In Matters for Debate, David Singmaster (DS) discusses some topics relating to the use and misuse of decimal points: the use of a full stop in writing times of the day, confusion between the decimal point and a dot used for multiplication, and writing amounts of money.

In 1355 the Italian professor of law Bartolus of Saxoferrato (1313-1357) wrote a treatise on the division of alluvial deposit. The problem he discussed is the following (figure 1). Some landowners, Bartolus calls them Gaius, Lucius, and Ticius, have neighbouring properties beside the bank of a river. The river deposits silt so that new land is formed at the riverside. How is this new fertile soil to be divided up ?

Among the ways in which a teacher can kindle a pupil's interest in mathematics is by invoking spirits from the subjects past: spirits of men full of imagination and determination; enterprising individuals brimming over with new ideas; pioneers who not only changed their particular discipline, but who in some cases even altered our perception of the world. The Scots have a heritage of which to be proud in science and mathematics. This article discusses four pioneers in statistics.

I have long been convinced that the teaching of mathematics suffers from the premature introduction of abstraction without adequate attention to the concrete facts from which the abstractions are derived. Perhaps I cannot better begin my argument than by taking as text a passage from the end of the first chapter of Todhunter’s Differential Calculus :

If z is a function of y having a differential coefficient at a certain point, and y is a function of x having a differential coefficient at the corresponding point, then z is a function of x having a differential coefficient at that point, and this differential coefficient is given by the formula

This theorem, thought not always stated so carefully, will be found in all texts on the calculus; but, so far as I am aware, no English writer, not even the most exact, offers a valid proof.

If particles of positive mass lie on a continuous curve whose concavity is always upwards, their centroid clearly lies above the curve and below the chord joining the extreme particles.

This obvious property gives a simple formula which includes several of the standard inequalities of the Algebra text-books.