Volume 42
, Issue 2

2006

As we go to press, media around the world have been reporting the latest round of awards of the coveted Fields Medal (popularly called the "Nobel Prize for Mathematics") which are awarded every four years.

We sometimes see in newspapers or on television situations where a straight line is drawn so as to approximately fit some data points. This can always be done by eye, using human judgment, but the results would then tend to vary depending on the person drawing the line.

Two separate events happily combined to suggest the topic for this issue’s column. In the first place, I devoted my previous column to a somewhat controversial attempt to apply Mathematics to the "softer sciences" such as Biology and Linguistics.

Support vector machines emerged in the mid-1990s as a flexible and powerful means of classification. Classification is a very old problem in Statistics but, in our increasingly data-rich age, remains as important as ever.

Problem 1. An American football field is 100 yards long, and its width is half the average of its length and its diagonal. Find its area.

Prize Winners – Senior Division

First Prize
Graham Robert White                        James Ruse Agricultural High School

Q1211. Solve
$$ (2+\sqrt{2})^{\sin^2x} - (2+\sqrt{2})^{\cos^2x} + (2-\sqrt{2})^{\cos2x} = \left(1+\frac{1}{\sqrt{2}}\right)^{\cos 2x}$$

Q1201. Let $x_1$ and $x_2$ be the solutions of $x^2 - (a+d)x + ad - bc = 0.$ Prove that $x_1^3$ and $x_2^3$ are the solutions of
$$x^2 - (a^3 + d^3 + 3abc + 3bcd)x + (ad-bc)^3 = 0.$$