In Note 2449 (M.G. 1954, p. 213), Dr. F. G. Maunsell gave an account of two interesting figures, the flexagon (F), and a modified “hexahexaflexagram” (H). I have been prompted to investigate this subject further, and find that there is really an infinite family of such figures, whose properties become more vivid when they are studied as a group rather than in isolation.

The scope of the additive prime number theory is evident from its name. In this part of the theory of numbers we are concerned with the representation of integers as sums of primes; and here the central problem consists in the proof (or possibly refutation) of a celebrated conjecture made by Goldbach in 1742 to the effect that every even integer ≥4 can be represented as the sum of 2 primes. The truth of this conjecture is still unsettled; but though progress in this field has been slow, attempts to deal with the problem have led to a whole series of striking results.

The values of the Radii of Gyration have been worked out for some solid polyhedra, polyhedra with faces only, (shell or box-like), polyhedra with edges only (skeleton), polyhedra with vertices only. The results are given in the tables.

In two articles in the Mathematical Gazette, Pedal Triangles and Pedal Circles, July 1919, and Some Properties Relative to a Tetrastigm, Oct. 1920, J. H. Lawlor gave proofs of a number of properties of the pedal circles of the four vertices of a plane quadrangle ABCD with respect to the triangles formed by the remaining three vertices. The articles concluded with the statement of ten results, the first nine of which were fairly easily deducible from those already proved, but No. (10) was given as a conjecture. This was that the common chord of the pedal circles of A and D bisects BH1 and CH2, where H1and H2 are the orthocentres of the triangles BAD and CAD, and hence that BH2, CH1 meet on the common chord of the pedal circles of A and D. It can be seen that the second result would imply the former, for if h is the rectangular hyperbola through ABCD, which is unique unless the points are orthocentric, and if O is the centre of h, then H1 and H2 also lie on h, and it is known that the pedal circles pass through O. The meet of BH2, CH1 is a diagonal point of the quadrangle BH1H2C inscribed in h, and its join to the centre of h is the diameter conjugate to the parallel chords BH1CH2 and therefore bisects them.

The purpose of this article is twofold. In the first place it aims to give a general picture of the content and method of school mathematics teaching in a country in whose scientific and technical education the Western world is becoming increasingly interested. This general picture is here based entirely on publications of the Ministry of Education of the RSFSR (Russian Soviet Federal Socialist Republic) and on text- and other books in general use, mostly from the Russian Republic but a few from the Ukraine. It is not based on personal contact with the system or with teachers who have worked within it, but it is hoped to extend this article at a later date on the basis of first-hand experience. Aware of the diversity and flexibility of our own system of mathematics teaching, we would not expect a foreigner to understand it fully from publications alone. The Russian System, however, is less extensive and more unified, and we may therefore hope to obtain a useful understanding of it from books alone. We must remember, though, that it is in a process of change, and also that, as in England, there will be considerable variability from one school to another depending on the quality of the teachers. However oversimplified this introductory article may be, it should at least serve to give an orientation towards the subject.

In outlining the following course planned for girls of sixteen to eighteen years of age, I should make it clear that it occupied only a subordinate pla in school organisation. The orthodox General Certificate of education ordina level course is taken by all girls in the school for the first five ye (with the exception of perhaps two or three in the fifth year) a we have always had a strong group for Advanced level in the Six Indeed in the four girls’ schools which I have known intimately, the Mathematics course has always been highly popular and more successful (if judg by examination results) than most other school subjects. I do not believe on such facts as I have—that there is a sex difference in mathematical abili The lower total number of girls taking the General Certificate of Educati examination is, I fancy, explained on other grounds.