Lev Radzivilovsky, Weizmann
Title: Some three-dimensional problems presented with animations.
Abstract:
I plan to discuss two elementary geometric problems using three-dimensional GeoGebra animations.
The first problem is one of the Boris's favourite problems about the largest section of a tetrahedron.
The second problem is the problem about parabolas embracing circles (by Omri Solan and Yoav Krauz), which was the "green T-shirt problem" of Israeli math Olympiad 11 years ago. A parabola embraces a circle, if they have two tangent points. Given three circles, and three parabolas embracing different pairs of circles, the claim is that there is a line which is tangent to all three parabolas. The proof of that claim is 3-dimensional. The theorem was further generalized by Yaron Brodsky, Omri Peer and Omri Solan (one of generalizations has a 3-dimensional proof, another has a 4-dimensional proof).
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