User:David Eppstein/DYK

Did you know?[edit]

... that the Poniatowski gems, 19th-century forgeries of ancient engraved gems, have themselves been copied by other forgers? (23.07)
... that multiple mathematics competitions have made use of Sophie Germain's identity? (23.07)
... that the 17-animal inheritance puzzle has variously been stated with 17 camels, 17 elephants, or 17 horses? (23.07)

... that exercises in the fair division of food (example pictured) are often used to teach unit fractions? (23.04)
... that a simple polygon through all the points of a three-by-three grid must pass straight through some of the points, rather than turning at each of them? (23.03)
... that French astrochemist Christine Joblin co-created a webcomic to popularize her research on the origins of cosmic dust? (23.03)
... that after Archimedes first defined convex curves, mathematicians lost interest in their analysis until the 19th century, more than two millennia later? (23.01)

... that ten-sided gaming dice (examples pictured) have kite-shaped faces? (22.11)
... that Nicole Lloyd-Ronning returned to astrophysics research after a ten-year hiatus, aided by an American Physical Society award for women with interrupted careers? (22.11)
... that it took 90 years to replace the "unconvincing" original proof of Roberts's triangle theorem, on the number of triangles formed by systems of lines, with a correct proof? (22.11)
... that if you remove two opposite corners of a chessboard, you cannot cover all squares with dominos? (22.10)

... that circle packings in the form of a Doyle spiral (pictured) were used to model plant growth long before their mathematical investigation by Doyle? (22.10)
... that physical applications of Euclidean minimum spanning trees range in scale from the particles in bubble chambers to the dark matter halos of galaxies? (22.09)
... that Ellaisa Marquis has been called the "marquis player" of women's football in Saint Lucia? (22.07)
... that a folded paper lantern shows that certain mathematical definitions of surface area are incorrect? (22.06)
... that although the problem of squaring the circle with compass and straightedge goes back to Greek mathematics, it was not proven impossible until 1882? (22.06)

... that the recycling symbol (pictured) depicts a Möbius strip? (22.05)
... that the first player can win a game of Fibonacci nim unless it starts with a Fibonacci number of coins? (22.03)
... that although the Kepler triangle has similar proportions to the Great Pyramid of Giza, the triangle's connection to the golden ratio makes it unlikely to have been used in ancient Egypt? (22.03)
... that the mathematical infinity symbol ∞ may be derived from the Roman numerals for 1000 or for 100 million? (22.03)

... that an antiparallelogram (example pictured) is a crossed quadrilateral with two pairs of equal-length edges? (22.02)
... that factorials are more likely to begin with small digits? (22.01)
... that record-setting airplane spinner Catherine Cavagnaro is also a professional mathematician? (22.01)

... that Jessen's icosahedron (pictured) has been used for both the "Skwish" children's toy and a NASA proposal for a "super ball bot" to cushion space landers on other planets? (22.01)
... that certain bamboo species release large numbers of seeds in synchrony after numbers of years that have only 2, 3, and 5 as their prime factors? (22.01)

... that the number of cannonballs in a square pyramid (pictured) with $n$ cannonballs along each edge is ${\frac {n(n+1)(2n+1)}{6}}$ ? (22.01)
... that one can place 16 pawns on a chessboard such that no three pawns lie on the same line? (21.12)

