A characterization of the Euclidean ball in terms of concurrent sections of constant width

Geometriae Dedicata - Tập 37 - Trang 307-316 - 1991
Luis Montejano1
1Instituto de Matemáticas, Universidad Nacional Autónoma de México, Ciudad Universitaria, Circuito Exterior, México D.F., Mexico

Tóm tắt

We prove that the Euclidean ball is the unique convex body with the property that all its sections through a fixed point are convex bodies of constant width. Furthermore, we characterize those convex bodies which are sections of convex bodies of constant width.

Tài liệu tham khảo

Chakerian, G. D. and Groemer, H., ‘Convex bodies of constant width’, in Convexity and its Application (ed. Gruber and Wills), Birkhauser, Basel, 1983, pp. 49–96. Süss, W., ‘Eine charakteristische Eigenschaft der Kugel’, Jahresber. Deutsch. Math.-Verein. 34 (1926), 245–247.