Question

Three mutually tangent unit circles are circumscribed by a fourth circle as shown in the figure on the right. What proportion of the largest circle’s area is shaded ?

Answer 1

s the length of a diagonal across a square with sides of one unit of length; this follows the Pythagorean theorem. It was probably the first number known to be irrational.[citation needed]

As a good rational approximation for the square root of two, with a reasonably small denominator, the fraction 99/70 (≈ 1.4142857) is sometimes used.

The sequence A002193 in the OEIS consists of the digits in the decimal expansion of the square root of 2, here truncated to 65 decimal places: