers are skeptical that he could have actually seen them, as they are very dark and faint – others are not. In 1977, the rings of Uranus were discovered from earth by stellar occultation experiments made when Uranus occulted (passed in front of) a star and it was noticed that there were dips in the brightness of the star before and after it passed behind the body of Uranus. This data suggested that Uranus was surrounded by at least five rings. Four more rings were suggested by subsequent occultation measurements from the Earth, and two additional ones were found by space probe Voyager 2, bringing the total to 11. *TIS  Uranus has two sets of rings. The inner system of nine rings consists mostly of narrow, dark grey rings. There are two outer rings: the innermost one is reddish like dusty rings elsewhere in the solar system, and the outer ring is blue like Saturn's E ring.

*Wik





1981 Czechoslovakia issued a stamp picturing the philosopher/mathematician Bernhard Bolzano (1781–1848). [Scott #2352] *VFR

Bolzano made several original contributions to mathematics. His overall philosophical stance was that, contrary to much of the prevailing mathematics of the era, it was better not to introduce intuitive ideas such as time and motion into mathematics.[8] To this end, he was one of the earliest mathematicians to begin instilling rigor into mathematical analysis with his three chief mathematical works Beyträge zu einer begründeteren Darstellung der Mathematik (1810), Der binomische Lehrsatz (1816) and Rein analytischer Beweis (1817). These works presented "...a sample of a new way of developing analysis", whose ultimate goal would not be realized until some fifty years later when they came to the attention of Karl Weierstrass. *Wik



In 1982, a syzygy occurred when all nine planets aligned on the same side of the Sun. The planets are spread out over 98 degrees on this date. The four major planets, Jupiter, Saturn, Uranus, and Neptune, span an arc of some 73 degrees. *TIS The next "grand" syzygy is May 19, 2161, when eight planets (excluding Pluto) will be found within 69 degrees of each other, according to astronomers at the Kitt Peak National Observatory.


1988 An article in the Washington Post reported that young Japanese mathematician Yoichi Miyaoka had solved Fermat's Last Theorem. It would be followed with one in the New York Times the next day. Quickly however, a mistake was found. *Magnificent Mistakes in Mathematics by Alfred S. Posamentier, Ingmar Lehmann





BIRTHS

1622 Johann Heinrich Rahn (10 March 1622 in Zürich, Switzerland - 25 May 1676 in Zürich, Switzerland) mathematician who was the first to use the symbol "÷",called an obelus, for a division symbol in Teutsche Algebra (1659). The invention is also sometimes credited to British Mathematician John Pell. Here is more on the various symbols used for division .
 Pell's equation y^2=ax^2+1, where a is a non-square integer, was first studied by Brahmagupta and Bhaskara II. Its complete theory was worked out by Lagrange, not Pell. It is often said that Euler mistakenly attributed Brouncker's work on this equation to Pell. However the equation appears in a book by Rahn which was certainly written with Pell's help: some say entirely written by Pell. Perhaps Euler knew what he was doing in naming the equation. *SAU He introduced the division sign (obelus, ÷) into England. The obelus was first used by Johann Rahn (1622-1676) in 1659 in Teutsche Algebra. Rahn's book was interpreted into English and published, with additions made by John Pell. According to some sources, John Pell was a key influence on Rahn and he may be responsible for the development of the symbol. The word obelus comes from a Greek word meaning a "roasting spit." The symbol wasn't new. It had been used to mark passages in writings that were considered dubious, corrupt or spurious.*TIS
The obelus as used br Rahn (Pell?) was not a mathematical operator, but a shorthand for an operation.  In the cimage below you can see that down the left column he gives instructions for how to proceed in a solution.  Notice the obelus only appears in the left column, never as an operation.  In the columns where steps of solution occur, he uses a vinculum (division bar) as the division operator.






