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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.)

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.)

Advanced Engineering Mathematics
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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**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.
Transcribed Image Text:**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.
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