... that it is impossible to draw non-crossing lines from three houses to three utilities (pictured) in a plane? (21.12)
... that for round-robin sports tournaments, finding a ranking of the competitors that minimizes the number of upset games is an instance of the feedback arc set problem? (21.12)
... that whenever some of the people in a party shake hands, the number of people who shake an odd number of other people's hands is even? (21.11)
... that an equivalence between algebraic and geometric definitions of constructible numbers helps prove the impossibility of squaring the circle? (21.11)
... that 100 years after Mary Emily Sinclair wrote a master's thesis in mathematics on the discriminants of quintic polynomials, Helaman Ferguson based a sculpture on her work? (21.10)
... that dyadic rationals, fractions based on powers of two, can be easier to work with than other kinds of fractions for both schoolchildren and computers? (21.08)
... that although Steinitz's theorem is commonly used to describe convex polyhedra using graph theory, its original formulation did not use graphs? (21.08)
... that Shirley Chiang captured the first image of individual benzene molecules? (21.08)
... that mathematician Gunilla Kreiss, the daughter of Heinz-Otto Kreiss, later became his granddaughter? (21.08)
... that when a tree is a star, connecting its leaves in a cycle makes a wheel? (21.08)
... that the Cairo pentagonal tiling was a favorite pattern of M. C. Escher? (21.08)
... that after Euclid proved that every Mersenne prime leads to an even perfect number, it took more than 2000 years before Leonhard Euler proved that every even perfect number comes from a Mersenne prime? (21.07)
... that for polygons with integer coordinates, the area can be computed from the numbers of integer points inside and on the boundary of the polygon? (21.07)
... that in 1593, French amateur mathematician François Viète found the first formula in European mathematics to represent an infinite process, a product of square roots that he used to compute $π$ ? (21.07)
... that Sindee Simon studied ancient amber to show that glass does not flow? (21.06)
... that Gertrude Michelson sat on the board of trustees of Columbia University before it began admitting female students? (21.05)
... that when mathematician Josephine M. Mitchell married another University of Illinois faculty member, the university revoked her tenured position so her husband could keep his untenured one? (21.05)
... that one can accurately estimate the area of irregular objects such as plant leaves using only a transparent sheet printed with a grid of dots? (21.05)
... that when Ruth Stokes defended her dissertation on the theory of linear programming in 1931, she became the first person to earn a doctorate in mathematics from Duke University? (21.05)
... that a mathematical conjecture about tiling space by cubes was transformed into a problem in graph theory that became a benchmark for clique-finding algorithms? (21.04)
... that Theresa M. Korn turned down a scholarship to the Carnegie Institute of Technology in order to become the institute's first female engineer? (21.04)

... that the common depiction of the Borromean rings as three linked but pairwise-unlinked circles (pictured) is an impossible object, because they cannot actually be circular? (21.03)
... that Ted Cohen's romance was set to music by Isaac Asimov? (21.03)
... that Ronald Graham, president of the American Mathematical Society and the Mathematical Association of America, also became president of the International Jugglers' Association? (21.02)
... that although the Euclidean distance and the Pythagorean theorem are both ancient concepts, the Pythagorean formula for distance was not published until 1731? (20.12)
... that Laura Garwin, one of the first female Rhodes Scholars, left a career in science to become a full-time trumpeter? (20.12)
... that computer science professor Ruth Aylett performed with a robot poet in the Edinburgh Free Fringe? (20.12)

... that unlike their Euclidean equivalents, the ideal regular tetrahedron, octahedron, and dodecahedron can all tile hyperbolic space (pictured)? (20.10)
... that a book on polyhedra by Piero della Francesca fell victim to "probably the first full-blown case of plagiarism in the history of mathematics" when Luca Pacioli copied it in his Divina proportione? (20.09)

... that Perspectiva corporum regularium, a 1568 book of engraved polyhedra (pictured), demonstrates visually the medieval theory that the complexity of the physical world comes from four basic elements? (20.09)
... that among proofs of the Sylvester–Gallai theorem, Kelly's has been praised as "simply the best", but also criticized as "like using a sledge hammer to crack an almond"? (20.09)
... that the book Geometric Exercises in Paper Folding was inspired by one of the Froebel gifts for kindergarten children? (20.05)
... that the book Calendrical Calculations has been called "the most extensive and detailed publication on calendar systems" since Friedrich Karl Ginzel's work in the early 20th century? (20.04)
... that Chiara Daraio has used a version of Newton's cradle to create "sound bullets", and walls filled with ball bearings to create one-way barriers for sound? (20.03)
... that any tetrahedron that has integer edge lengths, face areas, and volume can be given integer vertex coordinates? (20.03)
... that former college basketball star Amy Langville is an expert in ranking systems, and has applied her ranking expertise to basketball bracketology? (20.02)
... that after world-record breaststroke swimmer Gordon Warner lost his left leg, he resumed practising the Japanese way of the sword and eventually became the discipline's highest-ranked Westerner? (20.01)

