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Sangaku Shinkō
Sangaku or San Gaku ( ja, 算額, lit=calculation tablet) are Japanese geometrical problems or theorems on wooden tablets which were placed as offerings at Shinto shrines or Buddhist temples during the Edo period by members of all social classes. History The Sangaku were painted in color on wooden tablets ( ema) and hung in the precincts of Buddhist temples and Shinto shrines as offerings to the kami and buddhas, as challenges to the congregants, or as displays of the solutions to questions. Many of these tablets were lost during the period of modernization that followed the Edo period, but around nine hundred are known to remain. Fujita Kagen (1765–1821), a Japanese mathematician of prominence, published the first collection of ''sangaku'' problems, his ''Shimpeki Sampo'' (Mathematical problems Suspended from the Temple) in 1790, and in 1806 a sequel, the ''Zoku Shimpeki Sampo''. During this period Japan applied strict regulations to commerce and foreign relations for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sangaku Of Konnoh Hachimangu 1859
Sangaku or San Gaku ( ja, 算額, lit=calculation tablet) are Japanese geometrical problems or theorems on wooden tablets which were placed as offerings at Shinto shrines or Buddhist temples during the Edo period by members of all social classes. History The Sangaku were painted in color on wooden tablets ( ema) and hung in the precincts of Buddhist temples and Shinto shrines as offerings to the kami and buddhas, as challenges to the congregants, or as displays of the solutions to questions. Many of these tablets were lost during the period of modernization that followed the Edo period, but around nine hundred are known to remain. Fujita Kagen (1765–1821), a Japanese mathematician of prominence, published the first collection of ''sangaku'' problems, his ''Shimpeki Sampo'' (Mathematical problems Suspended from the Temple) in 1790, and in 1806 a sequel, the ''Zoku Shimpeki Sampo''. During this period Japan applied strict regulations to commerce and foreign relations for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tangent
In geometry, the tangent line (or simply tangent) to a plane curve at a given point is the straight line that "just touches" the curve at that point. Leibniz defined it as the line through a pair of infinitely close points on the curve. More precisely, a straight line is said to be a tangent of a curve at a point if the line passes through the point on the curve and has slope , where ''f'' is the derivative of ''f''. A similar definition applies to space curves and curves in ''n''-dimensional Euclidean space. As it passes through the point where the tangent line and the curve meet, called the point of tangency, the tangent line is "going in the same direction" as the curve, and is thus the best straight-line approximation to the curve at that point. The tangent line to a point on a differentiable curve can also be thought of as a '' tangent line approximation'', the graph of the affine function that best approximates the original function at the given point. Similarly, t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Princeton University Press
Princeton University Press is an independent publisher with close connections to Princeton University. Its mission is to disseminate scholarship within academia and society at large. The press was founded by Whitney Darrow, with the financial support of Charles Scribner, as a printing press to serve the Princeton community in 1905. Its distinctive building was constructed in 1911 on William Street in Princeton. Its first book was a new 1912 edition of John Witherspoon's ''Lectures on Moral Philosophy.'' History Princeton University Press was founded in 1905 by a recent Princeton graduate, Whitney Darrow, with financial support from another Princetonian, Charles Scribner II. Darrow and Scribner purchased the equipment and assumed the operations of two already existing local publishers, that of the ''Princeton Alumni Weekly'' and the Princeton Press. The new press printed both local newspapers, university documents, ''The Daily Princetonian'', and later added book publishing to it ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Japanese Temple Geometry
Japanese may refer to: * Something from or related to Japan, an island country in East Asia * Japanese language, spoken mainly in Japan * Japanese people, the ethnic group that identifies with Japan through ancestry or culture ** Japanese diaspora, Japanese emigrants and their descendants around the world * Japanese citizens, nationals of Japan under Japanese nationality law ** Foreign-born Japanese, naturalized citizens of Japan * Japanese writing system, consisting of kanji and kana * Japanese cuisine, the food and food culture of Japan See also * List of Japanese people * * Japonica (other) * Japonicum * Japonicus * Japanese studies Japanese studies (Japanese: ) or Japan studies (sometimes Japanology in Europe), is a sub-field of area studies or East Asian studies involved in social sciences and humanities research on Japan. It incorporates fields such as the study of Japanese ... {{disambiguation Language and nationality disambiguation pages ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tony Rothman
Tony Rothman (born 1953) is an American theoretical physicist, academic and writer. Early life Tony is the son of physicist and science fiction writer Milton A. Rothman and psychotherapist Doris W. Rothman. He holds a B.A. from Swarthmore College, (1975) and a PhD from the University of Texas at Austin (1981), where he studied at the Center for Relativity. He continued on post-doctoral fellowships at University of Oxford, Oxford, Moscow State University and the University of Cape Town. Career Rothman worked briefly as an editor at ''Scientific American'', then taught at Harvard, Illinois Wesleyan University, Bryn Mawr College and from 2005 to 2013 at Princeton University. In January 2016 he joined the faculty of NYU Polytech, now known as the Tandon School of Engineering and retired from teaching there in 2019. Rothman's scientific research has been concerned mainly with general relativity and cosmology, for which he has made contributions to the study of the early universe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Daniel Pedoe
