|
Geometric Magic Square
A geometric magic square, often abbreviated to geomagic square, is a generalization of magic squares invented by Lee Sallows in 2001. A traditional magic square is a square array of numbers (almost always positive integers) whose sum taken in any row, any column, or in either diagonal is the same ''target number''. A geomagic square, on the other hand, is a square array of geometrical shapes in which those appearing in each row, column, or diagonal can be fitted together to create an identical shape called the ''target shape''. As with numerical types, it is required that the entries in a geomagic square be distinct. Similarly, the eight trivial variants of any square resulting from its rotation and/or reflection are all counted as the same square. By the ''dimension'' of a geomagic square is meant the dimension of the pieces it uses. Hitherto interest has focused mainly on 2D squares using planar pieces, but pieces of any dimension are permitted. Examples Figure 1 above shows a 3& ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geomagic Square - 3x3 Decominoes
Geomagic is the professional engineering software brand of 3D Systems. The brand began when Geomagic Inc., a software company based in Morrisville, North Carolina, was acquired by 3D Systems in February 2013 and combined with that company's other software businesses (namely Rapidform acquired by 3D Systems in October 2012 and Albre in July 2011). Geomagic was founded in 1997 by Ping Fu and Herbert Edelsbrunner. Geomagic-branded software products are focused on computer-aided design, with an emphasis on 3D scanning and other non-traditional design methodologies, such as voxel-based modeling with haptic technology, haptic input. 3D Systems also markets 3D quality inspection software as well as 3D scanners under the Geomagic brand. Geomagic Products 3D Scanning Systems Geomagic Capture is an integrated system consisting of a blue LED structured-light 3D scanner and one of several pieces of application-specific software. The systems are marketed for use as scan-based design tools, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alex Bellos
Alexander Bellos (born 1969) is a British writer, broadcaster and mathematics communicator.Alex Bellos He is the author of books about Brazil and mathematics, as well as having a column in ''The Guardian'' newspaper. Education and early life Alex Bellos was born in Oxford and grew up in Edinburgh and Southampton. He was educated at Hampton Park Comprehensive School and Richard Taunton Sixth Form College in Southampton. He went on to study mathematics and philosophy at Corpus Christi College, Oxford, where he was the editor of the student paper ''Cherwell''. Career Bellos's first job was working for '' The Argus'' in Brighton before moving to ''The Guardian'' in London. From 1998 to 2003 he was South America correspondent of ''The Guardian'', and wrote ''Futebol: the Brazilian Way of Life''. The book was well received in the UK, where it was nominated for sports book of the year at the British Book Awards. In the US, it was included as one of '' Publishers Weekly's'' books ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Macau
Macau or Macao (; ; ; ), officially the Macao Special Administrative Region of the People's Republic of China (MSAR), is a city and special administrative region of China in the western Pearl River Delta by the South China Sea. With a population of about 680,000 and an area of , it is the most densely populated region in the world. Formerly a Portuguese colony, the territory of Portuguese Macau was first leased to Portugal as a trading post by the Ming dynasty in 1557. Portugal paid an annual rent and administered the territory under Chinese sovereignty until 1887. Portugal later gained perpetual colonial rights in the Sino-Portuguese Treaty of Peking. The colony remained under Portuguese rule until 1999, when it was transferred to China. Macau is a special administrative region of China, which maintains separate governing and economic systems from those of mainland China under the principle of " one country, two systems".. The unique blend of Portuguese and Chinese arc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Macau Stamp Featuring Geometric Magic Square
Macau or Macao (; ; ; ), officially the Macao Special Administrative Region of the People's Republic of China (MSAR), is a city and special administrative region of China in the western Pearl River Delta by the South China Sea. With a population of about 680,000 and an area of , it is the most densely populated region in the world. Formerly a Portuguese colony, the territory of Portuguese Macau was first leased to Portugal as a trading post by the Ming dynasty in 1557. Portugal paid an annual rent and administered the territory under Chinese sovereignty until 1887. Portugal later gained perpetual colonial rights in the Sino-Portuguese Treaty of Peking. The colony remained under Portuguese rule until 1999, when it was transferred to China. Macau is a special administrative region of China, which maintains separate governing and economic systems from those of mainland China under the principle of "one country, two systems".. The unique blend of Portuguese and Chinese archi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Self-tiling Tile Set
