Answer by Anton Petrunin for Is the sphere the only surface with circular...
The first two questions (and others) are discussed in the following two papers of Kuzminykh, A. V.: An isoprojection property of the sphere (1973) Reconstructibility of a convex body from the set of...
View ArticleAnswer by sleepless in beantown for Is the sphere the only surface with...
Might I also point out the unstated assumptions in your question and in the fine answers thus far by Bill Thurston and Sergei Ivanov?The unstated assumption is that we are speaking about opaque objects...
View ArticleAnswer by Bill Thurston for Is the sphere the only surface with circular...
Warm-upLet's start in the plane.A curve of constant width can be thought of in terms of a slab in the plane of the given width that moves around as a function of angle. A moving slab has an envelope,...
View ArticleAnswer by Sergei Ivanov for Is the sphere the only surface with circular...
The answer to the title question is yes (well, I assume that by a "surface" you mean something reasonable, like a boundary of a convex set).Let $AB$ be the longest segment with endpoints on the...
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Is the sphere the only surface with circular projections? Or: Can we deduce a...
Several ancient arguments suggest a curved Earth, such asthe observation that ships disappear mast-last over thehorizon, andEratosthenes'surprisingly accurate calculation of the size of theEarthby...
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