**Problem 3:**Someone selects five arbitrary points in the interior of an equilateral triangle with a side length of 1 cm. Demonstrate that there are at least two of these points that are at a distance of no more than 1/2 cm from each other. *Hint:* Divide the triangle in a suitable way and apply the pigeonhole principle.

Answered: 3. Someone selects five arbitrary…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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3. Someone selects five arbitrary points in the interior of an equilateral triangle of side 1 cm. Show that there are at least two of them at a distance of no more than 1/2 cm. (Hint: Divide the triangle in a suitable way and use the pigeonhole principle.)