A self-tiling tile set, or ''setiset'', of order ''n'' is a set of ''n'' shapes or pieces, usually planar, each of which can be tiled with smaller replicas of the complete set of ''n'' shapes. That is, the ''n'' shapes can be assembled in ''n'' different ways so as to create larger copies of themselves, where the increase in scale is the same in each case. Figure 1 shows an example for ''n'' = 4 using distinctly shaped decominoes. The concept can be extended to include pieces of higher dimension. The name setisets was coined by Lee Sallows in 2012, but the problem of finding such sets for ''n'' = 4 was asked decades previously by C. Dudley Langford, and examples for polyaboloes (discovered by Martin Gardner, Wade E. Philpott and others) and polyominoes (discovered by Maurice J. Povah) were previously published by Gardner.''Polyhexes and Polyaboloes'' in ''Mathematical Magic Show'', by Martin Gardner, Knopf, 1977, pp 146-159 Examples and definitions From the above definition it fol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geomagic Square - Self-tiler
Geomagic is the professional engineering software brand of 3D Systems. The brand began when Geomagic Inc., a software company based in Morrisville, North Carolina, was acquired by 3D Systems in February 2013 and combined with that company's other software businesses (namely Rapidform acquired by 3D Systems in October 2012 and Albre in July 2011). Geomagic was founded in 1997 by Ping Fu and Herbert Edelsbrunner. Geomagic-branded software products are focused on computer-aided design, with an emphasis on 3D scanning and other non-traditional design methodologies, such as voxel-based modeling with haptic input. 3D Systems also markets 3D quality inspection software as well as 3D scanners under the Geomagic brand. Geomagic Products 3D Scanning Systems Geomagic Capture is an integrated system consisting of a blue LED structured-light 3D scanner and one of several pieces of application-specific software. The systems are marketed for use as scan-based design tools, wherein a physica ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geomagic Square - Maancubes
Geomagic is the professional engineering software brand of 3D Systems. The brand began when Geomagic Inc., a software company based in Morrisville, North Carolina, was acquired by 3D Systems in February 2013 and combined with that company's other software businesses (namely Rapidform acquired by 3D Systems in October 2012 and Albre in July 2011). Geomagic was founded in 1997 by Ping Fu and Herbert Edelsbrunner. Geomagic-branded software products are focused on computer-aided design, with an emphasis on 3D scanning and other non-traditional design methodologies, such as voxel-based modeling with haptic input. 3D Systems also markets 3D quality inspection software as well as 3D scanners under the Geomagic brand. Geomagic Products 3D Scanning Systems Geomagic Capture is an integrated system consisting of a blue LED structured-light 3D scanner and one of several pieces of application-specific software. The systems are marketed for use as scan-based design tools, wherein a physica ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Broken Diagonal
In recreational mathematics and the theory of magic squares, a broken diagonal is a set of ''n'' cells forming two parallel diagonal lines in the square. Alternatively, these two lines can be thought of as wrapping around the boundaries of the square to form a single sequence. In pandiagonal magic squares A magic square in which the broken diagonals have the same sum as the rows, columns, and diagonals is called a pandiagonal magic square. Examples of broken diagonals from the number square in the image are as follows: 3,12,14,5; 10,1,7,16; 10,13,7,4; 15,8,2,9; 15,12,2,5; and 6,13,11,4. The fact that this square is a pandiagonal magic square can be verified by checking that all of its broken diagonals add up to the same constant: : 3+12+14+5 = 34 : 10+1+7+16 = 34 : 10+13+7+4 = 34 One way to visualize a broken diagonal is to imagine a "ghost image" of the panmagic square adjacent to the original: The set of numbers of a broken diagonal, wrapped around the original square ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Panmagic Square
A pandiagonal magic square or panmagic square (also diabolic square, diabolical square or diabolical magic square) is a magic square with the additional property that the broken diagonals, i.e. the diagonals that wrap round at the edges of the square, also add up to the magic constant. A pandiagonal magic square remains pandiagonally magic not only under rotation or reflection, but also if a row or column is moved from one side of the square to the opposite side. As such, an n \times n pandiagonal magic square can be regarded as having 8n^2 orientations. 3×3 pandiagonal magic squares It can be shown that non-trivial pandiagonal magic squares of order 3 do not exist. Suppose the square :\begin \hline \!\!\!\; a_ \!\!\! & \!\! a_\!\!\!\!\; & \!\! a_ \!\!\\ \hline \!\!\!\; a_ \!\!\! & \!\! a_\!\!\!\!\; & \!\! a_ \!\!\\ \hline \!\!\!\; a_ \!\!\! & \!\! a_\!\!\!\!\; & \!\! a_ \!\!\\ \hline \end is pandiagonally magic with magic constant . Adding sums and results in . Subtracting ... [...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] |
Jean-Paul Delahaye
Jean-Paul Delahaye (born 29 June 1952 in Saint-Mandé Seine) is a French computer scientist and mathematician. Career Delahaye has been a professor of computer science at the Lille University of Science and Technology since 1988 and a researcher in the school's computer sciences lab since 1983. Since 1991 he has written a monthly column in Pour la Science, the French version of Scientific American, dealing with mathematical games and recreations, logic, and computer science. He is a contributing author of the online scientific journal Interstices and a science and mathematics advisor to the Encyclopædia Britannica. Delahaye won the 1998 d'Alembert prize from the Société mathématique de France Lactalis is a French multinational dairy products corporation, owned by the Besnier family and based in Laval, Mayenne, France. The company's former name was Besnier SA. Lactalis is the largest dairy products group in the world, and is the sec ... for his books and articles popul ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
