Pat'sBlog

Sunday, 29 March 2026

Rhombus from Math Terms Notes

The rhombus is a quadrilateral with four sides of congruent length(and whether you include squares, or don't, is a matter of taste.) It is sometimes called a rhomb, and sometimes a diamond and sometimes, if you are French especially, a lozenge. In classical Latin, a rhombus was a diamond shaped instrument that was whirled on a string to make a whirring sound, aha, but why.

If you have ever been to a rodeo, you have probably been impressed with the agility and courage of the rodeo clowns as they distract the bull after the rider departs from the bull. You may even think it was a sport created by cowboys of the old American west. The truth however, is that playing tag with a bull may date back to the ancient Greek civilizations around 2000 BC. Archaeologists working on Minoan ruins found pots with illustrations that seemed to show that taunting a bull was a popular pastime for young males of that culture. The picture below is from a fresco found when the castle of King Minos was excavated.

It seems that sometimes, however, the bull was bored by the whole routine. It is hard to be macho if the bull is doing his "Ferdinand" routine and smelling the daisies so, to prod the animal into more ferocious activity, the young men began twirling an object on a string around their heads that made a roaring noise.

The bullroarer, rhombus, or turndun, is an ancient ritual musical instrument and a device historically used for communicating over great distances. It consists of a piece of wood attached to a string, which when swung in a large circle produces a roaring vibration sound. *Wik

Bullroarers from Africa in the Pitt Rivers Museum

You may have seen other objects used to make a sound in a similar manner. Hopi Indians use something like that in their dances and you may have seen your science teacher twirl a length of plastic tube to make various "roaring" sounds. Such objects today are called bull roarers. I always thought it was because they were presumed to sound like a bull. Now I am less sure. The ancient Minoan object that twisted as it twirled and made the roaring sound was called a rhomb. The root began to be used in words that suggested rotation or twisting motions, such as spinning tops, but none of the others seem to have made it into modern language. The use that did prevail was for shapes that looked like the four sided object that they swung on the end of the string. This is how we came to call the equilateral quadrilateral a rhombus... and that's no bull.

Euclid uses the word rombos and in his translation Heath says it is apparently drawn from the Greek word rembw, to turn round and round. He also points out that Archimedes used the term solid rhombus for two right circular cones sharing a common base. Euclid extended the idea in using rhomboid to name the shape we more commonly call a parallelogram. Since the definition of rhomboid (romboeides) comes before the definition of parallel lines, Euclid defines the rhomboid as (in Heath's words)," that which has its opposite sides and angles equal to one another but is neither equilateral nor right-angled."

The term rhomb is often used for the same shape, and many people, particularly young students, refer to a rhombus as a diamond. Some use the term only for non-square rhombi (or rhombuses). It is especially interesting to work with early elementary students who will identify a shape as a square when the sides are horizontal and vertical, and then call it a diamond when the shape is rotated 45 degrees, even while they watch. The word diamond seems to be a mutation of the word adamant. A person is adamant if they are firm or unyielding in their attitude or position. The origin seems to be from the common root anti and the Greek word deme which meant to force or break (as in training an animal) which is the root of our present word domesticate. Together the two roots meant unbreakable, and the word was commonly used for hard metals and gems, and extremely difficult people.

The French word lozenge is also used for the non-square rhombus by some people, although I have never seen the term in a current math book. The word comes from the Gaulish word lausa for "flat stone".

Lozenge was used by Robert Recorde in 1551 in Pathway to Knowledge: "Defin., The thyrd kind is called losenges or diamondes whose sides bee all equall, but it hath neuer a square corner" *J Miller

As with many geometric terms, there are two common definitions that are still in use for a rhombus. Some think of geometric names with an inclusive approach, and they usually define rhombus as it is defined in The Concise Oxford English Dictionary, "rhombus n. ( pl. rhombuses or rhombi / -b / ) Geometry a quadrilateral whose sides all have the same length." Notice that in this definition, a square would be a rhombus also. Others, who want definitions to describe how things are different from each other will define it the way it is defined in The Oxford American Dictionary of Current English, "rhombus n. a parallelogram with oblique angles and equal sides." Note that the Oblique angles rules out the case of a square.

The word Rhomboid which means rhom-like was commonly used in the 19th century for a parallelogram which was neither a rectangle nor a rhombus. Today it is more often used for a solid figure with six faces in which each face is a parallelogram and opposite faces in pairs lie in parallel planes. Some crystals are formed in 3D rhomboids. It is also sometimes called a rhombic prism and others refer to it as a rhombohedron. The term shows up frequently in science terminology referring to both its two and three dimensional meaning.

My thanks to Mary O'Keeffe for the suggestions to explore the origins of this word.

On This Day in Math - March 29

construction of Regular Heptadecagon

Natural selection is a mechanism for generating an exceedingly high degree of improbability.
~R. A. Fisher

The 88th day of the year; 88² = 7744, it is one of only 5 numbers known whose square has no isolated digits. (Can you find the others?) [Thanks to Danny Whittaker @nemoyatpeace for a correction on this.]

There are only 88 narcissistic numbers in base ten, (an n-digit number that is the sum of the nth power of its digits, 153=1³ + 5³ + 3³

88 is also a chance to introduce a new word. 88 is strobogrammatic, a number that is the same when it is rotated 180^o about its center... 69 is another example. If they make a different number when rotated, they are called invertible (109 becomes 601 for example). *Prime Curios (Note that this rule is not strictly enforced.

And with millions (billions?) of stars in the sky, did you ever wonder how many constellations there are? Well, according to the Internationals Astronomical Union, there are 88.

Currently, 14 men and women, 9 birds, two insects, 19 land animals, 10 water creatures, two centaurs, one head of hair, a serpent, a dragon, a flying horse, a river and 29 inanimate objects are represented in the night sky (the total comes to more than 88 because some constellations include more than one creature.)

And if you chat with Chinese friends, the cool way to say bye-bye is with 88, from Mandarin for 88, "bā ba".

Not too far from my home near Possum Trot, Ky, there is a little place called Eighty-eight, Kentucky. One story of the naming (there could be as many as 88 of them) is that the town was named in 1860 by Dabnie Nunnally, the community's first postmaster. He had little faith in the legibility of his handwriting, and thought that using numbers would solve the problem. He then reached into his pocket and came up with 88 cents.
In the 1948 presidential election, the community reported 88 votes for Truman and 88 votes for Dewey, which earned it a spot in Ripley's Believe It or Not.

And expanding the "88 is strobogrammatic" theme, INDER JEET TANEJA came up with this beautiful magic square with a constant of 88 that was used in a stamp series in Macao in 2014 and 2015. This image shows the reflections both horizontally and vertically, as well as the 180 degree rotation, each is a magic square.

