If you wish to know the day of the week on which a historical date fell, and no tables are immediately available for this purpose, you may be glad to know a method, easy to remember, of calculating the day.

In Cundy and Rollett’s invaluable book on Mathematical Models, the authors begin their Chapter on Polyhedra by remarking that “The most suitable, and in many ways the most attractive, subject for an experiment in the construction of mathematical models is a set of polyhedra.” Various methods are in general use to produce finished models of polyhedra for the showcase, and similar methods form the basis of those considered suitable for constructing the simpler polyhedra in the classroom. That most commonly adopted is to draw the net of the required solid on a sheet of cardboard, allow for tabs as necessary, cut it out, score the creases half-through, fold up, and stick the tabs with some suitable quick-drying cement. For class-room use the major drawback to model making on these lines is the time-consuming and potentially messy process of sticking; and it is the object of this article to develop a method which dispenses with the use of paste or cement altogether. In fact I shall show how, using paper and scissors only, firm, neat models can be made, which in the case of the simpler solids could easily be produced in the classroom, and which in the case of the more complex polyhedra reveal by their construction in a striking manner some of the geometrical relationships of these solids.

Would you indicate 3 + 3 + 3+3 as 4x3 or as 3x4† Most colleagues and boys that I have asked plump for the former. 4x3 means to them “four threes” or “four times three”, which is emphatically not the meaning “four multiplied by three”. Clearly “four times three” is the same as “three multiplied by four”; (I do not mean that they are equal, I mean that the expressions are two ways of saying the same thing). If we indicate this common meaning by the symbols 4x3, we are in fact doing the opposite of what we do in the case of the other three arithmetical processes. 4 + 3 means (to most people) “take four and add to it three”, or “four increased by three”; 4-3 means “take four and subtract three from it” , or “four diminished by three”; so 4 + 3 means “take four and divide it by three”. Obviously, then, 4x3 must mean “take four, and multiply it by three”; i.e. “four taken three times” or three fours.

Functional analysis is the study of functions defined on certain abstract sets; these sets may vary greatly in their structure and the nature of their elements but they have in common the property that it is possible to define in them the notions of convergence, limit and so on: in other words, they are topological spaces. Most of the spaces studied in functional analysis have in addition algebraic properties: that is to say, addition and sometimes multiplication of their elements is possible.