Michael Fox

The ‘stop after k girls or N children’ policy

1. Introduction In the article [1], a follow-up to my article [2], Christian and Trustrum cite empirical evidence that the probability of a family giving birth to a boy or to a girl may vary from family to family. Letting b i and g i = 1 − b i respectively denote the probability of the i th family giving birth to a boy or to a girl, the suggestion is that b i may be distinct from b j for distinct i and j . As they point out, this has implications for the expected society-wide number of boys and girls. Following my discussion of the ‘stop after k girls’ policy, Christian and Trustrum introduce the related policy ‘stop after k girls or N children’. They argue that the expected number of children under this latter policy is an increasing function of b i (when 0 k N ). The present article complements their discussion by examining this alternative stopping policy in more detail.

The Soddy spheres of a 4-ball tetrahedron: Part 1

New discoveries about the Soddy circles of a triangle were published in the Gazette [1] in 1995; they are summarised below. Extensions of wellknown results in the geometry of the triangle to that of the tetrahedron were presented by Zeeman in his 2004 Presidential Address at the Mathematical Association Conference in York [2]. Using the computer software package Cabri 3D , we have discovered new results which extend the Soddy circles of a triangle to Soddy spheres of a special class of tetrahedra. This article is the first of two which present our discoveries, as well as relevant aspects of the established geometry of tetrahedra, together with their proofs.