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Unformatted text preview: The details 1. The two atomic t riangles Plato notes (54a1) that there is only one kind of isosceles right t rianglenamely, the 45/45/90 t rianglewhereas there are infinitely many kinds of scalene. But of these, he tells us, we posit one as the most excellent (54a7), one whose longer side squared is always triple its shorter side (54b56). Plato describes the same scalene t riangle, equivalently, as one whose hypotenuse is twice the length of its shorter side (54d67). (The angles of this t riangle are thus 30/60/90.) Ill call the 30/60/90 t riangles a t riangles and the 45/45/90 t riangles b t riangles. a t riangle (scalene, 30/60/90) b t riangle (isosceles, 45/45/90) 2. Construction of faces of particles out of the atomic t riangles o Each face is either an equilateral triangle ( t ) or a square ( s )....
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 Spring '09
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