... that it is possible to pack 27 equal cuboids (pictured) into a cube? (19.12)
... that William Chapple discovered Euler's theorem and Poncelet's porism? (19.12)
... that before becoming a professional mathematician, Chikako Mese was a record-breaking high school softball player? (19.12)
... that Aaron Hawkins uses nail polish to guide laser light into optofluidic devices to detect antibiotic resistance? (19.11)
... that Anne C. Morel was the first woman to become a full professor of mathematics at the University of Washington? (19.11)
... that mathematician Dona Strauss left South Africa over apartheid, lost a faculty job at Dartmouth for joining an anti-war protest, and helped found European Women in Mathematics? (19.10)
... that J. J. Stiffler's "unparalleled" and "landmark" Theory of Synchronous Communications (1971) sprang from NASA's need for power-efficient synchronization of data transmission for its space probes? (19.09)
... that Pandrosion may have been an earlier female contributor to mathematics than Hypatia? (19.09)
... that the work of C. Doris Hellman on the Great Comet of 1577 led historians of science to recognize the comet's key role in the success of the Copernican Revolution? (19.09)
... that according to a study conducted by epidemiologist Xifeng Wu and her colleagues, fifteen minutes of moderate exercise per day can increase lifespan by an average of three years? (19.07)
... that every Garden of Eden contains an orphan? (19.06)
... that Lloyd Trefethen and Lloyd Trefethen showed that, when shuffling playing cards, five riffles are enough? (19.06)
... that Fields Medal-winning mathematician Klaus Roth performed so poorly on the Mathematical Tripos that his tutor suggested he take "some commercial job with a statistical bias"? (19.05)

... that although the Grünbaum–Rigby configuration (pictured) has been studied since 1879, it was not depicted in its realization as three overlaid heptagrams until 1990? (19.05)
... that Freeman Dyson used a result by Marian Pour-El on the mathematical undecidability of the wave equation as evidence for the superiority of analog to digital forms of life? (19.02)
... that photographer Lola Álvarez Bravo was described by Alfonso Michel as Mexico's most important painter? (19.01)
... that Joan L. Mitchell co-invented JPEG? (18.11)
... that racist graffiti on mathematician Chawne Kimber's college campus, along with George Carlin's seven dirty words, inspired her to politicize her quilting? (18.11)
... that decorative patterns using isosceles triangles date back to the Early Neolithic? (18.10)
... that photographer Evgenia Arbugaeva won the trust of a Siberian mammoth-tusk hunter by stitching up his injured hand? (18.10)
... that a story by Argentine mathematician Magdalena Mouján about a Basque family that travels back in time to their homeland was blocked by the Franco regime? (18.08)
... that a solar-powered device for extracting water from the air, co-designed by Evelyn Wang, has been compared to the moisture vaporators in Star Wars? (18.08)
... that the witch of Agnesi comes from a circle and kisses it? (18.07)
... that the tennis ball theorem concerns curves that, like the seam of a tennis ball, cut the surface of a sphere into two equal areas? (18.06)
... that Deborah Bial uses Lego to test whether students are ready for college? (18.06)

