This investigation began in the refectory, when we noticed that the unwrapped foil on a four-section Kit Kat did not have its edges parallel to the edges of the chocolate bar. We wondered whether or not the angle between the two had been selected to reduce the cost of the foil by minimising the area covered by more than one sheet of foil, for example by overlap at the corners.

In the course of attacking a research problem recently, I came across a numerical dodge which, though really very simple, was new to me; in the course of using it I involuntarily gave myself an object lesson in the dangers of blind use of formulae. I hope there are readers of the Gazette who will appreciate learning of the dodge, and/or laughing at my misfortune.

The method of least squares is a well known technique of curve fitting, giving estimates for the values of the coefficients in equations such as y = ax, y = ax + b, etc, in terms of observed values of the variables x, y. It is less widely realised that the technique can be extended to estimating matrix coefficients.

The Fibonacci sequence

0, 1, 1, 2, 3, 5, 8, 13, …

is defined by u0 = 0, u1 = 1, and un = un−1 + un−2 for . There are many elementary formulae relating the various un, most of which, since the sequence is defined inductively, are themselves usually proved by induction.