Danny Kaye was an American actor, comedian, singer, and dancer. His performances featured physical comedy, idiosyncratic pantomimes, and rapid-fire novelty songs.
Thomas Andrew Lehrer is an American musician, singer-songwriter, satirist, and mathematician, who later taught mathematics and musical theater. He recorded pithy and humorous songs that became popular in the 1950s and 1960s. His songs often parodied popular musical forms, though they usually had original melodies. An exception is "The Elements", in which he set the names of the chemical elements to the tune of the "Major-General's Song" from Gilbert and Sullivan's Pirates of Penzance.
The tangram is a dissection puzzle consisting of seven flat polygons, called tans, which are put together to form shapes. The objective is to replicate a pattern generally found in a puzzle book using all seven pieces without overlap. Alternatively the tans can be used to create original minimalist designs that are either appreciated for their inherent aesthetic merits or as the basis for challenging others to replicate its outline. It is reputed to have been invented in China sometime around the late 18th century and then carried over to America and Europe by trading ships shortly after. It became very popular in Europe for a time, and then again during World War I. It is one of the most widely recognized dissection puzzles in the world and has been used for various purposes including amusement, art, and education.
In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry. As Euclidean geometry lies at the intersection of metric geometry and affine geometry, non-Euclidean geometry arises by either replacing the parallel postulate with an alternative, or relaxing the metric requirement. In the former case, one obtains hyperbolic geometry and elliptic geometry, the traditional non-Euclidean geometries. When the metric requirement is relaxed, then there are affine planes associated with the planar algebras, which give rise to kinematic geometries that have also been called non-Euclidean geometry.
Andrey Nikolaevich Kolmogorov was a Soviet mathematician who played a central role in the creation of modern probability theory. He also contributed to the mathematics of topology, intuitionistic logic, turbulence, classical mechanics, algorithmic information theory and computational complexity.
New Mathematics or New Math was a dramatic but temporary change in the way mathematics was taught in American grade schools, and to a lesser extent in European countries and elsewhere, during the 1950s–1970s.
Nikolai Ivanovich Lobachevsky was a Russian mathematician and geometer, known primarily for his work on hyperbolic geometry, otherwise known as Lobachevskian geometry, and also for his fundamental study on Dirichlet integrals, known as the Lobachevsky integral formula.
"The Elements" is a 1959 song with lyrics by musical humorist, mathematician and lecturer Tom Lehrer, which recites the names of all the chemical elements known at the time of writing, up to number 102, nobelium. Lehrer arranged the music of the song from the tune of the "Major-General's Song" from The Pirates of Penzance by Gilbert and Sullivan. The song can be found on Lehrer's albums Tom Lehrer in Concert, More of Tom Lehrer and An Evening Wasted with Tom Lehrer.
"The Secret Life of Walter Mitty" (1939) is a short story by James Thurber. The most famous of Thurber's stories, it first appeared in The New Yorker on March 18, 1939, and was first collected in his book My World and Welcome to It. It has since been reprinted in James Thurber: Writings and Drawings, is available on-line on the New Yorker website, and is one of the most anthologized short stories in American literature. The story is considered one of Thurber's "acknowledged masterpieces". It was made into a 1947 film of the same name, with Danny Kaye in the title role, though the film is very different from the original story. It was also adapted into a 2013 film, which is again very different from the original.
Theodorus of Cyrene was an ancient Greek mathematician. The only first-hand accounts of him that survive are in three of Plato's dialogues: the Theaetetus, the Sophist, and the Statesman. In the former dialogue, he posits a mathematical construction now known as the Spiral of Theodorus.
Sylvia Fine Kaye was an American lyricist, composer, and producer. Many of her compositions and productions were performed by her husband, comedian Danny Kaye. Fine was a Peabody Award-winner and was nominated for two Academy Awards and two Emmys during her career. She won an Emmy award in 1976 for a children's special.
Quasi-quotation or Quine quotation is a linguistic device in formal languages that facilitates rigorous and terse formulation of general rules about linguistic expressions while properly observing the use–mention distinction. It was introduced by the philosopher and logician Willard Van Orman Quine in his book Mathematical Logic, originally published in 1940. Put simply, quasi-quotation enables one to introduce symbols that stand for a linguistic expression in a given instance and are used as that linguistic expression in a different instance.
Brendan Damien McKay is an Australian computer scientist and mathematician. He is currently an Emeritus Professor in the Research School of Computer Science at the Australian National University (ANU). He has published extensively in combinatorics.
Trigonometry is a branch of mathematics concerned with relationships between angles and side lengths of triangles. In particular, the trigonometric functions relate the angles of a right triangle with ratios of its side lengths. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies. The Greeks focused on the calculation of chords, while mathematicians in India created the earliest-known tables of values for trigonometric ratios such as sine.
The Princeton Companion to Mathematics is a book providing an extensive overview of mathematics that was published in 2008 by Princeton University Press. Edited by Timothy Gowers with associate editors June Barrow-Green and Imre Leader, it has been noted for the high caliber of its contributors. The book was the 2011 winner of the Euler Book Prize of the Mathematical Association of America, given annually to "an outstanding book about mathematics".
Jonah Richard Lehrer is an American author and blogger. Lehrer studied neuroscience at Columbia University and was a Rhodes Scholar. Thereafter, he built a media career that integrated science and humanities content to address broad aspects of human behaviour. Between 2007 and 2012 Lehrer published three non-fiction books that became best-sellers, and also wrote regularly for The New Yorker and Wired.com.
Herbert Busemann was a German-American mathematician specializing in convex and differential geometry. He is the author of Busemann's theorem in Euclidean geometry and geometric tomography. He was a member of the Royal Danish Academy and a winner of the Lobachevsky Medal (1985), the first American mathematician to receive it. He was also a Fulbright scholar in New Zealand in 1952.
In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.
In geometry, the parallel postulate, also called Euclid's fifth postulate because it is the fifth postulate in Euclid's Elements, is a distinctive axiom in Euclidean geometry. It states that, in two-dimensional geometry:
If a line segment intersects two straight lines forming two interior angles on the same side that are less than two right angles, then the two lines, if extended indefinitely, meet on that side on which the angles sum to less than two right angles.
Pythagorean Triangles is a book on right triangles, the Pythagorean theorem, and Pythagorean triples. It was originally written in the Polish language by Wacław Sierpiński, and published in Warsaw in 1954. Indian mathematician Ambikeshwar Sharma translated it into English, with some added material from Sierpiński, and published it in the Scripta Mathematica Studies series of Yeshiva University in 1962. Dover Books republished the translation in a paperback edition in 2003. There is also a Russian translation of the 1954 edition.
