Volume 11
, Issue 1

1975 Most of you know what is meant by a Pythagorean triple. It is a set of three natural numbers $\left\{a,b,c\right\}$ such that $a^2 + b^2 = c^2$.

This crossnumber may have been hard - some people got it wrong!

Among the geometrical problems which have intrigued amateurs throughout the ages, the geometrical trisection (i.e. division in three equal parts) of an angle ranks high in popularity.

In an appendix to a Physics book, I found the derivation on infinite integrals of the type $$\int_0^\infty \frac{x^n}{e^x-1}dx.$$

During an investigation of polynomials, my class came across a problem which required finding a polynomial with roots that were reciprocals of the original polynomial's roots.

The game chosen for this issue of Parabola is quite a recent game. It was thought of by an American university student, William Black, in 1960.

"Coin Games and Puzzles" by Maxey Brooke

Contributed by Neil Bayles of Woden Valley High School.

Once upon a time Liethagoras, jealous of Pythagoras' fame, proposed a theorem.

Q.261 In a right-angled triangle, the shortest side is $a$ cm long, the longest side is $c$ cm long and the other side is $b$ cm long. If $a,b,c$ are all integers, when does $a^2 = b+c$?

J251 Framer Jones grew a square number of cabbages last year. This year he grew 41 more cabbages than last year and still grew a square number of cabbages.  How many did he grow this year?