|
Flexagon
In geometry, flexagons are flat models, usually constructed by folding strips of paper, that can be ''flexed'' or folded in certain ways to reveal faces besides the two that were originally on the back and front. Flexagons are usually square or rectangular (tetraflexagons) or hexagonal (hexaflexagons). A prefix can be added to the name to indicate the number of faces that the model can display, including the two faces (back and front) that are visible before flexing. For example, a hexaflexagon with a total of six faces is called a hexahexaflexagon. In hexaflexagon theory (that is, concerning flexagons with six sides), flexagons are usually defined in terms of ''pats''. Two flexagons are equivalent if one can be transformed to the other by a series of pinches and rotations. Flexagon equivalence is an equivalence relation. History Discovery and introduction The discovery of the first flexagon, a trihexaflexagon, is credited to the British mathematician Arthur H. Stone, whil ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trihexaflexagon Example
In geometry, flexagons are flat models, usually constructed by folding strips of paper, that can be ''flexed'' or folded in certain ways to reveal faces besides the two that were originally on the back and front. Flexagons are usually square or rectangular (tetraflexagons) or hexagonal (hexaflexagons). A prefix can be added to the name to indicate the number of faces that the model can display, including the two faces (back and front) that are visible before flexing. For example, a hexaflexagon with a total of six faces is called a hexahexaflexagon. In hexaflexagon theory (that is, concerning flexagons with six sides), flexagons are usually defined in terms of ''pats''. Two flexagons are equivalent if one can be transformed to the other by a series of pinches and rotations. Flexagon equivalence is an equivalence relation. History Discovery and introduction The discovery of the first flexagon, a trihexaflexagon, is credited to the British mathematician Arthur H. Stone, whil ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Games Column
Over a period of 24 years (January 1957 – December 1980), Martin Gardner wrote 288 consecutive monthly "Mathematical Games" columns for ''Scientific American'' magazine. During the next years, through June 1986, Gardner wrote 9 more columns, bringing his total to 297, as other authors wrote most of the "Mathematical Games" columns. The table below lists Gardner's columns. Twelve of Gardner's columns provided the cover art for that month's magazine, indicated by "over in the table with a hyperlink to the cover. Other articles by Gardner Gardner wrote 5 other articles for ''Scientific American''. His flexagon article in December 1956 was in all but name the first article in the series of ''Mathematical Games'' columns and led directly to the series which began the following month. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Martin Gardner
Martin Gardner (October 21, 1914May 22, 2010) was an American popular mathematics and popular science writer with interests also encompassing scientific skepticism, micromagic, philosophy, religion, and literatureespecially the writings of Lewis Carroll, L. Frank Baum, and G. K. Chesterton.Martin (2010) He was also a leading authority on Lewis Carroll. ''The Annotated Alice'', which incorporated the text of Carroll's two Alice books, was his most successful work and sold over a million copies. He had a lifelong interest in magic and illusion and in 1999, MAGIC magazine named him as one of the "100 Most Influential Magicians of the Twentieth Century". He was considered the doyen of American puzzlers. He was a prolific and versatile author, publishing more than 100 books. Gardner was best known for creating and sustaining interest in recreational mathematicsand by extension, mathematics in generalthroughout the latter half of the 20th century, principally through his "Mathema ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Möbius Strip
In mathematics, a Möbius strip, Möbius band, or Möbius loop is a surface that can be formed by attaching the ends of a strip of paper together with a half-twist. As a mathematical object, it was discovered by Johann Benedict Listing and August Ferdinand Möbius in 1858, but it had already appeared in Roman mosaics from the third century CE. The Möbius strip is a non-orientable surface, meaning that within it one cannot consistently distinguish clockwise from counterclockwise turns. Every non-orientable surface contains a Möbius strip. As an abstract topological space, the Möbius strip can be embedded into three-dimensional Euclidean space in many different ways: a clockwise half-twist is different from a counterclockwise half-twist, and it can also be embedded with odd numbers of twists greater than one, or with a knotted centerline. Any two embeddings with the same knot for the centerline and the same number and direction of twists are topologically equivalent. All of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arthur Harold Stone
Arthur Harold Stone (30 September 1916 – 6 August 2000) was a British mathematician born in London, who worked at the universities of Manchester and Rochester, mostly in topology. His wife was American mathematician Dorothy Maharam. Stone studied at Trinity College, Cambridge. His first paper dealt with squaring the square, he proved the Erdős–Stone theorem with Paul Erdős and is credited with the discovery of the first two flexagons, a trihexaflexagon and a hexahexaflexagon while he was a student at Princeton University in 1939. His Ph.D. thesis, ''Connectedness and Coherence'', was written in 1941 under the direction of Solomon Lefschetz. He served as a referee for ''The American Mathematical Monthly'' journal in the 1980s. The Stone metrization theorem has been named after him, and he was a member of a group of mathematicians who published pseudonymously as Blanche Descartes. He is not to be confused with American mathematician Marshall Harvey Stone. See also *Ha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Tukey