... that Rubens' painting Hercules' Dog Discovers Purple Dye (detail pictured) does not depict the right kind of snail? (18.06)
... that the three-gap theorem explains both the spacing of leaves on plant stems and the intervals between adjacent tones in certain musical tuning systems? (18.04)
... that Hungarian mathematician Márta Svéd earned her Ph.D. at age 75? (18.04)
... that prime numbers have been studied since the time of the ancient Greeks, but had few real-world applications until the invention of public-key cryptography in the 1970s? (18.04)
... that Emily Riehl, former bassist for the band Unstraight, wrote about "unstraightening" in her research as a professional mathematician? (18.03)
... that Mary Nomura, a singer who was sent to the Manzanar concentration camp as an orphaned teenager, became known as the "songbird of Manzanar"? (18.03)
... that Annalisa Crannell brings chopsticks to art galleries as a tool for finding vanishing points? (18.03)
... that Australian mathematician Katherine Heinrich was the first female president of the Canadian Mathematical Society? (18.02)
... that a silverback gorilla sat on Hilary Swarts' head? (17.12)
... that Marjorie Hahn, a retired mathematics professor and international senior-level tennis player, approaches tennis games with the same plan that she uses for mathematical proofs? (17.12)
... that before becoming director of the United States Census Bureau, Martha Farnsworth Riche earned a doctorate in French literature? (17.12)
... that Jeanne LaDuke worked alongside Natalie Wood as a child actor before becoming a professional mathematician? (17.11)
... that Amy H. Herring led a study whose data showed many American women were reportedly virgins at the birth of their first child? (17.11)
... that Barbara A. Bailar resigned from the United States Census Bureau in 1988 to protest a decision not to adjust the 1990 results for systematic undercounting of minorities? (17.11)
... that the sexagesimal approximation to the square root of 2 used by Babylonian tablet YBC 7289 appeared again much later in Ptolemy's Almagest? (17.11)
... that Barbara Everitt Bryant was the first woman to direct the United States Census Bureau? (17.11)
... that when Pál Turán was forced to work in a brick factory during World War II, the bumpy crossings of the cart tracks inspired him to ask how to draw graphs with few crossings? (17.10)
... that Anette Hosoi designed a robot snail that moved by rippling over artificial snail slime? (17.09)
... that a play by Babette Hughes was performed in 1938 by six blind actresses? (17.06)
... that Anne Penfold Street, one of Australia's leading mathematicians, earned bachelor's and master's degrees in chemistry before switching to mathematics? (17.05)
... that mathematician Donald G. Saari advocates deciding elections by the Borda count instead of plurality voting, because it leads less often to paradoxical outcomes? (17.05)

... that the website "Six Degrees to Harry Lewis" (Lewis pictured) was a precursor to Facebook? (17.04)
... that erection engineer Mark Barr had a business making rubbers, said bicycles stimulated ball development, and was elected to the screw committee? (17.04)
... that Thomas North Whitehead suggested that England give America one of the four surviving copies of the Magna Carta to win support for Lend-Lease? (17.03)

... that a Bricard octahedron (pictured) can change its shape without changing the shapes of its faces? (17.03)
... that Euclidean space can be completely filled without overlaps by copies of any plesiohedron, a type of convex shape whose known examples have up to 38 sides? (17.03)
... that it is unknown whether the Dehn invariant of a flexible polyhedron stays invariant as it flexes? (17.03)
... that Kokichi Sugihara's illusions make marbles appear to roll uphill and circular pipes look rectangular? (17.03)

... that, no matter how $n$ non-overlapping pennies are arranged on a table, at least $0.258 n$ of them will not touch each other? (17.03)
... that although mathematician Vojtěch Jarník is known to computer scientists for his minimum spanning tree algorithm, his main work was in number theory? (17.02)
... that Pasang Lhamu Sherpa, one of the first Nepali women to climb K2, was named after the first Nepali woman to climb Everest? (17.02)
... that the Furstenberg–Sárközy theorem shows that the first player in the game of subtract a square can win from most positions? (17.01)
... that mathematician Moon Duchin was inspired to break gender barriers in mathematics by a book on baseball player Jackie Robinson's struggles against racism? (17.01)
... that the number of ways to fold a strip of stamps is always divisible by the number of stamps in the strip? (16.12)
... that Ami Radunskaya, a mathematician who heads the Association for Women in Mathematics, spent ten years as a cellist and music composer between high school and college? (16.12)
... that the positions of nonzero digits in two reciprocal irrational numbers, 1/3.30033000000000033... = 0.30300000303..., are given by the Moser–de Bruijn sequence and its double? (16.12)

... that dual graphs can explain why the halls and walls of many mazes (example pictured) form interlocking trees? (16.11)
... that 2-satisfiability can be used to schedule round-robin tournaments so that teams alternate between home and away games as much or as little as possible? (16.10)
... that John Harvard may have been inspired by Clio? (16.10)

... that a 1923 book by Progressive Era activist Kate Claghorn (pictured) has been called "the one significant contemporary study of the immigrant and the American legal system"? (16.07)
... that Margaret Jarman Hagood, a sociologist who wrote a book on Mothers of the South, became a mother herself before completing her bachelor's degree? (16.07)
... that as acting commissioner of the Bureau of Labor Statistics, Aryness Joy Wickens was the highest-paid woman in the US civil service in 1954? (16.07)
... that Irene Barnes Taeuber "helped found the science of demography"? (16.07)
... that because of pedigree collapse, some family trees are better modeled mathematically as directed acyclic graphs than as trees? (16.06)