The stamps had denominations of 1 through 9 pataca and when two sheets were printed you could do your own Luo Shu magic square with the denominations. The Luo Shu itself was featured on the 12 pataca stamp.

EVENTS

1796 Gauss achieved the construction of the 17-gon and a week later he would obtain his first proof of the quadratic reciprocity law. These two accomplishments mark the emergence from the ingenious manipulations of his youth, to the polished proofs of the mature mathematician. *Merzbach, An Early Version of Guass' Disquisitiones Arithmeticae, Mathematical Perspectives Academic Press 1981

In 1807, Vesta 4, the only asteroid visible to the naked eye, thus the brightest on record, was first observed by the amateur astronomer Heinrich Wilhelm Olbers from Bremen. Vesta is a main belt asteroid with a diameter of 525-km and a rotation period of 5.34 hours. Pictures taken by the Hubble Space Telescope in 1995 show Vesta's complex surface, with a geology similar to that of terrestrial worlds - such as Earth or Mars - a surprisingly diverse world with an exposed mantle, ancient lava flows and impact basins. Though no bigger than the state of Arizona, it once had a molten interior. This contradicts conventional ideas that asteroids essentially are cold, rocky fragments left behind from the early days of planetary formation. *TIS Since the discovery of Ceres (by Giuseppe Piazzi) in 1801, and the asteroid Pallas (also discovered by Olbers) in 1802, he had corresponded and became close friends with Gauss. For that reason he allowed Gauss to name the new "planet".

NASA Spacecraft Dawn first image, Vesta

1933 Italy issued the world’s ﬁrst postage stamp portraying Galileo. [Scott #D16] *VFR
Galileo Galilei (1564–1642) made his first appearance on this stamp in 1933 for use in pneumatic postal systems (hence the wording “Posta Pneumatica” on the stamp). Pneumatic post involved placing letters in canisters which were then shot along pipes by compressed air from one Post Office to another. Pneumatic postal systems were set up in several European and American cities, including Rome, Naples, and Milan. Italy was the only country to issue stamps specifically for pneumatic postal use. Two of the designs showed Galileo – this one and a modified version with different face value and colour issued in 1945. The portrait is based on one by Justus Sustermans painted in 1636 when Galileo was aged 72. *Ian Ridpath, World's Oldest Astro Stamps page.

1938 In 1922 Issai Schur was elected to the Prussian Academy, proposed by Planck, the secretary of the Academy. Planck's address which listed Schur's outstanding achievements had been written by Frobenius, at least five years earlier, as Frobenius died in 1917.

On 29 March 1938 Bieberbach wrote below Schur's signature on a document of the Prussian Academy:- "I find it surprising that Jews are still members of academic commissions."

Just over a week later, on 7 April 1938, Schur resigned from Commissions of the Academy. However, the pressure on him continued and later that year he resigned completely from the Academy. Schur left Germany for Palestine in 1939, broken in mind and body, having the final humiliation of being forced to find a sponsor to pay the 'Reichs flight tax' to allow him to leave Germany. Without sufficient funds to live in Palestine he was forced to sell his beloved academic books to the Institute for Advanced Study in Princeton. He died two years later on his 66th birthday.

Only five years earlier "On 7 April 1933 the Nazis passed a law which, under clause three, ordered the retirement of civil servants who were not of Aryan descent, with exemptions for participants in World War I and pre-war officials. Schur had held an appointment before World War I which should have qualified him as a civil servant, but the facts were not allowed to get in the way, and he was 'retired'. M M Schiffer wrote :-When Schur's lectures were cancelled there was an outcry among the students and professors, for Schur was respected and very well liked. The next day Erhard Schmidt started his lecture with a protest against this dismissal and even Bieberbach, who later made himself a shameful reputation as a Nazi, came out in Schur's defence. Schur went on quietly with his work on algebra at home." #SAU

1983 Radio Shack introduces the TRS-80 Model 100, one of the first portable computers in a notebook-style form factor. The portability, simplicity, and built-in modem of the Model 100 made it very popular with journalists who could write stories in the field and transmit them back to their offices. *This Day in Tech History

The 224-page, spiral-bound User Manual is nearly the same size as the computer itself.

It was made by Kyocera, and originally sold in Japan as the Kyotronic 85. Although a slow seller for Kyocera, the rights to the machine were purchased by Tandy Corporation. The computer was sold through Radio Shack stores in the United States and Canada and affiliated dealers in other countries. It became one of the company's most popular models, with over 6 million units sold worldwide. The Olivetti M-10 and the NEC PC-8201 and PC-8300 were also built on the same Kyocera platform, with some design and hardware differences. *Wik

1989 Pixar Wins Academy Award for "Tin Toy":

Pixar wins an Academy Award for "Tin Toy," the first entirely computer-animated work to win in the best animated short film category. Pixar, now a division of Disney, continued its success with a string of shorts and the first entirely computer-animated feature-length film, the best-selling "Toy Story." *CHM

2012 Buzz Lightyear that flew in space joins Smithsonian collection. Launched May 31, 2008, aboard the space shuttle Discovery with mission STS-124 and returned on Discovery 15 months later with STS-128, the 12-inch action figure is the longest-serving toy in space. Disney Parks partnered with NASA to send Buzz Lightyear to the International Space Station and create interactive games, educational worksheets and special messages encouraging students to pursue careers in science, technology, engineering and mathematics (STEM). The action figure will go on display in the museum’s "Moving Beyond Earth" gallery in the summer. The Toy Story character became part of the National Air and Space Museum’s popular culture collection. *http://airandspace.si.edu [I still have a Buzz Lightyear toy on my book case given to me by some students because I used to use his trademark quote in (my very questionable) Latin, "ad infinitum, et ultra." ]

BIRTHS

1825 Francesco Faà di Bruno (29 March 1825–27 March 1888) was an Italian mathematician and priest, born at Alessandria. He was of noble birth, and held, at one time, the rank of captain-of-staff in the Sardinian Army. He is the eponym of Faà di Bruno's formula. In 1988 he was beatified by Pope John Paul II. Today, he is best known for Faà di Bruno's formula on derivatives of composite functions, although it is now certain that the priority in its discovery and use is of Louis François Antoine Arbogast: Faà di Bruno should be only credited for the determinant form of this formula. However, his work is mainly related to elimination theory and to the theory of elliptic functions.
He was the author of about forty original articles published in the "Journal de Mathématiques" (edited by Joseph Liouville), Crelle's Journal, "American Journal of Mathematics" (Johns Hopkins University), "Annali di Tortolini", "Les Mondes", "Comptes rendus de l'Académie des sciences", etc.*Wik

1830 Thomas Bond Sprague FRSE FFA FIA LLD (29 March 1830 – 29 November 1920) was a British actuary, barrister and amateur mathematician who was the only person to have been President of both the Institute of Actuaries (1882–1886) in London and the Faculty of Actuaries (1894–1896) in Edinburgh, prior to their merger in 2010.

