Volume 25

1989

Actuaries may be regarded as highly trained business mathematicians.

Physics and mathematics have interacted with each other in the course of centuries, each enriching the development of the other.

The aim of this article is to present an unusual application of an area of mathematics: assessing the validity of claims about astrology by using statistical techniques.

In the beginning, mathematically speaking, there were the whole numbers.

Q.782 Let $S_n = \frac{1}{1^2-\frac{1}{4}} + \frac{1}{2^2 - \frac{1}{4}}+ \frac{1}{3^2 - \frac{1}{4}} + \cdots + \frac{1}{n^2 - \frac{1}{4}}$. Simply this expression, and show that $n$ is large $S_n$ is approximately equal to 2.

Q.773 Prove that $\tan(36^\circ) \times \tan(72^\circ) = \sqrt{5}.$