... that Stanko Bilinski's 1960 rediscovery of the Bilinski dodecahedron (pictured) corrected a 75-year-old omission from the list of convex polyhedra with congruent rhombic faces? (16.06)
... that curve-shortening causes every smooth simple closed curve to become convex and then near-circular before it shrinks to a point? (16.05)
... that the name of the Chinese postman problem honors Chinese mathematician Meigu Guan, who first formulated it? (16.04)
... that Donald Knuth's analysis of the linear probing strategy for resolving collisions in hash tables has been called "a landmark in the analysis of algorithms"? (16.04)
... that Zvezdelina Stankova brought ideas from her Bulgarian mathematical education to California by founding the Berkeley Math Circle? (16.02)
... that binary logarithms can be used to determine the number of octaves between two musical tones? (16.01)
... that after mathematician Hinke Osinga studied invariant manifolds in her doctoral dissertation, she made a crochet model of one? (15.10)
... that a street in Rome is named after female Italian mathematician Pia Nalli? (15.10)
... that Hazel Findlay has free climbed El Capitán three times on three different routes, including two first female ascents? (15.10)
... that for conventional computers, Landauer's principle gives a nonzero lower bound on energy per step, but the energy usage of reversible cellular automata can be arbitrarily close to zero? (15.10)
... that Public Health Reports was established in 1878 to meet the requirements of the National Quarantine Act, which required American consulates abroad to report on epidemic diseases? (15.09)
... that mathematician Ed Posner wrote the University of Chicago's shortest doctoral thesis, only 26 pages long? (15.09)
... that a calculus textbook by David J. Foulis was used as a prop in The Sure Thing? (15.09)
... that the Anita Borg Institute gave blind computer scientist Chieko Asakawa their Women of Vision Award? (15.08)

... that six or more keys on a keyring can be distinguished from each other by coloring the keys using only two colors (pictured), but rings of fewer keys require more colors? (15.08)
... that Martha E. Sloan was the first female president of the Institute of Electrical and Electronics Engineers? (15.07)
... that Lixia Zhang coined the term "middlebox"? (15.07)

... that Leonardo da Vinci published a world map (pictured) in which eight octants of the earth were projected onto eight Reuleaux triangles? (15.06)
... that Marie-Louise Dubreil-Jacotin was the first female full professor of mathematics in France? (15.05)
... that James Colliander, Gigliola Staffilani, and Terence Tao are part of a collaborative group of mathematicians called the I-team? (15.01)
... that mathematician Linda Preiss Rothschild settled for graduate study at MIT after Princeton rejected her for being female? (15.01)
... that Ioana Dumitriu began taking graduate mathematics courses as a college freshman, and became the first female Putnam Fellow the following year? (15.01)
... that Fermat's only complete proof shows there is no integer right triangle with square area, pair of integer right triangles sharing two sides, or square gap between three equally spaced squares? (15.01)

... that the Laves graph (pictured), a highly symmetrical three-dimensional structure that forms one of the several crystal structures of carbon, is named after German crystallographer Fritz Laves? (14.12)

... that René Just Haüy modeled octahedral crystals mathematically as polycubes made of a centered octahedral number of cubes (pictured)? (14.09)
... that Northwest Coast artist Jim Hart is a hereditary chief of the Haida Nation? (14.08)
... that 19th-century French geometer Olry Terquem, writing as "Tsarphati", was an outspoken advocate of the Reform movement in Judaism? (14.07)
... that mathematician and author C. Stanley Ogilvy was an avid sailor who frequently competed in the Star World Championships? (14.07)
... that book embeddings of graphs have been used to model fault-tolerant computer systems, the phases of traffic lights, and pseudoknots in RNA molecules? (14.06)

... that a photograph (pictured) taken by Elena Mrozovskaya at the 1903 Ball in the Winter Palace in Saint Petersburg, Russia, was exhibited in the Hermitage Rooms in London 100 years later?(13.11)
... that the subjects of Marjorie Senechal's books include quasicrystals, Albania, and silk? (13.07)