Sprague was an undergraduate at St John's College, Cambridge, where he was elected to a fellowship following his ranking as Senior Wrangler in the Cambridge Mathematical Tripos of 1853. He was awarded the Smith's Prize of Cambridge University in the same year. After serving as the actuary to the Equity and Law life insurance company (1861–1873), he became chief executive (1873–1900) of the Scottish Equitable Life Assurance Society in Edinburgh. *Wik

He 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

1873 Tullio Levi-Civita (29 Mar 1873, 29 Dec 1941) Italian mathematician who was one of the founders of absolute differential calculus (tensor analysis) which had applications to the theory of relativity. In 1887, he published a famous paper in which he developed the calculus of tensors. In 1900 he published, jointly with Ricci, the theory of tensors Méthodes de calcul différentiel absolu et leurs applications. in a form which was used by Einstein 15 years later. Weyl also used Levi-Civita's ideas to produce a unified theory of gravitation and electromagnetism. In addition to the important contributions his work made in the theory of relativity, Levi-Civita produced a series of papers treating elegantly the problem of a static gravitational field. *TIS

1890 Sir Harold Spencer Jones (29 Mar 1890, 3 Nov 1960) English astronomer who was 10th astronomer royal of England (1933–55). His work was devoted to fundamental positional astronomy. While HM Astronomer at the Cape of Good Hope, he worked on poper motions and parallaxes. Later he showed that small residuals in the apparent motions of the planets are due to the irregular rotation of the earth. He led in the worldwide effort to determine the distance to the sun by triangulating the distance of the asteroid Eros when it passed near the earth in 1930-31. Spencer Jones also improved timekeeping and knowledge of the Earth’s rotation. After WW II he supervised the move of the Royal Observatory to Herstmonceux, where it was renamed the Royal Greenwich Observatory.*TIS

1893 Jason John Nassau (29 March 1893 in Smyrna, (now Izmir) Turkey - 11 May 1965 in Cleveland, Ohio, USA) was an American astronomer.
He performed his doctoral studies at Syracuse, and gained his Ph.D. mathematics in 1920. (His thesis was Some Theorems in Alternants.) He then became an assistant professor at the Case Institute of Technology in 1921, teaching astronomy. He continued to instruct at that institution, becoming the University's first chair of astronomy from 1924 until 1959 and chairman of the graduate division from 1936 until 1940. After 1959 he was professor emeritus.
From 1924 until 1959 he was also the director of the Case Western Reserve University (CWRU) Warner and Swasey Observatory in Cleveland, Ohio. He was a pioneer in the study of galactic structure. He also discovered a new star cluster, co-discovered 2 novae in 1961, and developed a technique of studying the distribution of red (M-class or cooler) stars.*Wik

1896 Wilhelm Friedrich Ackermann (29 March 1896 – 24 December 1962) was a German mathematician best known for the Ackermann function, an important example in the theory of computation.

In 1928, Ackermann helped David Hilbert turn his 1917 – 22 lectures on introductory mathematical logic into a text, Principles of Mathematical Logic. This text contained the first exposition ever of first-order logic, and posed the problem of its completeness and decidability (Entscheidungsproblem). Ackermann went on to construct consistency proofs for set theory (1937), full arithmetic (1940), type-free logic (1952), and a new axiomatization of set theory (1956).

Later in life, Ackermann continued working as a high school teacher. Still, he kept continually engaged in the field of research and published many contributions to the foundations of mathematics until the end of his life. He died in Lüdenscheid, West Germany in December 1962. *Wik

1912 Martin Eichler (29 March 1912 – 7 October 1992) was a German number theorist. He received his Ph.D. from the Martin Luther University of Halle-Wittenberg in 1936.
Eichler once stated that there were five fundamental operations of mathematics: addition, subtraction, multiplication, division, and modular forms. He is linked with Goro Shimura in the development of a method to construct elliptic curves from certain modular forms. The converse notion that every elliptic curve has a corresponding modular form would later be the key to the proof of Fermat's last theorem.*Wik

1912 Caius Jacob (29 March 1912 , Arad - 6 February 1992 , Bucharest ) was a Romanian mathematician and member of the Romanian Academy. He made contributions in the fields of fluid mechanics and mathematical analysis , in particular vigilance in plane movements of incompressible fluids, speeds of movement at subsonic and supersonic , approximate solutions in gas dynamics and the old problem of potential theory. His most important publishing was Mathematical introduction to the mechanics of fluids. *Wik

1941 Joseph Hooton Taylor, Jr. (March 29, 1941, ) is an American astrophysicist and Nobel Prize in Physics laureate for his discovery with Russell Alan Hulse of a "new type of pulsar, a discovery that has opened up new possibilities for the study of gravitation."

Taylor immediately went to the National Radio Astronomy Observatory's telescopes in Green Bank, West Virginia, and participated in the discovery of the first pulsars discovered outside Cambridge. Since then, he has worked on all aspects of pulsar astrophysics.

In 1974, Hulse and Taylor discovered the first pulsar in a binary system, named PSR B1913+16 after its position in the sky, during a survey for pulsars at the Arecibo Observatory in Puerto Rico. Although it was not understood at the time, this was also the first of what are now called recycled pulsars: Neutron stars that have been spun-up to fast spin rates by the transfer of mass onto their surfaces from a companion star.*Wik

DEATHS

1772 Emanuel Swedenborg (29 Jan 1688; 29 Mar 1772) Swedish scientist, philosopher and theologian. While young, he studied mathematics and the natural sciences in England and Europe. From Swedenborg's inventive and mechanical genius came his method of finding terrestrial longitude by the Moon, new methods of constructing docks and even tentative suggestions for the submarine and the airplane. Back in Sweden, he started (1715) that country's first scientific journal, Daedalus Hyperboreus. His book on algebra was the first in the Swedish language, and in 1721 he published a work on chemistry and physics. Swedenborg devoted 30 years to improving Sweden's metal-mining industries, while still publishing on cosmology, corpuscular philosophy, mathematics, and human sensory perceptions. *TIS

A mystic, he became best known for his book on the afterlife, Heaven and Hell (1758). His experiences culminated in a "spiritual awakening" in which he received a revelation that Jesus Christ had appointed him to write The Heavenly Doctrine to reform Christianity. According to The Heavenly Doctrine, the Lord had opened Swedenborg's spiritual eyes so that from then on, he could freely visit heaven and hell to converse with angels, demons and other spirits, and that the Last Judgment had already occurred in 1757.*Wik

The Flying Machine, sketched in his notebook from 1714. The operator would sit in the middle and paddle himself through the air.