1748 John Playfair (10 Mar 1748; 20 Jul 1819 at age 71) Scottish mathematician, He is responsible for introducing (although we now know that it was known to Proclus in the fifth century) the commonly used equivalent of Euclid’s Fifth Postulate: Through a given point not on a given straight line only one line parallel to the given line may be drawn. *VFR His Illustrations of the Huttonian Theory of the Earth (1802) gave strong support to James Hutton's principle of uniformitarianism, essential to a proper understanding of geology. Playfair was the first scientist to recognise that a river cuts its own valley, and he cited British examples of the gradual, fluvial origins of valleys, to challenge the catastrophic theory (based on the Biblical Flood in Genesis) that was still widely accepted. He was also the first to link the relocation of loose rocks to the movement of glaciers. Playfair published texts on geometry, physics, and astronomy.*TIS





1762 Jeremias Benjamin Richter (10 Mar 1762; 4 Apr 1807 at age 45) was a German chemist who discovered law of equivalent proportions. He studied chemistry in his spare time while in the Prussian army (1778-1785) and afterwards while earning a Ph.D. in mathematics (1789). Richter was much influenced by Kant, whose lectures he may have attended, in the contention that science is applied mathematics. Richter looked for mathematical relationships in chemisty, convinced that substances reacted with each other in fixed proportions. He showed such a relationship when acids and bases neutralize to produce salts (1791). Thus he was the first to establish stoichiometry, which became the basis of quantitative chemical analysis. He died of tuberculosis at age 45 years.*TIS





1818 Joel E. Hendricks, (March 10, 1818 - June 9, 1893) a noted mathematician, was born in Bucks County, Pennsylvania, March 10, 1818. He early developed a love of mathematics and began to teach school at nineteen years of age. He chanced to procure Moore's Navigation and Ostrander's Astronomy and, without instruction, soon became able to work in trigonometry and calculate solar and lunar eclipses. He took up algebra while teaching and soon became master of that science without instruction. He taught mathematics two years in Neville Academy, Ohio, and then occupied a position on a Government survey in Colorado in 1861. In 1864 he located in Des Moines, Iowa and pursued his mathematical studies. In 1874 he began the publication of the Analyst, a journal of pure and applied mathematics and soon won a reputation in Europe among eminent scholars as one of the most advanced mathematicians of the day. His Analyst was taken by the colleges and universities of Europe and found a place in the best foreign libraries. His name became famous among all mathematical experts of the world. Among his correspondents were Benjamin Silliman, John W. Draper and James D. Dana; while his journal was authority at Yale and Johns Hopkins Universities. For ten years, up to 1884, this world-famous Analyst was published at Des Moines by Dr. Joel E. Hendricks. Up to the time it was discontinued, no journal of mathematics had been published so long in America. It is one of the remarkable events of the Nineteenth Century that a self-educated man should, by his own genius and industry, without instruction, reach such an exalted place among the world's great scholars. Dr. Hendricks died in Des Moines on the 9th of June, 1893. *History of Iowa From the Earliest Times to the Beginning of the Twentieth Century/Volume 4 by Benjamin F. Gue
A more complete mathematical biography of Mr. Hendricks can be found in The American Mathematical Monthly, Vol 1, #3, 1894.

1864 William Fogg Osgood (March 10, 1864, Boston - July 22, 1943, Belmont, Massachusetts) From 1899 to 1902, he served as editor of the Annals of Mathematics and in 1904–1905 was president of the American Mathematical Society, whose Transactions he edited in 1909–1910.
The works of Osgood dealt with complex analysis, in particular conformal mapping and uniformization of analytic functions, and calculus of variations. He was invited by Felix Klein to write an article on complex analysis in the Enzyklopädie der mathematischen Wissenschaften which was later expanded in the book Lehrbuch der Funktionentheorie. Besides his research on analysis, Osgood was also interested in mathematical physics and wrote on the theory of the gyroscope. Osgood's cousin, Louise Osgood, was the mother of Bernard Koopman, the statistician. *Wik Although his nickname was “Foggy,” this was not an apt description of him as a teacher. He instilled the habit of careful thought in Harvard students for 43 years. His A First Course in Differential and Integral Calculus (1907) was revised once and reprinted 17 times.*VFR
An interesting anecdote about the book dates to about 1940. Osgood chose not to use limits in his book and used infinitesimals instead. Leonidas Alaoglu taught the course at Harvard, he apparently didn't agree with Osgood's choice, and instructed the class, "Gentleman, please take pages 123 to 150 (Chapter 7 on infinitesimals) between thumb and forefinger and tear them out." *Steven Krantz, Mathematical Apocrypha Redux




