Pool Circles

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 .

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DETAILS

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 as 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.
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Related Curriculum Standards

US Common Core State Standards, Mathematics