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Richard Evan Schwartz (born August 11, 1966) is an American mathematician notable for his contributions〔 to geometric group theory and to an area of mathematics known as billiards. Geometric group theory is a relatively new area of mathematics beginning around the late 1980s〔M. Gromov, ''Hyperbolic Groups'', in "Essays in Group Theory" (G. M. Gersten, ed.), MSRI Publ. 8, 1987, pp. 75-263.〕 which explores finitely generated groups, and seeks connections between their algebraic properties and the geometric spaces on which these groups act. He has worked on what mathematicians refer to as ''billiards'', which are dynamical systems based on a convex shape in a plane. He has explored geometric iterations involving polygons,〔 and he has been credited for developing the mathematical concept known as the pentagram map. In addition, he is a bestselling author of a mathematics picture book for young children. His published work usually appears under the name ''Richard Evan Schwartz''. In 2011 he is a professor of mathematics at Brown University. ==Career== Schwartz was born in Los Angeles on August 11, 1966. In his youth he played tennis and enjoyed video games. He attended John F. Kennedy High School in Los Angeles from 1981 to 1984, then earned a B. S. in mathematics from U.C.L.A. in 1987, and then a Ph. D. in mathematics from Princeton University in 1991 under the supervision of William Thurston.〔http://www.genealogy.math.ndsu.nodak.edu/id.php?id=18909〕 He taught at the University of Maryland. He is currently the Chancellor's Professor of Mathematics at Brown University. He lives with his wife and two daughters in Barrington, Rhode Island. Schwartz is credited by other mathematicians for introducing the concept of the pentagram map. According to Schwartz's conception, a convex polygon would be inscribed with diagonal lines inside it, by drawing a line from one point to the next point—that is, by skipping over the immediate point on the polygon. The intersection points of the diagonals would form an inner polygon, and the process could be repeated. Schwartz observed these geometric patterns, partly by experimenting with computers. He has collaborated with mathematicians Valentin Ovsienko and Sergei Tabachnikov to show that the pentagram map is "completely integrable." In his spare time he draws comic books,〔 writes computer programs, listens to music and exercises. He admired the late Russian mathematician Vladimir Arnold and dedicated a paper to him.〔 He played an April Fool's joke on fellow mathematics professors at Brown University by sending an email suggesting that students could be admitted randomly, along with references to bogus studies which purportedly suggested that there were benefits to having a certain population of the student body selected at random; the story was reported in the ''Brown Daily Herald''. Colleagues such as mathematician Jeffrey Brock describe Schwartz as having a "very wry sense of humor."〔 In 2003, Schwartz was teaching one of his young daughters about number basics and developed a poster of the first 100 numbers using colorful monsters. This project gelled into a mathematics book published in 2010, entitled ''You Can Count on Monsters'' for young children which became a bestseller.〔 Each monster has a graphic which gives a mini-lesson about its properties, such as being a prime number or a lesson about factoring; for example, the graphic monster for the number five was a five-sided star or pentagram.〔 He estimated that he wrote the book during 1000 hours.〔 A year after publication, it was featured prominently on ''National Public Radio'' in January 2011 and became a bestseller for a few days on the online bookstore Amazon〔 as well as earning international acclaim. The ''Los Angeles Times'' suggested that the book helped to "take the scariness out of arithmetic." Mathematician Keith Devlin, on ''NPR'', agreed, saying that Schwartz "very skillfully and subtly embeds mathematical ideas into the drawings." He's been compared to a mathematical version of Dr. Seuss. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Richard Schwartz」の詳細全文を読む スポンサード リンク
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