John Wilder Tukey (; June 16, 1915 – July 26, 2000) was an American mathematician and statistician, best known for the development of the fast Fourier Transform (FFT) algorithm and box plot. The Tukey range test, the Tukey lambda distribution, the Tukey test of additivity, and the Teichmüller–Tukey lemma all bear his name. He is also credited with coining the term 'bit' and the first published use of the word 'software'. Biography Tukey was born in New Bedford, Massachusetts in 1915, to a Latin teacher father and a private tutor. He was mainly taught by his mother and attended regular classes only for certain subjects like French. Tukey obtained a BA in 1936 and MSc in 1937 in chemistry, from Brown University, before moving to Princeton University, where in 1939 he received a PhD in mathematics after completing a doctoral dissertation titled "On denumerability in topology". During World War II, Tukey worked at the Fire Control Research Office and collaborated wi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Square (geometry)
In Euclidean geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, π/2 radian angles, or right angles). It can also be defined as a rectangle with two equal-length adjacent sides. It is the only regular polygon whose internal angle, central angle, and external angle are all equal (90°), and whose diagonals are all equal in length. A square with vertices ''ABCD'' would be denoted . Characterizations A convex quadrilateral is a square if and only if it is any one of the following: * A rectangle with two adjacent equal sides * A rhombus with a right vertex angle * A rhombus with all angles equal * A parallelogram with one right vertex angle and two adjacent equal sides * A quadrilateral with four equal sides and four right angles * A quadrilateral where the diagonals are equal, and are the perpendicular bisectors of each other (i.e., a rhombus with equal diagonals) * A convex quadrilateral with successiv ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jacob's Ladder (toy)
A Jacob's ladder (also magic tablets, Chinese blocks, and klick-klack toyFrauenfelder, Mark (2011). ''Make: Technology On Your Time, Vol. 26: Roll Your Own'', p.148. O'Reilly Media. .) is a Folk culture, folk toy consisting of toy block, blocks of wood held together by strings or ribbons. When the ladder is held at one end, blocks appear to cascade down the strings. This effect is a optical illusion, visual illusion which is the result of one block after another flipping over. It may be considered a Kinetic depth effect, kinetic illusion, where the blocks appear to change position when they do not. Its name ''Jacob's Ladder'' comes from the biblical Jacob's Ladder (Bible), ladder to heaven, mentioned in Genesis 28:12. Of unknown origin, the earliest known review of the Jacob's Ladder is an 1889 ''Scientific American'' article which tells how it is built and works: Construction An arrangement of interlaced ribbons allows each block to act as if hinged to the next one at either ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rubik's Magic
Rubik's Magic, like the Rubik's Cube, is a mechanical puzzle invented by Ernő Rubik and first manufactured by Matchbox in the mid-1980s. The puzzle consists of eight black square tiles (changed to red squares with goldish rings in 1997) arranged in a 2 × 4 rectangle; diagonal grooves on the tiles hold wires that connect them, allowing them to be folded onto each other and unfolded again in two perpendicular directions (assuming that no other connections restrict the movement) in a manner similar to a Jacob's ladder toy. The front side of the puzzle shows, in the initial state, three separate, rainbow-coloured rings; the back side consists of a scrambled picture of three interconnected rings. The goal of the game is to fold the puzzle into a heart-like shape and unscramble the picture on the back side, thus interconnecting the rings. Numerous ways to accomplish this exist, and experienced players can transform the puzzle from its initial into the solved state in less than 2 sec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Richard Himber
Richard Himber (born Herbert Richard Imber; February 20, 1899 – December 11, 1966) was an American bandleader, composer, violinist, magician and practical joker. Early life He was born as Herbert Richard Imber in Newark, New Jersey to the owner of a chain of meat stores. His parents gave him violin lessons, but when they found him performing in a seedy Newark dive, they took the instrument away from him and sent him to military school. In 1915, he stole away into New York City, where Sophie Tucker heard him play and hired him as a novelty act to play with her and the ''Five Kings of Syncopation'' where Himber was the highlight of the cabaret act. He worked his way through Vaudeville and down Tin Pan Alley. He managed Rudy Vallee's orchestra service, which sent out bands for private parties and society functions. A suave salesman and irrepressible idea man, he soon had his own band booking agency. In 1932, he acquired the first known "vanity" telephone number, ''R-HIMBER'', ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
