Volume 44

2008

Welcome to the final issue for 2008. I am delighted to let you know that the U-Committee of the University of New South Wales has generously provided us with funds to set up a website for online mathematics outreach to secondary school students throughout Australia.

In an earlier article in Parabola (Volume 42, Number 2, 2006), I showed how we could find a straight line which is drawn so as to  approximately fit some data points via the process of least-squares fitting.

The German publishing house Springer-Verlag puts out a continuing series of volumes on biomathematics, the application of mathematics in a biological context of one kind or another.  Volume 22 of this series, published in 1978, was entitled The Golden Age of Theoretical Ecology: 1923-1940.

Q1281 Prove that for any real numbers $a$ and $b$ there holds

$$\frac{1+|a|}{1+|b|} \le 1 + |a-b|.$$

Q1271 Solve simultaneously
\begin{align*}
x^2 + xy + y^2 &= 189 \\
x - \sqrt{xy} + y &= 9.
\end{align*}
ANS: (suggested by Julius Guest, Victoria, and Keith Anker, Victoria)