The famous formula of Heron connects the sides, $a,b,c$ of a triangle with the area, $A$ of the triangle, i.e.
$$ A = \sqrt{s(s-a)(s-b)(s-c)}$$
It is impossible to overestimate our debt to the ancient Greeks in a wide range of subjects including mathematics.
School textbooks often give the impression that Mathematics has all been worked out. In fact, nothing could be further from the truth.
Peter Kanka, of James Cook Boys Technology High School, provided the following proof that $$\sin(18) = \frac{\sqrt{5} - 1}{4}.$$
Q.1. Let $n$ be a positive integer. If the polynomial
$$(x+1)(x+2)(x+3) \cdots (x+n)$$
is expanded (a) find the sum of all the coefficients; (b) find the sum of the coefficients of odd powers of $x$.
Q.949 (a) We have a collection of numbers, each of which is either zero or one.
Q.941 On my desk calendar two numbers are given: the number of days in the year up to today, and the number remaining.