This diagram illustrates proposition 10 from Book XIII of Euclid's
Elements. If S(n) is the length of a side of a
regular n-sided polygon inscribed in a circle of radius 1,
then this proposition states that S(5) squared equals S(6)
squared plus S(10) squared. Hence S(5), S(6), and S(10)
form a right-angled triangle, as you can see.
The ratio S(6):S(10) is the golden section 1.61803398...
Back to Antony Galton's page of odds and ends.