There have been many attempts to understand the portrait of the mathematician Luca Pacioli which now hangs in the Museo di Capodimonte, Naples (Plate 1), and which will be familiar to users of the Pacioli 2000 accountancy software. However none of these attempts by art historians engages with the mathematics of the picture, which the artist has gone to such trouble to detail. While to a connoisseur the painting might be thought wooden and peripheral to the history of art, I believe that the artist has recorded the most important meeting of the Renaissance.

Michael Deakin’s article (“A simple proof of the Beijing theorem” 76 pp251-4) will have set readers thoughts running in a number of directions. Mine turned backwards in time, towards rational approximations to the golden ratio and crystallography. The symmetries of the crystal lattice preclude the appearance of a regular pentagonal face or true 5-axis. However fair rational approximations are attained with surprising ease.

Consider the usual experience of a student who progresses far enough in school mathematics to begin to study the calculus. After motivation of the topic of “rates of change”, simple differentiation of polynomials is learned. More advanced functions are then considered, and eventually the student meets the product, quotient and chain rules. The result: with enough algebraic accuracy and persistence, the student can determine derived functions for virtually any sufficiently wellbehaved combination of standard functions.

A children's television game is played as follows: Four postcards from children who have written in to the programme are selected at random and the children's names are written on a board. The presenters then draw letters of the alphabet one by one from a bingo-style randomising machine and, after each letter is drawn, all occurrences of that letter in any of the children's names are crossed off. The winner of the game is the first child whose name is completely crossed off.

Any discussion of languages suitable to be taught in school mathematics classes must first attempt to answer the question as to whether computer programming ought to form any part of the mathematics curriculum. The answer is by no means obvious, especially when the view has been expressed by the editor of this journal that “all programming languages (though particularly BASIC) are inimical to mathematical thinking at a higher level ”.