Enigma 1206: Rounds unlimited
31 August 2015
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From New Scientist #2362, 28th September 2002 [link]
As a logo for its delivery service, Rounds Unlimited uses the geometric design shown.
It consists of an equilateral triangle with 24-centimetre sides and a large circle inside it touching each of its three sides.
Then in each corner there are smaller circles each touching the previous circle and two sides of the triangle. Then in each corner there are smaller circles each touching a previous circle and two sides of the triangle, and so on ad infinitum.
The total area of the circles is an exact whole number multiple of π cm².
What is that whole number?