1. L. J. Mordell has shown very simply (Math. Gaz. Lii (1968), p. 135) that the minimum value of the definite integral

A recent and fascinating application of statistics has been that of analysing the distribution of words in a written document in an attempt to determine the authorship. This article reviews some of the methods used and proposes a simplified test that could be performed using a desk calculator, although access to a digital computer would reduce the work required. An example of the test applied to a manuscript in the British Museum (Stowe 269) is given in detail to illustrate the method.

Mr. A. M. Cohen in his article (The Mathematical Gazette, LIII, Feb. 1969, p. 41) makes some suggestions for school work in numerical methods and number theory. These prompt me to describe some work actually done in which, for reasons which will appear, the emphasis is rather different from his.

At the Cambridge Conference, 1969, I proposed the following problem to several members:

Find a binary operation on the reals which is associative but not commutative.

Let xi , i = 1, 2, ... , n, be the roots of the polynomial equation

we first determine the value of the generalized Vandermonde determinant

In Note 2590 (Gazette 1956) I gave a very simple method for constructing a ring of 2n 0’s and 1’s in such a way that each set of consecutive n digits formed a unique number in the scale of 2. For instance with n = 4, the cycle 0111101100101000 provides in turn the numbers 0111 = 7, 1111 = 15, 1110 = 14, 1101 = 13, 1011 = 11, 0110 = 6, 1100 = 12, 1001 = 9, 0010 = 2, 0101 = 6, 1010 = 10, 0100 = 4, 1000 = 8, 0000 = 0, 0001 = 1, 0011 = 3.

In a previous article on the Spirograph, published in The Mathematical Gazette of December, 1966, I suggested that it could be used at sixth form level to illustrate some advanced work on cartesian coordinates. Following this up, I have found a number of links with calculus, algebra and trigonometry.