By Iakov Isaevich Khurgin
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Additional resources for Did You Say Mathematics?
33). A chess tournament can also be represented in the form of a graph. Draw circles on a sheet of paper to indicate the participants and equip each one with 59 Fig. 32 a number in accordance with the lots drawn. Then the result of a game involving each pair will be represented as an edge joining the two appropriate points, and the direction of the arrow will be from the winning side to the losing side. No arrow on the edge will mean that the sides drew even (Fig. 34). The tournament will be over when each circle is connected with all the remaining circles.
No matter what kind of tension we apply without tearing the sheet, the hole remains. We now have a good deal of observational material. What is there left in common to all these transformations of the rubber sheet? 46 MATHEMATICS AND ART Like art, mathematics takes note of phenomena in real life, combines analogous events, processes and facts, and then generalizes. People's Artist of the USSR, Obraztsov—the celebrated actor, painter and puppet-show man—shows us dogs and cats, and lions and rabbits and with their aid typifies (generalizes) certain humorous, pathetic or unpleasant qualities of human beings.
12 are a sort of caricature of the neat triangles in Fig. 10, but they have vertices and the two triangles are separate and do not overlap. Now let us draw two amoeba-like figures on the sheet: one solid and the other with a hole in the middle (Fig. 13). Then stretch the sheet tight over a drum (Fig. 14). The amoebas will remain amoebas, and the hole will be preserved as well. No matter what kind of tension we apply without tearing the sheet, the hole remains. We now have a good deal of observational material.