Geometric Etudes in Combinatorial Mathematics (1st ed. 1991. 2nd printing.)

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Geometric Etudes in Combinatorial Mathematics (1st ed. 1991. 2nd printing.)

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  • 製本 Paperback:紙装版/ペーパーバック版/ページ数 250 p./サイズ 300 illus.
  • 商品コード 9780387754697

基本説明

Originally published by Center of Excellence, 1991.

Full Description

A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas. A painter makes patterns with shapes and colours, a poet with words. A painter may embody an 'idea,' but the idea is usually commonplace and unimportant. In poetry, ideas count for a great deal more; but as Housman insisted, the importance of ideas in poetry is habitually exaggerated... A mathematician, on the other hand, has no material to work with but ideas, and so his patterns are likely to last longer, since ideas wear less with time than words. The mathematician's patterns, like the painter's or the poet's, must be beautiful; the ideas, like the colors or the words, must ?t together in a harmonious way. Beauty is the ?rst test: there is no permanent place in the world for ugly mathematics. —G.H.Hardy, A Mathematician's Apology, 1940 [Har, pp. 24-25] I grew up on books by Isaac M. Yaglom and Vladimir Bolty- ski. I read their books as a middle and high school student in Moscow. During my college years, I got to know Isaak Moiseevich Yaglom personally and treasured his passion for and expertise in geometry and ?ne art. In the midst of my xxv xxvi Preface college years, a group of Moscow mathematicians, including Isaak Yaglom, signed a letter protesting the psychiatric - prisonment of the famous dissident Alexander Esenin-Volpin.

Contents

ORIGINAL ETUDES.- Tiling a Checker Rectangle.- Proofs of Existence.- A Word About Graphs.- Ideas of Combinatorial Geometry.- NEW LANDSCAPE, OR THE VIEW 18 YEARS LATER.- Mitya Karabash and a Tiling Conjecture.- Norton Starr's 3-Dimensional Tromino Tiling.- Large Progress in Small Ramsey Numbers.- The Borsuk Problem Conquered.- Etude on the Chromatic Number of the Plane.

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