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Fold-and-cut Problem
The fold-and-cut theorem states that any shape with straight sides can be cut from a single (idealized) sheet of paper by folding it flat and making a single straight complete cut. Such shapes include polygons, which may be concave, shapes with holes, and collections of such shapes (i.e. the regions need not be connected space, connected). The corresponding problem that the theorem solves is known as the fold-and-cut problem, which asks what shapes can be obtained by the so-called fold-and-cut method. A particular instance of the problem, which asks how a particular shape can be obtained by the fold-and-cut method, is known as ''a'' fold-and-cut problem. History The earliest known description of a fold-and-cut problem appears in ''Wakoku Chiyekurabe'' (Mathematical Contests), a book that was published in 1721 by Kan Chu Sen in Japan. An 1873 article in ''Harper's New Monthly Magazine'' describes how Betsy Ross may have proposed that stars on the American flag have five points, b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Connected Space
In topology and related branches of mathematics, a connected space is a topological space that cannot be represented as the union of two or more disjoint non-empty open subsets. Connectedness is one of the principal topological properties that are used to distinguish topological spaces. A subset of a topological space X is a if it is a connected space when viewed as a subspace of X. Some related but stronger conditions are path connected, simply connected, and n-connected. Another related notion is ''locally connected'', which neither implies nor follows from connectedness. Formal definition A topological space X is said to be if it is the union of two disjoint non-empty open sets. Otherwise, X is said to be connected. A subset of a topological space is said to be connected if it is connected under its subspace topology. Some authors exclude the empty set (with its unique topology) as a connected space, but this article does not follow that practice. For a topologi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Erik Demaine
Erik D. Demaine (born February 28, 1981) is a professor of computer science at the Massachusetts Institute of Technology and a former child prodigy. Early life and education Demaine was born in Halifax, Nova Scotia, to artist sculptor Martin L. Demaine and Judy Anderson. From the age of 7, he was identified as a child prodigy and spent time traveling across North America with his father. He was home-schooled during that time span until entering university at the age of 12. Demaine completed his bachelor's degree at 14 years of age at Dalhousie University in Canada, and completed his PhD at the University of Waterloo by the time he was 20 years old. Demaine's PhD dissertation, a work in the field of computational origami, was completed at the University of Waterloo under the supervision of Anna Lubiw and Ian Munro. This work was awarded the Canadian Governor General's Gold Medal from the University of Waterloo and the NSERC Doctoral Prize (2003) for the best PhD thesis an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Betsy Ross
Elizabeth Griscom Ross (née Griscom;Addie Guthrie Weaver, ''"The Story of Our Flag..."'', 2nd Edition, A. G. Weaver, publ., 1898, p. 73 January 1, 1752 – January 30, 1836), also known by her second and third married names, Ashburn and Claypoole, was an American upholsterer who was credited by her relatives in 1870 with making the first officialPreceded unofficially by the Grand Union Flag U.S. flag, accordingly known as the Betsy Ross flag. Though most historians dismiss the story, Ross family tradition holds that General George Washington, commander-in-chief of the Continental Army and two members of a congressional committee— Robert Morris and George Ross—visited Mrs. Ross in 1776. Mrs. Ross convinced George Washington to change the shape of the stars in a sketch of a flag he showed her from six-pointed to five-pointed by demonstrating that it was easier and speedier to cut the latter. However, there is no archival evidence or other recorded verbal tradition to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harry Houdini
Harry Houdini (, born Erik Weisz; March 24, 1874 – October 31, 1926) was a Hungarian-American escape artist, magic man, and stunt performer, noted for his escape acts. His pseudonym is a reference to his spiritual master, French magician Robert-Houdin (1805–1871). He first attracted notice in vaudeville in the United States and then as "Harry 'Handcuff' Houdini" on a tour of Europe, where he challenged police forces to keep him locked up. Soon he extended his repertoire to include chains, ropes slung from skyscrapers, straitjackets under water, and having to escape from and hold his breath inside a sealed milk can with water in it. In 1904, thousands watched as he tried to escape from special handcuffs commissioned by London's ''Daily Mirror'', keeping them in suspense for an hour. Another stunt saw him buried alive and only just able to claw himself to the surface, emerging in a state of near-breakdown. While many suspected that these escapes were faked, Houdini prese ... [...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] |
Scientific American
''Scientific American'', informally abbreviated ''SciAm'' or sometimes ''SA'', is an American popular science magazine. Many famous scientists, including Albert Einstein and Nikola Tesla, have contributed articles to it. In print since 1845, it is the oldest continuously published magazine in the United States. ''Scientific American'' is owned by Springer Nature, which in turn is a subsidiary of Holtzbrinck Publishing Group. History ''Scientific American'' was founded by inventor and publisher Rufus Porter (painter), Rufus Porter in 1845 as a four-page weekly newspaper. The first issue of the large format newspaper was released August 28, 1845. Throughout its early years, much emphasis was placed on reports of what was going on at the United States Patent and Trademark Office, U.S. Patent Office. It also reported on a broad range of inventions including perpetual motion machines, an 1860 device for buoying vessels by Abraham Lincoln, and the universal joint which now can be found ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Checkerboard