1794 Marie Jean Antoine Nicolas de Caritat, Marquis of Condorcet (French: [; 17 September 1743 – 29 March 1794), known as Nicolas de Condorcet, was a French philosopher and mathematician. His ideas, including support for a liberal economy, free and equal public instruction, constitutional government, and equal rights for women and people of all races, have been said to embody the ideals of the Age of Enlightenment, of which he has been called the "last witness", and Enlightenment rationalism. A critic of the constitution proposed by Marie-Jean Hérault de Séchelles in 1793, the Convention Nationale — and the Jacobin faction in particular — voted to have Condorcet arrested. He died in prison after a period of hiding from the French Revolutionary authorities.

From 1765 to 1774, he focused on science. In 1765, he published his first work on mathematics, entitled Essai sur le calcul intégral, which was well received, launching his career as a mathematician. He went on to publish more papers, and on 25 February 1769, he was elected to the Académie royale des Sciences.

Condorcet worked with Leonhard Euler and Benjamin Franklin. He soon became an honorary member of many foreign academies and philosophic societies, including the American Philosophical Society (1775), the Royal Swedish Academy of Sciences (1785), the American Academy of Arts and Sciences (1792) and also in Prussia and Russia.

In 1785, Condorcet published his Essay on the Application of Analysis to the Probability of Majority Decisions, one of his most important works. This work described several now famous results, including Condorcet's jury theorem, which states that if each member of a voting group is more likely than not to make a correct decision, the probability that the highest vote of the group is the correct decision increases as the number of members of the group increases, and Condorcet's paradox, which shows that majority preferences can become intransitive with three or more options – it is possible for a certain electorate to express a preference for A over B, a preference for B over C, and a preference for C over A, all from the same set of ballots.

The paper also outlines a generic Condorcet method, designed to simulate pair-wise elections between all candidates in an election. He disagreed strongly with the alternative method of aggregating preferences put forth by Jean-Charles de Borda (based on summed rankings of alternatives). Condorcet was one of the first to systematically apply mathematics in the social sciences.[citation needed]

He also considered the instant-runoff voting elimination method, as early as 1788, though only to condemn it, for its ability to eliminate a candidate preferred by a majority of voters.

Condorcet's statue by Jacques Perrin, on Quai de Conti in Paris, France

1806 John Thomas Graves (4 December 1806, Dublin, Ireland–29 March 1870, Cheltenham, England) was an Irish jurist and mathematician. He was a friend of William Rowan Hamilton, and is credited both with inspiring Hamilton to discover the quaternions and with personally discovering the octonions, which he called the octaves. He was the brother of both the mathematician Charles Graves and the writer and clergyman Robert Perceval Graves.
In his twentieth year (1826) Graves engaged in researches on the exponential function and the complex logarithm; they were printed in the Philosophical Transactions for 1829 under the title An Attempt to Rectify the Inaccuracy of some Logarithmic Formulæ. M. Vincent of Lille claimed to have arrived in 1825 at similar results, which, however, were not published by him till 1832. The conclusions announced by Graves were not at first accepted by George Peacock, who referred to them in his Report on Algebra, nor by Sir John Herschel. Graves communicated to the British Association in 1834 (Report for that year) on his discovery, and in the same report is a supporting paper by Hamilton, On Conjugate Functions or Algebraic Couples, as tending to illustrate generally the Doctrine of Imaginary Quantities, and as confirming the Results of Mr. Graves respecting the existence of Two independent Integers in the complete expression of an Imaginary Logarithm. It was an anticipation, as far as publication was concerned, of an extended memoir, which had been read by Hamilton before the Royal Irish Academy on 24 November 1833, On Conjugate Functions or Algebraic Couples, and subsequently published in the seventeenth volume of the Transactions of the Royal Irish Academy. To this memoir were prefixed A Preliminary and Elementary Essay on Algebra as the Science of Pure Time, and some General Introductory Remarks. In the concluding paragraphs of each of these three papers Hamilton acknowledges that it was "in reflecting on the important symbolical results of Mr. Graves respecting imaginary logarithms, and in attempting to explain to himself the theoretical meaning of those remarkable symbolisms", that he was conducted to "the theory of conjugate functions, which, leading on to a theory of triplets and sets of moments, steps, and numbers" were foundational for his own work, culminating in the discovery of quaternions.
For many years Graves and Hamilton maintained a correspondence on the interpretation of imaginaries. In 1843 Hamilton discovered the quaternions, and it was to Graves that he made on 17 October his first written communication of the discovery. In his preface to the Lectures on Quaternions and in a prefatory letter to a communication to the Philosophical Magazine for December 1844 are acknowledgments of his indebtedness to Graves for stimulus and suggestion. After the discovery of quaternions, Graves employed himself in extending to eight squares Euler's four-square identity, and went on to conceive a theory of "octaves" (now called octonions) analogous to Hamilton's theory of quaternions, introducing four imaginaries additional to Hamilton's i, j and k, and conforming to "the law of the modulus".
Graves devised also a pure-triplet system founded on the roots of positive unity, simultaneously with his brother Charles Graves, the bishop of Limerick. He afterwards stimulated Hamilton to the study of polyhedra, and was told of the discovery of the icosian calculus. *Wik

The icosian calculus is a non-commutative algebraic structure discovered by the Irish mathematician William Rowan Hamilton in 1856. In modern terms, he gave a group presentation of the icosahedral rotation group by generators and relations.

Hamilton's discovery derived from his attempts to find an algebra of "triplets" or 3-tuples that he believed would reflect the three Cartesian axes. The symbols of the icosian calculus can be equated to moves between vertices on a dodecahedron. Hamilton's work in this area resulted indirectly in the terms Hamiltonian circuit and Hamiltonian path in graph theory. He also invented the icosian game as a means of illustrating and popularizing his discovery.

