## Convex Bodies Associated with a Convex BodyUnited States Atomic Energy Commission, Technical Information Service, 1950 - Convex bodies - 23 pages |

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affine transformations area swept associated body C(r associated sets C(r b0 b3 bk b1 and b2 b2 and b3 b3 ba boundary of C(r boundary point C-ri C-rl Cb(r central curve Centroid closed convex body completely reducible concludes the proof containing the endpoints convex set critical point critical ratio diameter b1 b2 diameter in F diameters of C(r diameters with endpoints divides a chord endpoints in b1 essential diameters extended diameters extensions of diameters F intersects F of diameters family F family of diameters higher dimensions interior point irreducible convex body least one diameter Let b1 b2 m1 and m2 maximum ratio r(x midpoints obtained by expand pair of parallel parallel contact lines parallel line segments passing through b1 point of C(r point x exterior proof of Lemma proof of Theorem ratio 2r-l ratio rl respective endpoints satisfying properties semicircle similitude simply cover triangle b0 b1 unique diameter x1 and x2