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Rigid Origami
Rigid origami is a branch of origami which is concerned with folding structures using flat rigid sheets joined by hinges. That is, unlike in traditional origami, the panels of the paper cannot be bent during the folding process; they must remain flat at all times, and the paper only folded along its hinges. A rigid origami model would still be foldable if it was made from glass sheets with hinges in place of its crease lines. However, there is no requirement that the structure start as a single flat sheet – for instance shopping bags with flat bottoms are studied as part of rigid origami. Rigid origami is a part of the study of the mathematics of paper folding, and rigid origami structures can be considered as a type of mechanical linkage. Rigid origami has great practical utility. Mathematics The number of standard origami bases that can be folded using rigid origami is restricted by its rules. Rigid origami does not have to follow the Huzita–Hatori axioms, the fold l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Convex Polyhedron
In geometry, a polyhedron (: polyhedra or polyhedrons; ) is a three-dimensional figure with flat polygonal faces, straight edges and sharp corners or vertices. The term "polyhedron" may refer either to a solid figure or to its boundary surface. The terms solid polyhedron and polyhedral surface are commonly used to distinguish the two concepts. Also, the term ''polyhedron'' is often used to refer implicitly to the whole structure formed by a solid polyhedron, its polyhedral surface, its faces, its edges, and its vertices. There are many definitions of polyhedron. Nevertheless, the polyhedron is typically understood as a generalization of a two-dimensional polygon and a three-dimensional specialization of a polytope, a more general concept in any number of dimensions. Polyhedra have several general characteristics that include the number of faces, topological classification by Euler characteristic, duality, vertex figures, surface area, volume, interior lines, Dehn invar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kaleidocycle
A kaleidocycle or flextangle is a flexible polyhedron connecting six tetrahedra (or tetragonal disphenoid, disphenoids) on opposite edges into a cycle. If the faces of the disphenoids are equilateral triangles, it can be constructed from a stretched triangular tiling net with four triangles in one direction and an even number in the other direction. The kaleidocycle has degenerate pairs of coinciding edges in transition, which function as hinges. The kaleidocycle has an additional property that it can be continuously twisted around a ring axis, showing 4 sets of 6 triangular faces. The kaleidocycle is invariant under twists about its ring axis by k\pi/2, where k is an integer, and can therefore be continuously twisted. Kaleidocycles can be constructed from a single piece of paper (with dimensions l \times 2l) without tearing or using adhesive. Because of this and their continuous twisting property, they are often given as examples of simple origami toys. The kaleidocycle is someti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Flexagon
In geometry, flexagons are Plane (geometry), 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 hexagon, 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 of the hexaflexagon The discovery of the first flexagon, a trihexaflexagon, is credited to t ... [...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 magic, scientific skepticism, micromagic, philosophy, religion, and literatureespecially the writings of Lewis Carroll, L. Frank Baum, and G. K. Chesterton.Martin (2010) He was 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.Martin Gardner obituary (2010) He had a lifelong interest in magic and illusion and in 1999, ''MAGIC'' magazine named him as one of the "10 ... [...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 The Massachusetts Institute of Technology (MIT) is a Private university, private research university in Cambridge, Massachusetts, United States. Established in 1861, MIT has played a significant role in the development of many areas of moder ... (MIT). Demaine attended Medford High School (Massachusetts), 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 Miramichi Bay and lat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Erik Demaine
Erik D. Demaine (born February 28, 1981) is a Canadian-American 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 mathematician and 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 (200 ... [...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] |
Solar Panel
A solar panel is a device that converts sunlight into electricity by using photovoltaic (PV) cells. PV cells are made of materials that produce excited electrons when exposed to light. These electrons flow through a circuit and produce direct current (DC) electricity, which can be used to power various devices or be stored in battery (electricity), batteries. Solar panels are also known as solar cell panels, solar electric panels, or PV modules. Solar panels are usually arranged in groups called arrays or systems. A photovoltaic system consists of one or more solar panels, an solar inverter, inverter that converts DC electricity to alternating current (AC) electricity, and sometimes other components such as charge controller, controllers, Measuring instrument, meters, and solar tracker, trackers. Most panels are in solar farms or Rooftop solar power, rooftop solar panels which grid-connected photovoltaic system, supply the electricity grid. Some advantages of solar panels are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Miura Fold
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 general ... [...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-hard
In computational complexity theory, a computational problem ''H'' is called NP-hard if, for every problem ''L'' which can be solved in non-deterministic polynomial-time, there is a polynomial-time reduction from ''L'' to ''H''. That is, assuming a solution for ''H'' takes 1 unit time, ''H''s solution can be used to solve ''L'' in polynomial time. As a consequence, finding a polynomial time algorithm to solve a single NP-hard problem would give polynomial time algorithms for all the problems in the complexity class NP. As it is suspected, but unproven, that P≠NP, it is unlikely that any polynomial-time algorithms for NP-hard problems exist. A simple example of an NP-hard problem is the subset sum problem. Informally, if ''H'' is NP-hard, then it is at least as difficult to solve as the problems in NP. However, the opposite direction is not true: some problems are undecidable, and therefore even more difficult to solve than all problems in NP, but they are probably not NP- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