Dan Pedoe (29 October 1910, London – 27 October 1998, St Paul, Minnesota, USA) was an English-born mathematician and geometer with a career spanning more than sixty years. In the course of his life he wrote approximately fifty research and expository papers in geometry. He is also the author of various core books on mathematics and geometry some of which have remained in print for decades and been translated into several languages. These books include the three-volume ''Methods of Algebraic Geometry'' (which he wrote in collaboration with W. V. D. Hodge), ''The Gentle Art of Mathematics'', ''Circles: A Mathematical View'', ''Geometry and the Visual Arts'' and most recently ''Japanese Temple Geometry Problems: San Gaku'' (with Hidetoshi Fukagawa). Early life Daniel Pedoe was born in London in 1910, the youngest of thirteen children of Szmul Abramski, a Jewish immigrant from Poland who found himself in London in the 1890s: he had boarded a cattleboat not knowing whether it was b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Seki Takakazu
, Selin, Helaine. (1997). ''Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures,'' p. 890 also known as ,Selin, was a Japanese mathematician and author of the Edo period. Seki laid foundations for the subsequent development of Japanese mathematics, known as ''wasan''. He has been described as "Japan's Newton". He created a new algebraic notation system and, motivated by astronomical computations, did work on infinitesimal calculus and Diophantine equations. Although he was a contemporary of German polymath mathematician and philosopher Gottfried Leibniz and British polymath physicist and mathematician Isaac Newton, Seki's work was independent. His successors later developed a school dominant in Japanese mathematics until the end of the Edo period. While it is not clear how much of the achievements of ''wasan'' are Seki's, since many of them appear only in writings of his pupils, some of the results parallel or anticipate those discovered i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Recreational Mathematics
Recreational mathematics is mathematics carried out for recreation (entertainment) rather than as a strictly research and application-based professional activity or as a part of a student's formal education. Although it is not necessarily limited to being an endeavor for amateurs, many topics in this field require no knowledge of advanced mathematics. Recreational mathematics involves mathematical puzzles and games, often appealing to children and untrained adults, inspiring their further study of the subject. The Mathematical Association of America (MAA) includes recreational mathematics as one of its seventeen Special Interest Groups, commenting: Mathematical competitions (such as those sponsored by mathematical associations) are also categorized under recreational mathematics. Topics Some of the more well-known topics in recreational mathematics are Rubik's Cubes, magic squares, fractals, logic puzzles and mathematical chess problems, but this area of mathematics incl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Problem Of Apollonius
In Euclidean plane geometry, Apollonius's problem is to construct circles that are tangent to three given circles in a plane (Figure 1). Apollonius of Perga (c. 262 190 BC) posed and solved this famous problem in his work (', "Tangencies"); this work has been lost, but a 4th-century AD report of his results by Pappus of Alexandria has survived. Three given circles generically have eight different circles that are tangent to them (Figure 2), a pair of solutions for each way to divide the three given circles in two subsets (there are 4 ways to divide a set of cardinality 3 in 2 parts). In the 16th century, Adriaan van Roomen solved the problem using intersecting hyperbolas, but this solution does not use only straightedge and compass constructions. François Viète found such a solution by exploiting limiting cases: any of the three given circles can be shrunk to zero radius (a point) or expanded to infinite radius (a line). Viète's approach, which uses simpler limit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Japanese Theorem For Concyclic Quadrilaterals
In geometry, the Japanese theorem states that the centers of the incircles of certain triangles inside a cyclic quadrilateral are vertices of a rectangle. Triangulating an arbitrary cyclic quadrilateral by its diagonals yields four overlapping triangles (each diagonal creates two triangles). The centers of the incircles of those triangles form a rectangle. Specifically, let be an arbitrary cyclic quadrilateral and let , , , be the incenters of the triangles , , , . Then the quadrilateral formed by , , , is a rectangle. Note that this theorem is easily extended to prove the Japanese theorem for cyclic polygons. To prove the quadrilateral case, simply construct the parallelogram tangent to the corners of the constructed rectangle, with sides parallel to the diagonals of the quadrilateral. The construction shows that the parallelogram is a rhombus, which is equivalent to showing that the sums of the radii of the incircles tangent to each diagonal are equal. The quadrilateral cas ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Japanese Theorem For Concyclic Polygons
__notoc__ In geometry, the Japanese theorem states that no matter how one triangulates a cyclic polygon, the sum of inradii of triangles is constant.Johnson, Roger A., ''Advanced Euclidean Geometry'', Dover Publ., 2007 (orig. 1929). Conversely, if the sum of inradii is independent of the triangulation, then the polygon is cyclic. The Japanese theorem follows from Carnot's theorem; it is a Sangaku problem. Proof This theorem can be proven by first proving a special case: no matter how one triangulates a cyclic ''quadrilateral'', the sum of inradii of triangles is constant. After proving the quadrilateral case, the general case of the cyclic polygon theorem is an immediate corollary. The quadrilateral rule can be applied to quadrilateral components of a general partition of a cyclic polygon, and repeated application of the rule, which "flips" one diagonal, will generate all the possible partitions from any given partition, with each "flip" preserving the sum of the inradii. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equal Incircles Theorem
In geometry, the equal incircles theorem derives from a Japanese Sangaku, and pertains to the following construction: a series of rays are drawn from a given point to a given line such that the inscribed circles of the triangles formed by adjacent rays and the base line are equal. In the illustration the equal blue circles define the spacing between the rays, as described. The theorem states that the incircles of the triangles formed (starting from any given ray) by every other ray, every third ray, etc. and the base line are also equal. The case of every other ray is illustrated above by the green circles, which are all equal. From the fact that the theorem does not depend on the angle of the initial ray, it can be seen that the theorem properly belongs to analysis, rather than geometry, and must relate to a continuous scaling function which defines the spacing of the rays. In fact, this function is the hyperbolic sine. The theorem is a direct corollary of the following lemma: ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
