To Infinity and Beyond: A Cultural History of the Infinite
Eli Maor examines the role of infinity in mathematics and geometry and its cultural impact on the arts and sciences. He evokes the profound intellectual impact the infinite has exercised on the human mind--from the "horror infiniti" of the Greeks to the works of M. C. Escher; from the ornamental designs of the Moslems, to the sage Giordano Bruno, whose belief in an infinite universe led to his death at the hands of the Inquisition. But above all, the book describes the mathematician's fascination with infinity--a fascination mingled with puzzlement. "Maor explores the idea of infinity in mathematics and in art and argues that this is the point of contact between the two, best exemplified by the work of the Dutch artist M. C. Escher, six of whose works are shown here in beautiful color plates".--Los Angeles Times "[Eli Maor's] enthusiasm for the topic carries the reader through a rich panorama".--Choice "Fascinating and enjoyable.... places the ideas of infinity in a cultural context and shows how they have been espoused and molded by mathematics".--Science
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A New Look at Geometry
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angle artist astronomer Axiom of Choice axioms calculus Cantor circle concept converge counting numbers curve decimal deﬁned deﬁnition denumerable discovery distance earth entire equal equation Escher Heirs c/o Euclid's Euclidean Euclidean geometry example fact ﬁgure ﬁnal ﬁnally ﬁnd ﬁnite ﬁrst ﬁsh ﬁve ﬁxed stars formula galaxies Gauss geometric series Georg Cantor Greek harmonic series Heirs c/o Cordon indeﬁnitely inﬁnite sets inﬁnite universe integers intersection inversion irrational numbers known limit logarithmic spiral M.C. Escher M.C. Escher Heirs mathematician mathematics mirrors Mobius strip motion natural numbers non-Euclidean geometry number line object original paradox parallel lines Parallel Postulate pattern physical plane point at inﬁnity prime number projective geometry proof rational numbers real numbers reﬂection regular polygons Reprinted scientiﬁc segment sequence set theory sphere square straight line subset surface symmetry groups tessellations theorem tion triangle York zero