So far as I know the properties of a tetrahedron are not given in any mathematical text-book. In the late Dr. Wolstenholme’s Examples for Practice in the use of Seven-figure Logarithms, the formulae which are necessary to determine the plane and dihedral angles and the volume of the tetrahedron, having given the six edges, are stated, but nothing beyond this. Dr. Wolstenholme worked at the subject for some years, and several of his results were sent as problems to the Educational Times, where they appeared for the most part after his death. In one set of questions he remarks that they are “the equations I have been looking for for years,” and so I think we may fairly infer that these questions represent the more advanced results of his investigations. The solutions of these questions, so far as I have been able to find them, are practically all given in this paper. “With regard to the rest of the matter, I hardly dare claim any originality. Wolstenholme must have known all or nearly all the results, and any one seriously attacking the subject must come upon them. All I can say is that I have never seen them in print, and that under any circumstances the bringing of them together must be helpful to students in many branches of mathematics.

Two days before his death in the summer of 1901 Peter Guthrie Tait gave his son some handwritten notes on quaternions for safekeeping. Though he had distinguished himself in many areas of mathematical physics and had influenced the work of Thomson and Maxwell it was his evangelical promotion of quaternions which would be remembered in the years to follow and it was fitting that his last energies be devoted to the cause.

A persistent problem of the mathematics teacher is the motivation of students especially those not particularly interested in numerical work. In this paper we present a notational device for analysing relationships based on binary notation and show its application to the problem of incest. The authors developed this theory in the course of their study of the rabbinic law on this subject and present this application here, though it could be applied to any legal system. It is hoped that the use of this approach may be useful to introduce mathematical modes of thought to previously uninterested pupils.

Boys who have learned to find π using jam jars and string are often mystified to learn that the number has been calculated to thousands of decimal places: the infinite series and products usually quoted cannot be justified without analysis.

This article is about a method whose derivation involves only elementary algebra and trigonometry (including square roots and Pythagoras), and whose use is a feasible proposition even when only four-figure tables are available for the square roots.