Volume 31


A professor of mathematics at the University of Queensland recently recounted that when she telephoned Griffith University some years ago and asked for the Mathematics Department the receptionist replied, 'We do not have a Mathematics Department. Mathematics is not relevant to the Human Condition".

In the last two issues of Parabola two different proofs - one trigonometric and one geometric - were given of Heron's formula for the area of a triangle and reference was made to Brahmagupta's formula for the area of a quadrilateral.

This article has two aims:

  1. To clear up some misunderstanding about mathematical induction;
  2. To draw attention to the fact that mathematical induction is an axiom and to explain the significance of this.

A fraction is a number of the form $\frac{a}{b}$ where $a,b$ are integers and $b\neq 0$. We learn to add, subtract, multiply and divide fractions on our mothers knee.

Combinatorial mathematics or combinatorics, as it is often called, is concerned with problems of arrangement and counting.

Q.957 Solve the three simultaneous equations
$$ \frac{ab}{a+ b} = \frac{1}{2}, \frac{bc}{b+c} = \frac{1}{3}, \frac{ac}{a+c} = \frac{1}{9}$$

Q.949 (a) We have a collection of numbers, each of which is either zero or one.