1873 Francesco Zantedeschi (born 1797, 29 Mar 1873) Italian priest and physicist, who published papers (1829, 1830) on the production of electric currents in closed circuits by the approach and withdrawal of a magnet, preceding Faraday's classic experiment of 1831. Studying the solar spectrum, Zantedeschi was among the first to recognize the marked absorption by the atmosphere of the red, yellow, and green light. Though not confirmed, he also thought he detected a magnetic action on steel needles by ultra-violet light (1838), at least suspecting a connection between light and magnetism many years before Clerk-Maxwell's announcement (1867) of the electromagnetic theory of light. He experimented on the repulsion of flames by a strong magnetic field.*TIS

1912 Robert Falcon Scott, (6 June 1868 - 29 March 1912) was a Royal Navy officer and explorer who led two expeditions to the Antarctic regions: the Discovery Expedition, 1901–04, and the ill-fated Terra Nova Expedition, 1910–13. During this second venture, Scott led a party of five which reached the South Pole on 17 January 1912, only to find that they had been preceded by Roald Amundsen's Norwegian expedition. On their return journey, Scott and his four comrades all died from a combination of exhaustion, starvation and extreme cold. *Wik

Shackleton, Scott, and Wilson before their march south during the Discovery expedition, 2 November 1902

1944 Grace Chisholm Young (née Chisholm; 15 March 1868 – 29 March 1944) was an English mathematician. She was educated at Girton College, Cambridge, England and continued her studies at Göttingen University in Germany. Her early writings were published under the name of her husband, William Henry Young, and they collaborated on mathematical work throughout their lives. For her work on calculus (1914–16), she was awarded the Gamble Prize.
Her son, Laurence Chisholm Young, was also a prominent mathematician. One of her living granddaughters, Sylvia Wiegand (daughter of Laurence), is also a mathematician (and a past president of the Association for Women in Mathematics.)*Wik.

Chisholm entered Girton in 1889 to study mathematics. One of her classmates and special friends was Isabel Maddison. At the end of their first year, when the Mays list came out, Maddison was top of the Second class with Grace next below her. That same year, also, Philippa Fawcett became the first woman to score above the (male) Senior Wrangler on Part I of the Mathematical Tripos. Women could not earn formal degrees at Cambridge at that time, but in 1892 Chisholm passed her final examinations (Mathematics Tripos Part I) and scored the equivalent of a first-class degree. She also took (unofficially, on a challenge, with Isabel Maddison) the exam for the Final Honours School in mathematics at the University of Oxford on which she out-performed all the Oxford students. Mary Cartwright writes that she believed "they were the first women to sit for the Final Honours School of Mathematics, and that they did it to refute a suggestion from one of their coaches that it was more difficult for a woman to obtain a first at Oxford than at Cambridge." Chisholm then remained at Cambridge for an additional year to compete Part II of the Mathematical Tripos, "a most unusual thing for a woman to do in those days" according to Cartwright. *Agnes Waypoints

1980 William Gemmell Cochran (15 July 1909, Rutherglen – 29 March 1980, Orleans, Massachusetts)In 1934 R A Fisher left Rothamsted Experimental Station to accept the Galton chair at University College, London and Frank Yates became head at Rothamsted. Cochran was offered the vacant post but he had not finished his doctoral course at Cambridge. Yates later wrote:-
... it was a measure of good sense that he accepted my argument that a PhD, even from Cambridge, was little evidence of research ability, and that Cambridge had at that time little to teach him in statistics that could not be much better learnt from practical work in a research institute.
Cochran accepted the post at Rothamsted where he worked for 5 years on experimental designs and sample survey techniques. During this time he worked closely with Yates. At this time he also had the chance to work with Fisher who was a frequent visitor at Rothamsted.
Cochran visited Iowa Statistical Laboratory in 1938, then he accepted a statistics post there in 1939. His task was to develop the graduate programe in statistics within the Mathematics Department. In 1943 he joined Wilks research team at Princeton.
At Princeton he was involved in war work examining probabilities of hits in naval warfare. By 1945 he was working on bombing raid strategies.
He joined the newly created North Carolina Institute of Statistics in 1946, again to develop the graduate programe in statistics. From 1949 until 1957 he was at Johns Hopkins University in the chair of biostatistics. Here he was more involved in medical applications of statistics rather than the agricultural application he had studied earlier.
From 1957 until he retired in 1976 Cochran was at Harvard. His initial task was to help set up a statistics department, something which he had a great deal of experience with by this time. He had almost become a professional at starting statistics within universities in the USA. *SAU

1983 Sir Maurice George Kendall, FBA (6 September 1907 – 29 March 1983) was a British statistician, widely known for his contribution to statistics. The Kendall tau rank correlation is named after him.*Wik He was involved in developing one of the first mechanical devices to produce (pseudo-) random digits, eventually leading to a 100,000-random-digit set commonly used until RAND's (once well-known) "A Million Random Digits With 100,000 Normal Deviates" in 1955.
Kendall was Professor of Statistics at the London School of Economics from 1949 to 1961. His main work in statistics involved k-statistics, time series, and rank-correlation methods, including developing the Kendall's tau stat, which eventually led to a monograph on Rank Correlation in 1948. He was also involved in several large sample-survey projects. For many, what Kendall is best known for is his set of books titled The Advanced Theory of Statistics (ATS), with Volume I first appearing in 1943 and Volume II in 1946. Kendall later completed a
rewriting of ATS, which appeared in three volumes in 1966, which were updated by collaborator Alan Stuart and Keith Ord after Kendall's death, appearing now as "Kendall's Advanced Theory of Statistics". *David Bee

1999 Boris A. Kordemsky ( 23 May 1907 – 29 March, 1999) was a Russian mathematician and educator. He is best known for his popular science books and mathematical puzzles. He is the author of over 70 books and popular mathematics articles.
Kordemsky received Ph.D. in education in 1956 and taught mathematics at several Moscow colleges.
He is probably the best-selling author of math puzzle books in the history of the world. Just one of his books, Matematicheskaya Smekalka (or, Mathematical Quick-Wits), sold more than a million copies in the Soviet Union/Russia alone, and it has been translated into many languages. By exciting millions of people in mathematical problems over five decades, he influenced generations of solvers both at home and abroad. *Age of Puzzles, by Will Shortz and Serhiy Grabarchuk (mostly)

*A personal favorite

1991 John Bardeen (23 May 1908; 30 Jan 1991 at age 82) American physicist who was cowinner of the Nobel Prize for Physics in both 1956 and 1972. He shared the 1956 prize with William B. Shockley and Walter H. Brattain for their joint invention of the transistor. With Leon N. Cooper and John R. Schrieffer he was awarded the 1972 prize for development of the theory of superconductors, usually called the BCS-theory (after the initials of their names). *TIS

Bardeen, Schockley, Brattain

2017 Alexei Alexeyevich Abrikosov (June 25, 1928 – March 29, 2017) is a Soviet and Russian theoretical physicist whose main contributions are in the field of condensed matter physics. He was awarded the Nobel Prize in Physics in 2003.
In two works in 1952 and 1957, Abrikosov explained how magnetic flux can penetrate a class of superconductors. This class of materials is known as type-II superconductors. The accompanying arrangement of magnetic flux lines is called the Abrikosov vortex lattice.
Abrikosov was awarded the Lenin Prize in 1966, the Fritz London Memorial Prize in 1972, and the USSR State Prize in 1982. In 1989 he received the Landau Prize from the Academy of Sciences, Russia. Two years later, in 1991, Abrikosov was awarded the Sony Corporation’s John Bardeen Award. The same year he was elected a Foreign Honorary Member of the American Academy of Arts and Sciences. He is also a member of the Royal Academy of London, a fellow of the American Physical Society, and in 2000 was elected to the prestigious National Academy of Sciences. He was the co-recipient of the 2003 Nobel Prize in Physics, with Vitaly Ginzburg and Anthony James Leggett, for theories about how matter can behave at extremely low temperatures. *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

