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Mathematics Of Paper Folding
The discipline of origami or paper folding has received a considerable amount of mathematical study. Fields of interest include a given paper model's flat-foldability (whether the model can be flattened without damaging it), and the use of paper folds to solve mathematical equations up to the third order. Computational origami is a recent branch of computer science that is concerned with studying algorithms that solve paper-folding problems. The field of computational origami has also grown significantly since its inception in the 1990s with Robert Lang's TreeMaker algorithm to assist in the precise folding of bases. Computational origami results either address origami design or origami foldability."Lecture: Recent Results in Computational Origami". ''Origami USA: We are the American national society devoted to origami, the art of paperfolding''. Retrieved 2022-05-08. In origami design problems, the goal is to design an object that can be folded out of paper given a specific targ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Miura-Ori CP
The is a method of folding a flat surface such as a sheet of paper into a smaller area. The fold is named for its inventor, Japanese astrophysicist Kōryō Miura. The crease patterns of the Miura fold form a tessellation of the surface by parallelograms. In one direction, the creases lie along straight lines, with each parallelogram forming the mirror reflection of its neighbor across each crease. In the other direction, the creases zigzag, and each parallelogram is the translation of its neighbor across the crease. Each of the zigzag paths of creases consists solely of mountain folds or of valley folds, with mountains alternating with valleys from one zigzag path to the next. Each of the straight paths of creases alternates between mountain and valley folds.. Reproduced in ''British Origami'', 1981, and online at the British Origami Society web site. The Miura fold is related to the Kresling fold, the Yoshimura fold and the Hexagonal fold, and can be framed as a generaliza ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
NP-complete
In computational complexity theory, NP-complete problems are the hardest of the problems to which ''solutions'' can be verified ''quickly''. Somewhat more precisely, a problem is NP-complete when: # It is a decision problem, meaning that for any input to the problem, the output is either "yes" or "no". # When the answer is "yes", this can be demonstrated through the existence of a short (polynomial length) ''solution''. # The correctness of each solution can be verified quickly (namely, in polynomial time) and a brute-force search algorithm can find a solution by trying all possible solutions. # The problem can be used to simulate every other problem for which we can verify quickly that a solution is correct. Hence, if we could find solutions of some NP-complete problem quickly, we could quickly find the solutions of every other problem to which a given solution can be easily verified. The name "NP-complete" is short for "nondeterministic polynomial-time complete". In this name, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Barry Hayes
Barry may refer to: People and fictional characters * Barry (name), including lists of people with the given name, nickname or surname, as well as fictional characters with the given name * Dancing Barry, stage name of Barry Richards (born c. 1950), former dancer at National Basketball Association games Places Canada * Barry Lake, Quebec *Barry Islands, Nunavut United Kingdom * Barry, Angus, Scotland, a village ** Barry Mill, a watermill ** Barry Links railway station * Barry, Vale of Glamorgan, Wales, a town ** Barry Island, a seaside resort ** Barry Railway Company ** Barry railway station United States * Barry, Illinois, a city * Barry, Minnesota, a city * Barry, Texas, a city * Barry County, Michigan * Barry County, Missouri * Barry Township (other), in several states * Fort Barry, Marin County, California, a former US Army installation Elsewhere * Barry Island (Debenham Islands), Antarctica * Barry, New South Wales, Australia, a village * Barry, Hautes-Pyrén� ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Marshall Bern
Marshall may refer to: Places Australia *Marshall, Victoria, a suburb of Geelong, Victoria ** Marshall railway station Canada * Marshall, Saskatchewan * The Marshall, a mountain in British Columbia Liberia * Marshall, Liberia Marshall Islands * Marshall Islands, an island nation in the Pacific Ocean United States of America * Marshall, Alaska * Marshall, Arkansas * Marshall, California * Lotus, California, former name Marshall * Marshall, Colorado * Marshall Pass, a mountain pass in Colorado * Marshall, Illinois * Marshall, Indiana * Marshall, Michigan * Marshall, Minnesota * Marshall, Missouri * Marshall, New York * Marshall, North Carolina * Marshall, North Dakota * Marshall, Oklahoma * Marshall, Texas, the largest U.S. city named Marshall * Marshall, Virginia * Marshall, Wisconsin (other) ** Marshall, Dane County, Wisconsin ** Marshall, Richland County, Wisconsin ** Marshall, Rusk County, Wisconsin Businesses * Marshall Aerospace and Defence Group, a Br ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robert J