1869 Benjamin Fedorovich Kagan (10 March 1869 in Shavli, Kovno (now Kaunas, Lithuania)
- 8 May 1953 in Moscow, USSR) Kagan worked on the foundations of geometry and his first work was on Lobachevsky's geometry. In 1902 he proposed axioms and definitions very different from Hilbert. Kagan studied tensor differential geometry after going to Moscow because of an interest in relativity.
Kagan wrote a history of non-euclidean geometry and also a detailed biography of Lobachevsky. He edited Lobachevsky's complete works which appeared in five volumes between 1946 and 1951. *SAU




1872 Mary Ann Elizabeth Stephansen (10 March 1872 in Bergen, Norway - 23 Feb 1961 in Espeland, Norway)received her Ph.D. in mathematics from the University of Zurich in 1902. She was the first woman from Norway to receive a doctoral degree in any subject. Her thesis area was in partial differential equations. It was not until 1971 that another Norwegian woman obtained a doctorate in mathematics. Stephansen taught at the Norwegian Agricultural College from 1906 until her retirement in 1937. She began as an assistant in physics and mathematics, then was appointed to a newly created docent position in mathematics in 1921. She published four mathematical research papers on partial differential equations and difference equations.
A extensive biography of Elizabeth Stephansen is available as a pdf document at the web site of Professor Kari Hag. This also includes description of her mathematical work. *Agnes Scott College Web site




1912 Frank Smithies FRSE (10 March 1912 Edinburgh, Scotland – 16 November 2002 Cambridge, England) was a British mathematician who worked on integral equations, functional analysis, and the history of mathematics. He was elected as a fellow of the Royal Society of Edinburgh in 1961.*Wik

Funded by a Carnegie Fellowship and a St John's College studentship, Smithies then spent two years at the Institute for Advanced Study at Princeton. There he did some joint work with von Neumann and some with R P Boas. One of the notable results of a collaboration with Boas was the article Contribution to the Mathematical Theory of Big Game Hunting. After returning to Cambridge in 1938, Smithies taught at St John's College and continued his research. However from the summer of 1940 he was engaged in war work at the Ministry of Supply. His work there was very varied, involving theoretical and experimental work on anti-aircraft guns, statistical work on quality control, and the responsibility for "miscellaneous mathematical problems". In 1942 he helped set up the Advisory Service on Statistical Quality Control in the Ministry of Supply and about the same time he met Nora Arone who had just started working for the Ministry. Smithies took up his duties again at St John's College in September 1945 and three months later he married Nora.*SAU





1923 Val Logsdon Fitch (March 10, 1923 – February 5, 2015) American particle physicist who was co-recipient with James Watson Cronin of the Nobel Prize for Physics in 1980 for an experiment conducted in 1964 that disproved the long-held theory that particle interaction should be indifferent to the direction of time. Working with Leo James Rainwater, Fitch had been the first to observe radiation from muonic atoms; i.e., from species in which a muon is orbiting a nucleus rather than an electron. This work indicated that the sizes of atomic nuclei were smaller than had been supposed. He went on to study kaons and in 1964 began his collaboration with James Cronin, James Christenson, and René Turley which led to the discovery of violations of fundamental symmetry principles in the decay of neutral K-mesons. *TIS His birthplace is in Merriman, a village in Cherry County, Nebraska, United States. The population was 118 at the 2000 census.





DEATHS

1825 Karl Brandan Mollweide (3 Feb 1774 in Wolfenbüttel, Brunswick, now Germany - 10 March 1825 in Leipzig, Germany) He is remembered for his invention of the Mollweide projection of the sphere, a map projection which he produced to correct the distortions in the Mercator projection, first used by Gerardus Mercator in 1569. Mollweide announced his projection in 1805. While the Mercator projection is well adapted for sea charts, its very great exaggeration of land areas in high latitudes makes it unsuitable for most other purposes. In the Mercator projection the angles of intersection between the parallels and meridians, and the general configuration of the land, are preserved but as a consequence areas and distances are increasingly exaggerated as one moves away from the equator. To correct these defects, Mollweide drew his elliptical projection; but in preserving the correct relation between the areas he was compelled to sacrifice configuration and angular measurement.
The second piece of work to which Mollweide's name is attached today is the Mollweide equations which are sometimes called Mollweide's formulas. These trigonometric identities ares


sin(½(A - B)) / cos(½C) = (a - b) / c, and

cos(½(A - B)) / sin(½C) = (a + b) / c,


where A, B, C are the three angles of a triangle opposite to sides a, b, c, respectively. These trigonometric identities appear in Mollweide's paper Zusätze zur ebenen und sphärischen Trigonometrie (1808). *SAU