Saturday, 28 March 2026

On This Day in Math - March 28

*George W. Hart, Sculpture

`The introduction of the cipher 0 or the group concept was general nonsense too, and mathematics was more or less stagnating for thousands of years because nobody was around to take such childish steps ...'.
Alexandre Grothendieck in a letter in 1982 to Ronald Brown

The 87th day of the year; the sum of the squares of the first four primes is 87. $87 = 2^2 + 3^2 + 5^2 + 7^2 $

87 = 3 * 29, $87^2 + 3^2 + 29^2$ and $ 87^2 - 3^2 - 29^2 $ are both primes

Among Australian cricket players, it seems, 87 is an unlucky score and is referred to as "the devil's number", supposedly because it is 13 runs short of 100.
87 is the third consecutive day that is semiprime (the product of two primes)

And 87 is, of course, the number of years between the signing of the U.S. Declaration of Independence and the Battle of Gettysburg, immortalized in Abraham Lincoln's Gettysburg Address with the phrase "fourscore and seven years ago..."

87 is the largest number that yields a prime when any of the one-digit primes 2, 5 or 7 is inserted between any two digits. The only other such number is 27 (and trivially, the 1 digit numbers). *Prime Curios

5! - 4! - 3! - 2! - 1! = 87. Remember the old puzzle of making numbers with four 4's. What numbers could you make with the first five factorials using only the four basic arithmetic functions between them

EVENTS

In 1747, the fascination with electricity upon reaching the American colonies was the subject of Benjamin Franklin's first of the famous series of letters in which he described his experiments on electricity to Peter Collinson, Esq., of London. He thanked Collison for his “kind present of an electric tube with directions for using it” with which he and others did electrical experiments. “For my own part I never was before engaged in any study that so totally engrossed my attention and my time as this has lately done; for what with making experiments when I can be alone, and repeating them to my friends and acquaintances, who, from the novelty of the thing, come continually in crowds to see them, I have, during some months past, had little leisure for anything else.”*TIS

1764 In a second trial of John Harrison's marine timekeeper, his son William departed for Barbados aboard the Tartar. As with the first trial, William used H4 to predict the ship's arrival at Madeira with extraordinary accuracy. The watch's error was computed to be 39.2 seconds over a voyage of 47 days, three times better than required to win the maximum reward of £20,000. *Royal Museum Greenwich

H4 is housed in silver pair cases some 5.2 inches (13 cm) in diameter. The clock's movement is highly complex for that period, resembling a larger version of the then-current conventional movement

1802 Olbers, while observing the constellation Virgo, had observed a "star" of the seventh-magnitude not found on the star charts. Over the following week he would observe the motion and determined that it was a planet. In early April he sent the data to Gauss to compute the orbit. On the 18th of April, Gauss computed the orbit in only three hours, placing the orbit between Mars and Jupiter. Olbers named the new planetoid Pallas, and predicted there would be others found in the same area. John Herschel dismissed this speculation as "dreams in which astronomers... indulge" but over 1000 such planetoids have been observed. *Dunnington, Gray, & Dohse; Carl Friedrich Gauss: Titan of Science

Pallas, the third largest asteroid in the asteroid belt and the second such object to be discovered, following the discovery of Ceres,discovered on 1 January 1801, by Giuseppe Piazzi.

In 1596, Johannes Kepler wrote, "Between Mars and Jupiter, I place a planet," in his Mysterium Cosmographicum, stating his prediction that a planet would be found there. While analyzing Tycho Brahe's data, Kepler thought that too large a gap existed between the orbits of Mars and Jupiter to fit Kepler’s then-current model of where planetary orbits should be found.

In an anonymous footnote to his 1766 translation of Charles Bonnet's Contemplation de la Nature, the astronomer Johann Daniel Titius of Wittenberg noted an apparent pattern in the layout of the planets, now known as the Titius-Bode Law. If one began a numerical sequence at 0, then included 3, 6, 12, 24, 48, etc., doubling each time, and added four to each number and divided by 10, this produced a remarkably close approximation to the radii of the orbits of the known planets as measured in astronomical units, provided one allowed for a "missing planet" (equivalent to 24 in the sequence) between the orbits of Mars (12) and Jupiter (48).

1809 Gauss ﬁnished work on his Theoria Motus. It explains his methods of computing planetary orbits using least squares. [Springer’s 1985 Statistics Calendar] *VFR

The first step toward least squares may have began with "errors decrease with aggregation rather than increase, perhaps first expressed by Roger Cotes in 1722."

The first clear and concise exposition of the method of least squares was published by Legendre in 1805. The technique is described as an algebraic procedure for fitting linear equations to data and Legendre demonstrates the new method by analyzing the same data as Laplace for the shape of the Earth. Within ten years after Legendre's publication, the method of least squares had been adopted as a standard tool in astronomy and geodesy in France, Italy, and Prussia, which constitutes an extraordinarily rapid acceptance of a scientific technique.

In 1809 Carl Friedrich Gauss published his method of calculating the orbits of celestial bodies. In that work he claimed to have been in possession of the method of least squares since 1795. This naturally led to a priority dispute with Legendre. However, to Gauss's credit, he went beyond Legendre and succeeded in connecting the method of least squares with the principles of probability and to the normal distribution. He had managed to complete Laplace's program of specifying a mathematical form of the probability density for the observations, depending on a finite number of unknown parameters, and define a method of estimation that minimizes the error of estimation.

1935: Near Roswell, New Mexico, Robert H. Goddard successfully launched the first gyroscopically-stabilized liquid-fueled rocket. In a 20-second flight, the A Series rocket, number A-5, reached an altitude of 4,800 feet (1,463 meters) and traveled 13,000 feet (3,962 meters) down range. Its speed was 550 miles per hour (885 kilometers per hour). During the flight, the rocket corrected its flight path several times. *Today in Aviation History

Dr. Robert H. Goddard with one of his liquid-fueled A-series rockets at Roswell, New Mexico, circa 1935. (National Air and Space Museum Archives, Smithsonian Institution)

In 1946, the Census Bureau and the National Bureau of Standards met to discuss the purchase of a computer. The agencies agreed to buy UNIVAC, the world's first general all-purpose business computer, from Presper Eckert and John Mauchly for a mere $225,000. Unfortunately, UNIVAC cost far more than that to develop. Eckert and Mauchly's venture floundered as the company continued to build and program UNIVACs for far less than the development cost. Eventually, the company was purchased by Remington Rand. *TIS

1949 The phrase "Big Bang" is created. Shortly after 6:30 am GMT on BBC's The Third Program, Fred Hoyle used the term in describing theories that contrasted with his own "continuous creation" model for the Universe. "...based on a theory that all the matter in the universe was created in one big bang ... ". *Mario Livio, Brilliant Blunders

"Suddenly, an explosive expansion began, ballooning our universe outwards faster than the speed of light. This was a period of cosmic inflation that lasted mere fractions of a second — about 10^-32 of a second, according to physicist Alan Guth’s 1980 theory that changed the way we think about the Big Bang forever." *Space.com

Big Bang Background Radiation *ESA Planck

1959 Germany issued a stamp commemorating the 400th anniversary of the death of Adam Riese [Scott #799] *VFR I understand that the German expression "nach Adam Riese", is still used today. It means "according to Adam Riese" and it is used in saying something is exactly correct.

