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Given an equilateral triangle with side length 2, the radius

of any of the inscribed equal circles depends on the number of circles inscribed. Before reading Details, see if you can notice a pattern in the answer as you vary

Contributed by: Abraham Gadalla

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For a given

, the radius of a circle is

. The ratio of the total area of the circles to the area of the triangle is

, which approaches

approaches

This Demonstration is based on [1], problem 15, Chapter 11.

Reference

[1] J. Stewart, Calculus: Early Transcendentals, 5th ed., Belmont, CA: Brooks/Cole, 2007.

Abraham Gadalla

"Pool Circles"
http://demonstrations.wolfram.com/PoolCircles/
Wolfram Demonstrations Project
Published: July 18, 2011

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Pool Circles

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