Copyright © University of Cambridge. All rights reserved.

'Circles Ad Infinitum' printed from http://nrich.maths.org/

Show menu


A circle of radius 1 cm is inscribed in an equilateral triangle. A smaller circle is inscribed at each vertex touching the first circle and tangent to the two 'containing' sides of the triangle. This process is continued ad infinitum....

circles in a triangle

What is the sum of the circumferences of all the circles?

What is the sum of their areas?

Adding all the circumferences or adding all the areas, which sum grows faster?