Geoffrey Coombs

The problem of finding the minimum (or the maximum) of a function is a familiar application of calculus. However, if the derivative of the function in question is not known, one must resort to numerical methods.

R.S. Horsfield

In 1678 Christiaan Huygens developed a wave theory of light in contradiction of Newton’s corpuscular theory. It was not published until 1690.

Peter Brown

Suppose your teacher asks you to find the area of the following triangle.

The law of motion for a freely falling body was first enunciated by Galileo in the 17th century.

**Q.941** On my desk calendar two numbers are given: the number of days in the year up to today, and the number remaining.

**Q.931** In a large flat area of bushland there are two fire-spotting towers, one exactly 20km east of the other.

Esther Szekeres The famous formula of Heron connects the sides, a,b,c of a triangle with the area, A of the triangle, i.e.

A=√(s(s−a)(s−b)(s−c))

Peter G Brown.

Some years ago I saw the following problem in a mathematics competition. Solve the simultaneous equations

x+y+z=1

x^{2}+y^{2}+z^{2}=29

x^{3}+y^{3}+z^{3}=-29

**JUNIOR DIVISION**

Find the smallest positive integer n such that 13n is a perfect cube, 15n a perfect fifth power and 17n a perfect seventh power.

**Q.1001** On the island described in question 2 of the Junior Division for this year’s mathematics competition, each town entered one Australian Rules football team in the national championship.

**Q.1001** On the island described in question 2 of the Junior Division for this year’s mathematics competition, each town entered one Australian Rules football team in the national championship.

**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.

Derek W. Robinson

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".

Ian Woodhouse 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.

Rob Neurath

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.

N. J. Wildberger

A fraction is a number of the form a/b where a,b are integers and b≠0 . We learn to add, subtract, multiply and divide fractions on our mothers knee.

Peter Brown

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

**Q.957** Solve the three simultaneous equations

ab/(a+b)=1/2 , bc/(b+c)=1/3 , ac/(a+c)=1/9

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