Volume 26


The subject of this paper is the mathematical theory of catastrophes. A catastrophe is a disaster. But there is, implicit in the word, the idea of a sudden change for the worse.

We all know and have used the approximation $\pi \simeq \frac{22}{7}$. It may have occurred to you to ask why this is a worthwhile value.

The geometrical proposition, named after the Greek mathematician and philosopher, Pythagoras, (~ 570-550 BC), deals with a unique property of right-angled triangles.

Q.817 Find all integers $x,y$ such that $x(3y - 5) = y^2 +1$.

Q.805 Solve for $x$ and $y$:
$$\sqrt{x+y} + \sqrt{x-y} = 5\sqrt{x^2 - y^2}$$
$$ \frac{2}{\sqrt{x+y}} - \frac{1}{\sqrt{x-y}} = 1 $$