1888  Lucy Myers Wright Mitchell ( March 20, 1845 – March 10, 1888) Persian-American archaeologist who, though self-taught, was one of the first American women in the field, and became an internationally recognized authority on ancient Greek and Roman sculpture. She spoke Syriac, Arabic, French, German, and Italian and pursued an interest in the study of languages in classical literature. By 1873 she changed her focus to classical archeology, and subsequently became one of the foremost archeologists of her time. In Rome (1876-78) she gave parlour lectures to ladies on Greek and Roman sculpture, and also them to the museums. She was given aid and encouragement by many of the leading European archeologists. Her book, A History of Ancient Sculpture, was one of the first in the field by an American. *TIS




1900 George James Symons (6 Aug 1838 - 10 Mar 1900) British meteorologist who strove to provide reliable observational data by imposing standards of accuracy and uniformity on meteorological measurements and by substantially increasing the number of reporting stations from 168 to 3,500. He was elected to Royal Meteorological Society (1856) when only 17 years old. He established the British Rainfall Organization (1860) and issued annual rainfall reports (1860-98). Symons's Monthly Meteorological Magazine first appeared in 1866. He wrote hundreds of articles and several books, and he amassed the UK's most comprehensive collection of meteorological books, many of great historical interest.*TIS



1921 Francis Robbins Upton (born 1852 in Peabody, Mass, 10 Mar 1921) American mathematician and physicist who, as assistant to Thomas Edison, contributed to the development of the American electric industry. Upton was the best educated of Edison's Menlo Park assistants. He was recruited by investors who felt it couldn't hurt to supplement Edison's wizardry with some advanced scientific training. He joined Edison in 1878, working at Edison's Menlo Park laboratory on mathematical problems relating to the development of the light bulb, the watt-hour meter and large dynamos. He later became a partner and general manager of the Edison Lamp Company (est. 1880). Upton's articles for Scientific American and Scribner's Monthly introduced many of Edison's inventions to the public. *TIS Upton graduated from Phillips Academy, Andover in 1870. He studied at Bowdoin College in Brunswick, Maine, at Princeton University where he received his M.S., and in Berlin, where he worked together with Hermann von Helmholtz.*Wik




1948 Evgeny Evgenievich Slutsky (19 April 1880 in Novoe, Yaroslavl guberniya, Russia - 10 March 1948 in Moscow, USSR) Slutsky was important in the application of mathematical methods in economics. Slutsky introduced stochastic concepts of limits, derivatives and integrals between 1925 to 1928 while he worked at the Conjuncture Institute. In 1927 he showed that subjecting a sequence of independent random variables to a sequence of moving averages generated an almost periodic sequence. This work stimulated the creation of stationary stochastic processes. He also studied correlations of related series for a limited number of trials. He obtained conditions for measurability of random functions in 1937. He applied his theories widely, in addition to economics mentioned above he also studied solar activity using data from 500 BC onwards. Other applications were to diverse topics such as the pricing of grain and the study of chromosomes. *SAU




1971 Lester Halbert Germer (10 Oct 1896, Chicago, Ill; 10 Mar 1971) was a American physicist who, with his colleague Clinton Joseph Davisson, conducted an experiment (1927) that first demonstrated the wave properties of the electron. They showed that a beam of electrons scattered by a crystal produces a diffraction pattern characteristic of a wave. This experiment confirmed the hypothesis of Louis-Victor de Broglie, a founder of wave mechanics, that the electron should show the properties of an electromagnetic wave as well as a particle. He also studied thermionics, erosion of metals, and contact physics.*TIS
Lester Germer (right) with Clinton Joseph Davisson (left) 1927




1981 Yaroslav Borisovich Lopatynsky (9 Nov 1906 in Tbilisi, Georgia, Russia - 10 March 1981 in Donetsk, USSR) Lopatynsky's contributions to the theory of differential equations are particularly important, with important contributions to the theory of linear and nonlinear partial differential equations. He worked on the general theory of boundary value problems for linear systems of partial differential equations of elliptic type, finding general methods of solving boundary value problems. *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