... that every knotted polygon in three-dimensional space can be touched at four points by a quadrisecant line (pictured)? (13.07)
... that according to the Gilbert–Shannon–Reeds model of probability distribution, a deck of playing cards should be riffled seven times in order to thoroughly randomize it? (13.07)

... that M. C. Escher's woodcut Circle Limit III was inspired by an illustration of a hyperbolic tessellation (example pictured) in a paper by H. S. M. Coxeter? (13.07)
... that mathematician Andrew Gleason liked to say that proofs "really aren't there to convince you that something is true—they're there to show you why it is true"? (13.04)
... that Latvian-American mathematician Lipman Bers was also a human rights activist and a founder of the Committee on Human Rights of the National Academy of Sciences? (13.04)
... that circular layouts, in which the nodes of a graph are drawn on a circle, have been used to visualize the cyclic parts of metabolic networks? (13.03)
... that William Allen Whitworth was the first mathematician to publish Bertrand's ballot theorem, one of many misnamed mathematical theorems? (13.03)
... that because of the possibility of dead heats, the number of possible outcomes of a horse race is not a factorial, but an ordered Bell number? (13.03)
... that in the square of a graph, all vertices with a distance of no more than two in the original graph are adjacent? (13.03)
... that Karl Beth is considered one of the founding fathers of the psychology of religion? (12.10)
... that William W. Cooper, a pioneer of management science, dropped out of high school and worked as a professional boxer before becoming an academic? (12.10)
... that Andrew Vázsonyi became past president of The Institute of Management Sciences without ever having been its president? (12.10)

... that Pieter Nieuwland (pictured), an 18th-century child prodigy and polymath who died a year after becoming a professor, has been called the Dutch Isaac Newton? (12.09)
... that a tomahawk may be used to split an angle into three equal parts, despite the impossibility of doing so with compass and straightedge? (12.09)
... that John Hilliard's Cause of Death (1974) suggested four different interpretations of one photographic negative? (12.09)

... that Prince Rupert's cube, named for Prince Rupert of the Rhine, can pass through a square hole drilled into a smaller cube (pictured)? (12.09)
... that Nicolas de Bruijn was inspired to prove De Bruijn's theorem on packing bricks into boxes by his seven-year-old son's inability to pack some bricks into a box without wasted space? (12.09)
... that the shape that encloses two given volumes and has the minimum possible surface area is the double bubble commonly formed by soap bubbles? (12.07)

... that the success of the multi-language wall poems (pictured) in Leiden, South Holland, inspired similar projects in Sofia, Bulgaria, and in Paris, France? (12.06)
... that Albert Brahms kept the first known records of the tide levels on the North Sea coast of Germany? (12.05)
... that artist Tina Mion, of Winslow, Arizona, grew up visiting the museums of her birthplace, Washington, D.C., whose National Portrait Gallery now holds two of her works in its permanent collection? (12.05)
... that the number of ways to place $n$ diagonally symmetric rooks on an $n\times n$ chessboard in such a way that no two rooks attack each other is a telephone number? (12.04)
... that swarms of Japanese soldier crabs of the species Mictyris guinotae, named after French biologist Danièle Guinot, can be used in place of the billiard balls in billiard-ball computers? (12.04)
... that the Latvian mathematician Emanuels Grīnbergs lost his job and his doctoral degree for serving in the German Army during World War II, but then regained both by writing a new thesis? (12.04)
... that the Healdsburg Memorial Bridge in Healdsburg, California, was the first steel bridge across the Russian River? (12.01)

... that the Temple of Kwan Tai in Mendocino, California (pictured) was founded by a survivor from a fleet of seven Chinese junks, two of which landed on the California coast in 1854? (12.01)
... that Hendy Woods State Park, an old-growth coast redwood forest in the Anderson Valley of northern California, is scheduled to be closed in 2012 because of state budget cuts? (12.01)

... that the central chameleon cage in M. C. Escher's 1948 woodcut Stars has the shape of a compound of three octahedra (pictured)? (11.12)
... that despite leaving school at age 14, Thomas Kirkman became one of 19th-century England's leading mathematicians and helped found combinatorial design theory? (11.10)

