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Question: If you get bored on New Year's Eve...

Question:If you get bored on New Year's Eve...

Alfred_F 260 Maple 2024
geometry
December 28 2024
1

Given 4 hummingbirds, each located at the vertex of a unit tetrahedron.
The birds begin to fly in such a way that all birds fly at the same speed and:
(1) Bird #1 always flies directly toward bird #2
(2) Bird #2 always flies directly toward bird #3
(3) Bird #3 always flies directly toward bird #4
(4) Bird #4 always flies directly toward bird #1
As one can imagine, the flying birds eventually meet and collide. (Assume the birds are very small.)

What is needed is the distance to the collision point of the hummingbirds.
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