The X on the stamp with numbers is from Riese's method of checking operations by casting out nines from his book Rechnung auff der linihen on the use of a counting board, shown on the cover page.

The horizental lines have values of 1, 10, 100, and stones placed between the lines were half the upper line, 5, 50, 500.

To add for instance, stones for two (or more) numbers were placed on or between the lines to add up to the given values. Then for every five on a line, they are replaced with a stone between this line and the one above (so five tens would be replaced by a fifty stone). Two stones between lines would be replaced with a stone on the line above. Rules for all the arithmetic operations were included.

In 2006, a substantial "lost" book of manuscripts by Robert Hooke in his own handwriting was bought for the Royal Society by donations of nearly £1 million. The book was just minutes before going on the auction block when a last-minute purchase agreement was made and kept the precious document in Britain. Hooke is now often overlooked, except for his law of elasticity, although in his time, he was a prolific English scientist and contributed greatly to planning the rebuilding of London after the Great Fire of 1666. The document of more than 520 pages of manuscripts included the minutes of the Royal Society from 1661-82. It had been found in a cupboard in a private house by an antiques expert there to value other items. *TIS

BIRTHS 1847 Gyula Farkas (28 March 1847 in Sárosd, Fejér County, Hungary - 27 Dec 1930 in Pestszentlorinc, Hungary) He is remembered for Farkas theorem which is used in linear programming and also for his work on linear inequalities. In 1881 Gyula Farkas published a paper on Farkas Bolyai's iterative solution to the trinomial equation, making a careful study of the convergence of the algorithm. In a paper published three years later, Farkas examined the convergence of more general iterative methods. He also made major contributions to applied mathematics and physics, particularly in the areas of mechanical equilibrium, thermodynamics, and electrodynamics.*SAU

1923 Israel Nathan Herstein (March 28, 1923, Lublin, Poland – February 9, 1988, Chicago, Illinois) was a mathematician, appointed as professor at the University of Chicago in 1951. He worked on a variety of areas of algebra, including ring theory, with over 100 research papers and over a dozen books.
He is known for his lucid style of writing, as exemplified by the classic and widely influential Topics in Algebra, an undergraduate introduction to abstract algebra that was published in 1964, which dominated the field for 20 years. A more advanced classic text is his Noncommutative Rings in the Carus Mathematical Monographs series. His primary interest was in noncommutative ring theory, but he also wrote papers on finite groups, linear algebra, and mathematical economics.*Wik

1928 Alexander Grothendieck (28 Mar 1928-13 November 2014) In 1966 he won a Fields Medal for his work in algebraic geometry. He introduced the idea of K-theory and revolutionized homological algebra. Within algebraic geometry itself, his theory of schemes is used in technical work. His generalization of the classical Riemann-Roch theorem started the study of algebraic and topological K-theory. His construction of new cohomology theories has left consequences for algebraic number theory, algebraic topology, and representation theory. His creation of topos theory has appeared in set theory and logic.
One of his results is the discovery of the first arithmetic Weil cohomology theory: the ℓ-adic étale cohomology. This result opened the way for a proof of the Weil conjectures, ultimately completed by his student Pierre Deligne. To this day, ℓ-adic cohomology remains a fundamental tool for number theorists, with applications to the Langlands program.
Grothendieck influenced generations of mathematicians after his departure from mathematics. His emphasis on the role of universal properties brought category theory into the mainstream as an organizing principle. His notion of abelian category is now the basic object of study in homological algebra. His conjectural theory of motives has been behind modern developments in algebraic K-theory, motivic homotopy theory, and motivic integration. *Wik

DEATHS

1678 Claude François Milliet Dechales (1621 in Chambéry, France - 28 March 1678 in Turin, Italy) Dechales is best remembered for Cursus seu mundus mathematicus published in Lyons in 1674, a complete course of mathematics. Topics covered in this wide ranging work included practical geometry, mechanics, statics, magnetism and optics as well as topics outwith the usual topics of mathematics such as geography, architecture, astronomy, natural philosophy and music. In 1678 he published in Lausanne his edition of Euclid, The Elements of Euclid Explained in a New but Most Easy Method: Together with the Use of Every Proposition through All Parts of the Mathematics, written in French by That Most Excellent Mathematician, F Claude Francis Milliet Dechales of the Society of Jesus. This work covers Books 1 to 6, together with Books 11 and 12, of Euclid's Elements. A second edition was published in 1683, then an edition revised by Ozanam was published in Paris in 1753. An English translation was published in London by M Gillyflower and W Freeman, the translation being by Reeve Williams. A second edition of this English translation appeared in 1696. Schaap writes, "Dechales's separate edition of Euclid, long a favourite in France and elsewhere on the Continent, never became popular in England." *SAU

1794 Marie Jean Antoine Nicolas de Caritat, marquis de Condorcet (17 September 1743 – 28 March 1794), known as Nicolas de Condorcet, was a French philosopher, mathematician, and early political scientist whose Condorcet method in voting tally selects the candidate who would beat each of the other candidates in a run-off election. Unlike many of his contemporaries, he advocated a liberal economy, free and equal public education, constitutionalism, and equal rights for women and people of all races. His ideas and writings were said to embody the ideals of the Age of Enlightenment and rationalism, and remain influential to this day. He died a mysterious death in prison after a period of being a fugitive from French Revolutionary authorities.*Wik
Condorcet committed suicide by poisoning while in jail so that the republican terrorists could not take him to Paris. *VFR (The St Andrews site has the date of his death one day later.)