... that the Pythagorean tiling, a pattern of squares of two sizes that can be used to prove the Pythagorean theorem, appears in a painting (pictured) by Dutch Golden Age artist Jacob Ochtervelt? (11.10)
... that the Sint Servaasbrug in Maastricht has been called the oldest bridge in the Netherlands, and was built in the 13th century to replace a Roman bridge that gave its name to the city? (11.10)
... that Michel Demazure, a mathematician from the pseudonymous Nicolas Bourbaki group, led two French science museums, the Palais de la Découverte and the Cité des Sciences et de l'Industrie? (11.08)
... that the De Bruijn–Erdős theorem may be used to extend the four-color theorem from finite planar graphs to planar graphs with infinitely many vertices? (11.07)
... that the Theil–Sen estimator can accurately fit a line to a set of sample points even when up to 29% of the points have been arbitrarily corrupted? (11.07)
... that the Malfatti circles, three tangent circles inside a triangle, are named after Malfatti because of an incorrect conjecture he made, and were studied earlier by Ajima and di Cecco? (11.06)
... that the widest path problem forms the algorithmic basis of the Schulze method used by Wikimedia to decide the winners of multiway elections? (11.05)

... that according to Kawasaki's theorem, an origami crease pattern with one vertex may be folded flat (pictured) if and only if the sum of every other angle between consecutive creases is 180º? (11.04)
... that John R. Isbell was the primary contributor to the mathematical theory of uniform spaces? (11.04)
... that Edgar Gilbert investigated the mathematics of shuffling playing cards? (11.03)
... that, in the Rule 90 cellular automaton, any finite pattern eventually fills the whole array of cells with copies of itself? (11.02)
... that The Princeton Companion to Mathematics is the 2011 winner of the Mathematical Association of America's Euler Book Prize? (11.02)
... that block cellular automata, invented by Norman Margolus, can be used to simulate lattice gases, sand piles, and billiard-ball computers? (11.02)

... that Charles Fletcher, the first European settler in what is now Navarro River Redwoods State Park, built an inn in 1865 that remained open until the 1970s? (11.02)
... that Andreu Mas-Colell, currently the Minister of Economy and Knowledge of Catalonia, Spain, has studied general equilibrium theory by using differential topology? (11.01)
... that Graciela Chichilnisky, who proposed the Kyoto Protocol's market for carbon credit trading, obtained her PhDs in mathematics and economics without ever having been an undergraduate? (11.01)
... that Starr's corollary to the Shapley–Folkman lemma was proved by an undergraduate student of Kenneth Arrow? (10.10)
... that Paul Erdős challenged Jon Folkman to solve mathematical problems immediately after Folkman's surgery for brain cancer? (10.10)
... that every round-robin tournament either has a set of players who win all games against players outside the set, or its graph of wins and losses is pancyclic, having directed cycles of all lengths? (10.09)

... that the Albion River Bridge, the only wooden bridge on California State Route 1, has been proposed for replacement by the California Department of Transportation? (10.08)
... that Coretta Scott King called African-American civil rights activist Randolph Blackwell an "unsung giant" of nonviolent social change? (10.08)

... that the number of coho salmon spawning on the Ten Mile River in Mendocino County, California, has dropped precipitously since the 1960s? (10.08)
... that Konocti Harbor, a now-closed resort and music venue in Lake County, California, was originally founded in 1959 as low-cost vacation housing for members of a plumbers union? (10.08)
... that Mendocino, California, artist Bill Zacha learned to paint left-handed after injuring his right hand in a fall? (10.06)
... that Canadian astrophysicist Victoria Kaspi was one of the first to observe the cosmic recycling of pulsars? (10.02)

... that, according to the pizza theorem, a circular pizza that is sliced off-center into eight equal-angled wedges can still be divided equally between two people? (09.12)
... that the clique problem of programming a computer to find complete subgraphs in an undirected graph was first studied as a way to find groups of people who all know each other in social networks? (09.12)
... that psychiatrist Marie Nyswander, who developed the methadone treatment for heroin addicts, was herself addicted to cigarettes? (09.12)
... that Matthew T. Dickerson is a computational geometer, scholar of J. R. R. Tolkien and the Inklings, novelist, blues musician, fly fisherman, maple sugar farmer, and beekeeper? (09.11)

