An elementary algebraic problem attributed to Leonardo of Pisa is analysed and some illogical elements in its formulation and solution are exposed. The natural context in which the problem was formulated is then proposed, and some consequences are discussed.

How many times have you heard that somebody is a wizard? And how many times did you take it literally? Most likely, the answer to the second question is ‘never’. And yet, there are reasons to believe that some people among us are real wizards, of the kind described with so much charm in the recently published series of books on Harry Potter [ 1, 2, 3, 4 ]. These books have provided us with a wealth of details on wizards and their society.

The urgent necessity for examining thoroughly the content of the Mathematical Curriculum in all types of schools at the present time is my reason for introducing a subject which is becoming a well-worn one, and I hope that in the course of the afternoon I may be successful in showing you what I believe to be a fresh and more fundamental approach to the problems involved, and that by being provocative I may invite a discussion on a very important question.

In the following note, Stirling’s formula for a factorial is first found by a very simple process. The expression so obtained has a meaning for non-integral as well as integral values of the variable. The function it defines is easily seen (§§ 3 ff.) to possess the fundamental properties of the Gamma function, and provides an easy and natural avenue of approach to its study.

If a square pyramid is cut obliquely by a plane as shown in figure 1, a pentagonal cross-section PQSTR is generated. The “Beijing theorem” states that the only case in which this pentagon can be regular is that in which the pyramid is half an octahedron and (except for a complication to be discussed later) the coordinates of the points P, Q, R, S and T are uniquely determined.