Volume 7


This is an account of some elementary aspects of the subject known as "algebraic topology". It investigates the placing of nets on surfaces and Euler characteristics.

This machine is easily constructed from scrap material, using simple tools.

Despite appearances, the following subtraction is wrong:

The following problem was considered for publication in Parabola, but rejected as the editorial committee could find no reasonable way of solving it.

The following is a poem which describes how to solve the problem of these instantly insane blocks.

Man seems to have known of Pythagoras' Theorem since the early days of civilisation, although the Greek geometers were the first to provide a logical proof.

Since the last Parabola went to print, the following people have submitted answers.

In a certain country the number of boys born is approximately equal to the number of girls born.

While participating in a census, a census-taker arrived at a certain house in a certain street and proceeded to question the woman who answered, as to the number and ages of the occupants.

Essentially this reduces to proving that $x|y$ and $y|x$ simultaneously implies that $x=y$ which is a contradiction.

"Men of Mathematics Vols 1 & 2" by E.T. Bell.

J161 Find a whole number, $N$, satisfying the following conditions:
  (a) $N$ is the product of exactly four distinct prime numbers.

J151 (i) Prove that if $k$ is not a prime then neither is $2^k-1$