Volume 43
, Issue 1

2007 In July this year, Australia will be visited by many prominent international scientists attending a major international conference on General Relativity, Gravitation and Gravitational Waves. This will be the first International Conference on General Relativity and Gravitation to be held in the Australian region.

What shape is the Universe we live in? Does it go on for ever (like an infinite piece of paper) or if we go far enough will we end up back where we started (like on a sphere)?

This article is a combination of two articles I wrote over 12 years ago, the first ‘Time and Relativity’ (sections Special Relativity to The Twin Paradox) appeared in Parabola in 1993 and the second ‘Length and Relativity’ (sections Measuring Length to The Magician’s Assistant Paradox) in 1994.

There are two really fundamental theorems in metrical geometry. One of them you already know - it is Pythagoras’ theorem. The other one is the Triple quad formula, which you probably don’t know.

The number of students studying higher level mathematics in Australian high schools is declining.

This column is prompted by some correspondence with K R S Sastry, who for many years has been active in Mathematics, particularly Geometry. He has worked in his native India and also in Ethiopia, and has contributed prolifically to Mathematics journals over many years.

Q1231 Given $a>0$, prove that
$$\underbrace{\sqrt{a+\sqrt{a+\cdots+\sqrt{a}}}}_{n \text{ times}} <\frac{1+\sqrt{4a+1}}{2}.$$

Q1221 (submitted by Frank Drost, Research Associate, School of Mathematics and Statistics, UNSW. Edited.)
Complete the mathematical equations below by inserting the least number of mathematical symbols from the table