Volume 15
, Issue 2

1979

The following question appeared in the 1978 Higher School Certificate 2-unit and 3-unit Mathematics exams:

Take two twenty cent coins $A$ and $B$. If the coin $B$ is kept fixed and $A$ is rolled round $B$ without slipping, how many revolutions will $A$ make about its centre before it returns to its original position?

In the great temple of Benares, beneath the dome which marks the centre of the world, rests a brass plate in which are fixed three diamond needles, each a cubit high and as thick as the body of a bee.

The Poisson distribution often gives a useful statistical model to describe the occurrence of isolated events in an interval of time.

If examinations do nothing else, they at least produce vast quantities of numerical data.

$\pi$'s the limit

Our story begins in Ancient Greece at the start of the quest for perfection.

One of the great discoveries of the Pythagorean era was the fact that not all positive numbers are "commensurable", that is, expressible as a fraction $a/b$ where $a$ and $b$ are natural numbers.

We start with 24 sheets of paper. Some are selected and cut up into 10 pieces each.

In Parabola, Volume 14, Number 3, Brendan Joyce described how to build a pile of bricks so that the top brick completely overhangs the bottom one.

Q.417 Let $a$ and $b$ be integers. Show that $10a + b$ is a multiple of $7$ if and only if $a-2b$ is also.

Q.393 Show that if $n$ is any integer greater than 2, of the fractions $\frac{1}{n}, \frac{2}{n},\frac{3}{n}, \cdots ,\frac{n-1}{n}$ an even number are in lowest terms.