... that the Herschel graph (pictured) is the smallest possible polyhedral graph that does not have a Hamiltonian cycle? (09.10)
... that a casket discovered by Anant Sadashiv Altekar near Vaishali, on display at the Patna Museum, is said to contain the remains of the Buddha? (09.09)

... that Yreka phlox, an endangered flowering plant that grows in serpentine soil, is the official city flower of Yreka, California? (09.09)
... that Martin Demaine founded the first one-man art glass studio in Canada and home-schooled his son Erik to become MIT's youngest ever professor despite not having a college degree himself? (09.09)

... that the Frederick W. Panhorst Bridge (pictured), a concrete open-spandrel arch bridge in Russian Gulch State Park near Mendocino, California, replaced an earlier wooden trestle bridge in 1940? (09.08)
... that the Life without Death cellular automaton, a mathematical model of pattern formation, is a variant of Conway's Game of Life in which cells, once brought to life, never die? (09.06)
... that Donald G. Fink, later to become a prominent electrical engineer, was selected as the best orator in his county at a high school competition? (09.06)

... that one can list every positive rational number without repetition by breadth-first traversal of the Calkin–Wilf tree? (09.05)
... that the first textbook in Hungarian, an encyclopedia by János Apáczai Csere, was written and published in the Netherlands? (09.03)

... that the Hadwiger conjecture (diagram pictured) implies that any three-dimensional convex body can be illuminated by only eight light sources, but the best proven bound is that 16 lights are sufficient? (09.03)

... that an equitable coloring of a graph (pictured), in which the numbers of vertices of each color are as nearly equal as possible, may require far more colors than a graph coloring without this constraint? (09.03)
... that no matter how biased a coin one uses, flipping a coin to determine whether each edge is present or absent in a countably infinite graph will always produce the same graph, the Rado graph? (09.03)
... that Victor Vacquier escaped Russia by sleigh across the frozen Gulf of Finland and went on to pioneer the use of submarine detectors for investigating plate tectonics? (09.02)
... that there are 115,200 solutions to the ménage problem of permuting six couples at a twelve-person table so that men and women alternate and are seated away from their partners? (09.01)

... that mathematician Paul Erdős called the Hadwiger conjecture, a still-open generalization of the four-color problem, "one of the deepest unsolved problems in graph theory"? (08.05)
...that Dutch topologist Johannes De Groot is the academic grandfather, great-grandfather, and great-great-grandfather of his namesake via four different paths of academic supervision? (08.04)
...that Carl Størmer, "the acknowledged authority" on aurorae and the motion of charged particles in the magnetosphere, began his academic career inventing formulae for π? (08.03)
...that Scripps marine chemist Edward D. Goldberg suggested using mussels to measure the amount of pollution in the oceans? (08.03)
...that television pioneer Thomas T. Goldsmith, Jr. became the inventor of the video game when he took out a video game patent in 1948? (08.03)
...that in Floyd's algorithm for cycle detection, the tortoise and hare move at very different speeds, but always finish at the same spot? (07.10)
...that in graph theory, a pseudoforest can contain trees and pseudotrees, but cannot contain any butterflies, diamonds, handcuffs, or bicycles? (07.10)

...that it is not possible to configure two mutually inscribed quadrilaterals in the Euclidean plane, but the Möbius–Kantor graph (pictured) describes a solution in the complex projective plane? (07.09)
...that the six permutations of the vector (1,2,3) form a hexagon in 3d space, the 24 permutations of (1,2,3,4) form a truncated octahedron in four dimensions, and both are examples of permutohedra? (07.08)

...that Canadian sculptor John Hooper (sculpture pictured) previously lived in England, China, India, and South Africa, and was a captain in the British Army? (07.08)
...that the Rule 184 cellular automaton can simultaneously model the behavior of cars moving in traffic, the accumulation of particles on a surface, and particle-antiparticle annihilation reactions? (07.05)

...that a cyclic cellular automaton (pictured) is a system of simple mathematical rules that can generate complex patterns mixing random chaos, blocks of color, and spirals? (07.04)
...that a nonconvex polygon with three convex vertices is called a pseudotriangle? (07.04)