Spirals are among the most intriguing of geometrical patterns, frequently encountered in the world around us at all scales, from the cosmic spiral arms of galaxies to the microscopic structure of the DNA molecule. For centuries, humans have studied these patterns, classifying them, giving them different names, and describing them mathematically. The most common definition of a two-dimensional spiral is a curve on the plane traced by a point that winds around a certain fixed point (called the spiral's pole), while monotonically approaching or receding from it, depending on the direction of motion.

While looking at old copies of the journal Nature I chanced upon correspondence regarding the origin of the word radian. Textbooks today simply state it is an angular measure and have no interest in, nor space for, the history of the word. The Oxford English Dictionary states that the word first appears in print in 1879 in the second edition of the Treatise on natural philosophy by William Thomson (later Lord Kelvin) and Peter Guthrie Tait. In their discussion of angular velocity they wrote: “the usual unit angle is … that which subtends at the centre of a circle an arc whose length is equal to the radius. For brevity we shall call this angle a radian.”

In common with, I suspect, many people the author does not have access to the NAG library and so, when I was asked recently to calculate the value of the integral

correct to 10 decimal places my first reaction was to try several different calculators as well as several mathematical software packages. On doing so it was disappointing to find they either gave widely differing values such as 7.9065200767, 4.1317217452 or 0.9174196842 or an error message indicating that the method had not converged.

The National Council of Teachers of Mathematics in the USA took the occasion of the 1966 International Congress of Mathematicians as the opportunity for arranging with the Russian authorities a tour of Soviet mathematical centres by a small party of selected American mathematicians with special experience and interests in various aspects of education. The tour covered Kiev, Moscow and Leningrad and it was hoped that, in each city, a full range of mathematical education would be seen, from the department of mathematics in the University to the famous special boarding schools for pupils of outstanding mathematical ability and finally to the elementary level.

I was honoured to be invited to join the party as the only non-American and am very grateful to the Schools Council for enabling me to go by offering to meet the costs of travel and subsistence.

Since the time of Gutenberg the volume of printed information has been doubling roughly every fifteen years. Only relatively recently, however, has the growth of knowledge reached a point at which it challenges human intellectual capacity. Our society has responded by a progressive specialisation of intellectual roles. Very broadly, the nineteenth century saw the development of specialism in distinct fields; the twentieth, the growth of specialism within those fields. To take just mathematics, it has been estimated that, after allowing for redundancy, our present knowledge fills the equivalent of something of the order of 60 thousand average-sized volumes. While at the start of this century, according to Ostrowski, it was expected that a mathematics graduate would be prepared to deal with any question in any branch of mathematics, by mid century Von Neumann was estimating that a skilled mathematician might be familiar with some 10% of the whole field.

The article by C. C. Puckette in a recent issue of the Gazette (Vol. 37, No. 322, pp. 256–260) prompts me to give some results I obtained when investigating the pursuit of a bomber by an attacking fighter.