The name Robert is an ancient Germanic given name, from Proto-Germanic "fame" and "bright" (''Hrōþiberhtaz''). Compare Old Dutch ''Robrecht'' and Old High German ''Hrodebert'' (a compound of '' Hruod'' () "fame, glory, honour, praise, renown, godlike" and ''berht'' "bright, light, shining"). It is the second most frequently used given name of ancient Germanic origin.Reaney & Wilson, 1997. ''Dictionary of English Surnames''. Oxford University Press. It is also in use as a surname. Another commonly used form of the name is Rupert. After becoming widely used in Continental Europe, the name entered England in its Old French form ''Robert'', where an Old English cognate form (''Hrēodbēorht'', ''Hrodberht'', ''Hrēodbēorð'', ''Hrœdbœrð'', ''Hrœdberð'', ''Hrōðberχtŕ'') had existed before the Norman Conquest. The feminine version is Roberta. The Italian, Portuguese, and Spanish form is Roberto. Robert is also a common name in many Germanic languages, including En ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Regular Heptagon
In geometry, a heptagon or septagon is a seven-sided polygon or 7-gon. The heptagon is sometimes referred to as the septagon, using '' septa-'' (an elision of ''septua-''), a Latin-derived numerical prefix, rather than ''hepta-'', a Greek-derived numerical prefix (both are cognate), together with the suffix ''-gon'' for , meaning angle. Regular heptagon A regular heptagon, in which all sides and all angles are equal, has internal angles of 5π/7 radians (128 degrees). Its Schläfli symbol is . Area The area (''A'') of a regular heptagon of side length ''a'' is given by: :A = \fraca^2 \cot \frac \simeq 3.634 a^2. This can be seen by subdividing the unit-sided heptagon into seven triangular "pie slices" with vertices at the center and at the heptagon's vertices, and then halving each triangle using the apothem as the common side. The apothem is half the cotangent of \pi/7, and the area of each of the 14 small triangles is one-fourth of the apothem. The area of a regular he ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Humiaki Huzita
Humiaki Huzita (Japanese: 藤田文章, Hepburn romanization: ''Fujita Fumiaki'') was a Japanese-born mathematician and origami artist who later became an Italian citizen. He was also a geologist and a physicist who focuses specifically on nuclear physics. Huzita is best known for formulating the first six Huzita–Hatori axioms, which are rules associated with origami, the mathematics behind it, and the operations that form when folding a paper. Biography and education Humiaki Huzita was born in 1924 in Japan. After his basic education, he moved to Italy to attend the University of Padua. Here he studied nuclear physics and was eventually granted Italian citizenship. Though because of Japan's nationality laws, which do not allow dual citizenship, he was unable to live permanently in Japan following his retirement. Huzita, having lived in Japan and Italy, spoke both Japanese and Italian, however, he also spoke proficient English. This was advantageous for him and his cause, allo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jacques Justin
Jacques or Jacq are believed to originate from the Middle Ages in the historic northwest Brittany region in France, and have since spread around the world over the centuries. To date, there are over one hundred identified noble families related to the surname by the Nobility & Gentry of Great Britain & Ireland. Origins The origin of this surname comes from the Latin ' Iacobus', associated with the biblical patriarch Jacob. Ancient history A French knight returning from the Crusades in the Holy Lands probably adopted the surname from "Saint Jacques" (or "James the Greater"). James the Greater was one of Jesus' Twelve Apostles, and is believed to be the first martyred apostle. Being endowed with this surname was an honor at the time and it is likely that the Church allowed it because of acts during the Crusades. Indeed, at this time, the use of biblical, Christian, or Hebrew names and surnames became very popular, and entered the European lexicon. Robert J., a Knight Crusader ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Double The Cube
Doubling the cube, also known as the Delian problem, is an ancient geometric problem. Given the edge of a cube, the problem requires the construction of the edge of a second cube whose volume is double that of the first. As with the related problems of squaring the circle and trisecting the angle, doubling the cube is now known to be impossible to construct by using only a compass and straightedge, but even in ancient times solutions were known that employed other methods. According to Eutocius, Archytas was the first to solve the problem of doubling the cube (the so-called Delian problem) with an ingenious geometric construction. The nonexistence of a compass-and-straightedge solution was finally proven by Pierre Wantzel in 1837. In algebraic terms, doubling a unit cube requires the construction of a line segment of length , where ; in other words, , the cube root of two. This is because a cube of side length 1 has a volume of , and a cube of twice that volume (a volume of 2) ha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