1840 Simon Antoine Jean Lhuilier (24 April 1750 in Geneva, Switzerland - 28 March 1840 in Geneva, Switzerland) His work on Euler's polyhedra formula, and exceptions to that formula, were important in the development of topology. Lhuilier also corrected Euler's solution of the Königsberg bridge problem. He also wrote four important articles on probability during the years 1796 and 1797. His most famous pupil was Charles-François Sturm who studied under Lhuilier during the last few years of his career in Geneva. *SAU He won the mathematics section prize of the Berlin Academy of Sciences for 1784 in response to a question on the foundations of the calculus. The work was published in his 1787 book Exposition elementaire des principes des calculs superieurs. It was in this book that he first introduced the "lim." (the period would soon fall out use) notation for the limit of a function. he wrote, "lim.$ \frac{\delta x}{\delta x} $. The symbol reappeared in 1821 in Cours d'Analyse by Augustin Louis Cauchy. *Florian Cajori, The History of Notations on the Calculus.

1850 Bernt Michael Holmboe (23 March 1795 – 28 March 1850) was a Norwegian mathematician. Holmboe was hired as a mathematics teacher at the Christiania Cathedral School in 1818, where he met the future renowned mathematician Niels Henrik Abel. Holmboe's lasting impact on mathematics worldwide has been said to be his tutoring of Abel, both in school and privately. The two became friends and remained so until Abel's early death. Holmboe moved to the Royal Frederick University in 1826, where he worked until his own death in 1850.
Holmboe's significant impact on mathematics in the fledgling Norway was his textbook in two volumes for secondary schools. It was widely used, but faced competition from Christopher Hansteen's alternative offering, sparking what may have been Norway's first debate about school textbooks. *Wik

1874 Peter Andreas Hansen (8 Dec 1795; 28 Mar 1874) Danish astronomer whose most important work was the improvement of the theories and tables of the orbits of the principal bodies in the solar system. At Altona observatory he assisted in measuring the arc of meridian (1821). He became the director (1825) of Seeberg observatory, which was removed to Gotha in a new observatory built for him (1857). He worked on theoretical geodesy, optics, and the theory of probability. The work in celestial mechanics for which he is best known are his theories of motion for comets, minor planets, moon and his lunar tables (1857) which were in use until 1923. He published his lunar theory in Fundamenta ("Foundation") in 1838, and Darlegung ("Explanation") in 1862-64.*TIS

1950 Ernst David Hellinger (30 Sept 1883 in Striegau, Silesia, Germany (now Strzegom, Poland) - 28 March 1950 in Chicago, Illinois, USA) introduced a new type of integral: the Hellinger integral . Jointly with Hilbert he produced an important theory of forms. From 1907 to 1909 he was an assistant at Göttingen and, during this time, he ".. edited Hilbert's lecture notes and Felix Klein's influential Elementarmathematik vom höheren Standpunkte aus (Berlin, 1925) which was translated into English (New York, 1932).

On November 13, 1938, Hellinger was arrested, taken to the Festhalle, and then put into Dachau concentration camp. However, his friends were able to arrange a temporary job for Hellinger at Northwestern University at Evanston, Illinois, in the United States. He was released from the Dachau camp after six weeks, on condition that he emigrate immediately.

He joined the faculty at Northwestern University as lecturer in Mathematics in 1939. He became a U.S. citizen in 1944. Promoted to professor in 1945, he became emeritus in 1949. He died on March 28, 1950, in Chicago, Illinois, United States.

Years later the story is told that,

Shortly after his arrival at Northwestern, one of the professors in describing Northwest's mathematics program to him remarked that in the honours course Felix Klein's 'Elementary mathematics from an advanced standpoint' was used as a text and "perhaps Hellinger was familiar with it". At this Hellinger ... replied "familiar with it, I wrote it!".

*SAU

2011 Pilar Ribeiro (5 October 1911 – 28 March 2011) was a mathematician who was a founder of the Portuguese Mathematical Society (SPM) and also of the Gazeta de Matemática (Mathematics Gazette).

She graduated in Mathematics from the Faculty of Sciences of the University of Lisbon in 1933, at a time when it was still unusual for women to study such a subject. A year later, she married mathematician Hugo Baptista Ribeiro (1910–88), who she had met during the course. The couple shared an opposition to the established Estado Novo dictatorship and participated in activities of the Portuguese Communist Party. After graduating she taught mathematics in Lisbon as well as attending seminars given by the mathematician António Aniceto Monteiro. As a founding member of the Portuguese Mathematical Society, together with Bento de Jesus Caraça, she held the position of First Secretary for the 1941/1942 biennium. She returned to that same position in 1946/1947, when her husband was Secretary-General. The Mathematics Gazette, the Society’s publication, played an important role in the preservation and dissemination of the history of mathematics in Portugal and elsewhere in the 1940s.

Between 1942 and 1946, she accompanied her husband to Zurich, where he studied for his PhD. Pilar Ribeiro took the opportunity to attend several specialized courses in mathematics at the Federal Polytechnic School of Zurich. When her husband stopped receiving the Portuguese scholarship to which he was entitled, she started to work so that he could complete his doctorate. She also sent papers to Gazeta de Matemática, on teaching mathematics in Switzerland. Returning to Portugal, the couple faced opposition to science on the part of the Estado Novo, which condemned independent thinking. Together with José da Silva Paulo, she was responsible for the translation into Portuguese of David Hilbert's classic work, Grundlagen der Geometrie (Foundations of Geometry).

In January 2005, she donated her husband's estate to the National Library, consisting essentially of correspondence from national and foreign personalities, including a core of family letters and some drafts of letters sent. She died in Cascais, Portugal on 28 March 2011, a few months before she would have celebrated her 100th birthday. A Portuguese postage stamp featuring her was issued on the centenary of her birth.

2013 George Edward Pelham Box (18 October 1919, March 28, 2013, Madison, WI) is a statistician, who has made important contributions in the areas of quality control, time-series analysis, design of experiments, and Bayesian inference.
Box has written research papers and published books. These include Statistics for experimenters (1978), Time series analysis: Forecasting and control (1979, with Gwilym Jenkins) and Bayesian inference in statistical analysis. (1973, with George C. Tiao). Today, his name is associated with important results in statistics such as Box–Jenkins models, Box–Cox transformations, Box–Behnken designs, and others. Box married Joan Fisher, the second of Ronald Fisher's five daughters. In 1978, Joan Fisher Box published a biography of Ronald Fisher, with substantial collaboration of Box. *Wik

In his obituary for Box, Brad Jones of JMP recounted the following, with another fascinating Box quote,

"The last time I saw him was at the JMP Discovery Summit conference in 2009 where I introduced him to give a speech. George got a standing ovation from a crowd of several hundred fans of design of experiments and particularly his work. I will never forget his remarks as the applause died slowly away.

He said, "I feel like the son of the sultan on his 21st birthday when presented with 21 virgins. I know what to do. I just don't know where to start!"

Box died on 28 March 2013. He was 93 years old

My favorite Box quote (slightly shortened from his actual comment) is