It is a well-known fact that the number of hours of daylight varies with the time of year, except at points on the equator. It is sometimes thought that at latitudes between the Arctic and Antarctic circles the variation takes the form of a sine curve. However there is no theoretical basis for this idea, although it is true that a sine curve may give quite a good approximation.

James R. Newman observed that “the most painful thing about mathematics is how far away you are from being able to use it after you have learned it” ([1], Vol. 3, p. 1978). Perhaps there is some sort of natural justice, then, in the fact that one of the most pleasant things about mathematics is that you don’t need to know very much about the subject in order to enjoy the puzzles, pastimes and toys that the study of mathematics has produced.

This article gives instructions for a new way to construct the mathematician’s toy which is called a “rotating ring”. I publish it in hopes that it may give you some pleasure and also provide a means by which you can entice your students to study the more serious aspects of solid geometry.

One of the pleasant aspects of research into mathematical history is the way in which existing material, passed over in the conventional account, may allow us not only to establish the bare, if unexpected, fact of a priority but, more importantly, to assess the significance of major currents in mathematical thought with greater precision. Briggs’ partial discovery, in anticipation of Newton, of the general binomial expansion,

is an excellent case in point.

Some years ago there was a vogue for a series of books dealing imaginatively with the future and bearing such titles as Daedalus, or the Future of Science, Icarus, or the Future of Flying, and the like. I do not recall whether arithmetic was among the topics considered by the ingenious authors, but a further title, Archimedes, or the Future of Calculation, might certainly have been suggested by the developments of modern arithmometers.

Given n dimensions, the obvious way of representing n classes is by a hypercube of side 2. Such a hypercube contains 2n unit hypercubes, one for each combination of the n classes. With only one dimension available, it is still possible to represent each of the 2n combinations. Take a line OX with any point P1 marked on it. The interval OP1will represent all combinations excluding the first class A1 and the interval P1X all combinations containing it.

In maths lessons in secondary school, on certain occasions my teacher entertained our class with the following game. Each player starts with an empty 2 × 5 grid, as shown in Figure 1(a). In each round of the game, a die is rolled, and each player has to choose one of the empty boxes in their grid and fill it with the number rolled. For example, after 3 rounds, a player's grid may look like the one in Figure 1(b). After 10 rounds everyone's grid is filled, forming two 5-digit numbers. A player's score is the sum of her/his two 5-digit numbers. Players with the largest sum win the game. We shall call this the ‘dice-and-numbers game’. It is easy to think of other variants. Any child who is comfortable with column addition and understands how place value affects the size of numbers will develop a reasonable strategy for the game.