A checkerboard (American English) or chequerboard (British English; see spelling differences) is a board of checkered pattern on which checkers (also known as English draughts) is played. Most commonly, it consists of 64 squares (8×8) of alternating dark and light color, typically green and buff (official tournaments), black and red (consumer commercial), or black and white (printed diagrams). An 8×8 checkerboard is used to play many other games, including chess, whereby it is known as a chessboard. Other rectangular square-tiled boards are also often called checkerboards. Games and puzzles using checkerboards Martin Gardner featured puzzles based on checkerboards in his November 1962 Mathematical Games column in Scientific American. A square checkerboard with an alternating pattern is used for games including: * Amazons * Chapayev * Chess and some of its variants (see chessboard) * Czech draughts * Draughts, also known as checkers * Fox games * Frisian draughts * Gounki * In ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Latin Cross
A Latin cross or ''crux immissa'' is a type of cross in which the vertical beam sticks above the crossbeam, with the three upper arms either equally long or with the vertical topmost arm shorter than the two horizontal arms, and always with a much longer bottom arm. If displayed upside down it is called St. Peter's Cross, because he was reputedly executed on this type of cross.Joyce Mori, ''Crosses of Many Cultures'' (Harrisburg, PA: Morehouse Publishing, 1998), p. 32 When displayed sideways it is called St. Philip's cross for the same reason. History In a broad sense, the Latin cross is used to represent all of Christianity and Christendom, given that it teaches that Jesus sacrificed himself for humanity upon it, atoning for the sins of the world. It is especially used among the denominations of Western Christianity, including the Roman Catholic tradition and several Protestant traditions, such as Lutheranism, Moravianism, Anglicanism, Methodism, and Reformed Christianity, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Martin Demaine
Martin L. (Marty) Demaine (born 1942) is an artist and mathematician, the Angelika and Barton Weller artist in residence at the Massachusetts Institute of Technology (MIT). Demaine attended Medford High School in Medford, Massachusetts. After studying glassblowing in England, he began his artistic career by blowing art glass in New Brunswick in the early 1970s."Fluency", past exhibitions , Andrew and Laura McCain Art Gallery, Florenceville, New Brunswick, Canada, retrieved 2009-08-22. The Demaine Studio, located in and later at Opus Village in Mactaquac, was the first one-man g ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Anna Lubiw
Anna Lubiw is a computer scientist known for her work in computational geometry and graph theory. She is currently a professor at the University of Waterloo. Education Lubiw received her Ph.D from the University of Toronto in 1986 under the joint supervision of Rudolf Mathon and Stephen Cook. Research At Waterloo, Lubiw's students have included both Erik Demaine and his father Martin Demaine, with whom she published the first proof of the fold-and-cut theorem in mathematical origami. In graph drawing, Hutton and Lubiw found a polynomial time algorithm for upward planar drawing of graphs with a single source vertex. Other contributions of Lubiw include proving the NP-completeness of finding permutation patterns, and of finding derangements in permutation groups. Awards Lubiw was named an ACM Distinguished Member in 2009. Personal life As well her academic work, Lubiw is an amateur violinist, and chairs the volunteer council in charge of the University of Waterloo orchest ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Straight Skeleton
In geometry, a straight skeleton is a method of representing a polygon by a topological skeleton. It is similar in some ways to the medial axis but differs in that the skeleton is composed of straight line segments, while the medial axis of a polygon may involve parabolic curves. However, both are homotopy-equivalent to the underlying polygon.. Straight skeletons were first defined for simple polygons by ,. and generalized to planar straight-line graphs (PSLG) by . In their interpretation as projection of roof surfaces, they are already extensively discussed by . Definition The straight skeleton of a polygon is defined by a continuous shrinking process in which the edges of the polygon are moved inwards parallel to themselves at a constant speed. As the edges move in this way, the vertices where pairs of edges meet also move, at speeds that depend on the angle of the vertex. If one of these moving vertices collides with a nonadjacent edge, the polygon is split in two by the coll ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Circle Packing
In geometry, circle packing is the study of the arrangement of circles (of equal or varying sizes) on a given surface such that no overlapping occurs and so that no circle can be enlarged without creating an overlap. The associated ''packing density'', ''η'', of an arrangement is the proportion of the surface covered by the circles. Generalisations can be made to higher dimensions – this is called ''sphere packing'', which usually deals only with identical spheres. The branch of mathematics generally known as "circle packing" is concerned with the geometry and combinatorics of packings of arbitrarily-sized circles: these give rise to discrete analogs of conformal mapping, Riemann surfaces and the like. Densest packing In the two-dimensional Euclidean plane, Joseph Louis Lagrange proved in 1773 that the highest-density lattice packing of circles is the hexagonal packing arrangement, in which the centres of the circles are arranged in a hexagonal lattice (staggered rows, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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