CTK Insights

Archive for the 'geometry' Category

21 Oct

A. Soifer's Book, P. Erdos' Conjecture, B. Grunbaum's Counterexample

TweetA variant of Helly's Theorem states that if any three from an infinite sequence of convex planar sets have a nonempty intersection, the same holds for the intersection of all the sets, provided all of them are closed and at least one is compact. Neither closedness or compactness of at least one set can be […]

07 Oct

Broken Chord to the Rescue

TweetIn mathematics, even the most obvious properties need to be proved, unless of course they are accepted as axioms. The following one seems pretty much obvious and still requires a proof: P is a variable point on the arc of a circle cut off by the chord AB. Prove the intuitively obvious property that the […]

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