Year 1980- Volume 16
2020 - Present

John Mack

Newspaper readers may have noticed earlier this year, buried away on an inside page, a small item announcing that someone had recently found, in a Dutch bookshop under a pile of rubbish, an old book which happened to be the only known surviving copy of Gerandus Mercator's original World Map.

When I think of Euclid even now I have to wipe my sweaty brow.

This column will be devoted to comment and discussion on some of the questions from recent Higher School Certificate examination papers.

R. H. Crozier

The young R.A. Fisher is said to have visited a local museum and come across a labelled skeleton of a fish.

Scott Driver

In Parabola, Volume 15, Number 2, Paul Rider described a modified Pascal's triangle shown above.

This rather tricky problem appeared in Volume 15, Number 1

Editorial note: Question 454 is incorrectly labeled as 464

Q.441 Prove that the number 111⋯11 , consisting of 91 ones, is a composite number.

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.

M. D. Temperley

Meleda, or Chinese rings, is a game of Chinese origin which, so the story goes, was invented by the soldier hero Hung Ming (181-234 A.D.) who gave it to his wife when he went to war.

B. Musidlak

Counting is not always as simple as 1,2,3,⋯, but, as I hope to show in these articles, it can be a lot more interesting.

A. Johnston

The harmonic series:$S={1}^{-1}+{2}^{-1}+{3}^{-1}+{4}^{-1}+\cdots$

is divergent, that is if we add enough terms together, we can produce a partial sum which is as large as we like.

Is a degree in mathematics any use? I mathematics at university interesting? Is it fun?

Algernon announced that on his birthday this year his age would be equal to the sum of the digits of the year in which he was born. When was he born?

We shall consider some problems involving the roots $\alpha ,\beta$$\alpha, \beta$ and $\gamma$$\gamma$, say, of the cubic equation

${x}^{3}+qx+r=0$

Dear Sir, Do you think that there would be two people in your class whose birthdays fall on the same day and month?

Q.455 The rule for leap years runs as follows: A year which is divisible by 4 is a leap year except that years which are divisible by 100 are not leap years unless they are divisible by 400.

Q.429 Let $a$$a$ be a positive integer. Prove that the fraction \$(a^3 + 2a)/a^4 + 3a^2 + 1) is in its lowest terms.

A. Nikov

Summer is here and the school year is almost over!

B. Musidlak

Naturally, anyone interested in mathematics should be familiar with bridge, so we shall turn our attention to calculating the probabilities of various events at the bridge table.

The present treatise on Arithmetic, though written so as to be as far as possible complete in itself, is intended primarily for those who have already received some grounding in the subject.

B. Preston

A circle in two dimensions is easily described by its familiar equation

Nothing unites the English like war.
Nothing divides them like Picasso.

Problems in this topic have very little formal mathematical content, but clear logical thought is necessary, and it is essential to read the question accurately. Some nice examples are:

Readers were asked to turn their calculators to literary ends and to fill the numbers supplied by Messrs H.P. and T.I with previously unsuspected meanings.

We present below the second of our series of interviews with mathematics graduates from the University of New South Wales.

In a plane are 127 toothed cog-wheels, numbered $\left(1\right),\left(2\right),\cdots ,\left(127\right)$ engage those of wheel $\left(1\right)$ and similarly $\left(2\right)$ is engaged with $\left(3\right)$

Q.441 Prove that the number 111⋯11, consisting of 91 ones, is a composite number.