I’m just off to the pub otherwise I’d sit down and start a list of each integer in turn, just for the sheer fun of it. Be glad it’s too late for that.

Derek – what are some of ‘the other formulae from which pi may be derived’? And why should anyone want to know pi except for understanding the geometry of circles and related forms e.g spheres and cones? Incidentally the word ‘pi’ derivies from the greek letter ‘p’ and is a direct reference originally to ‘perimeter’.

Also what you say about generalising may be true of other constants but not, in any untrivial way, of numbers in general.

To be really strict the setter would have to say in full “name of value of relationship”, but just “relationship” as a convenience/expediency is okay by me, with “name of value of” left implicit.

The argument in the previous post could be generalised, as any valid argument should. In which case all numbers are relationships as they can all be derived from some equation or other. In which case the word number then becomes redundant. However, the word number isn’t redundant as it doesn’t mean relationship. So going back from the general to the particular, pi is a number.

The size of circles varies, and pi is a constant. It is also an irrational number. It is not part of or a product of the standard set of integers which have general reference. It exists simply as an expression of the relationship between geometrical features of a particular shape. If you ask what is the relationship between the diameter and the circumference of a circle, the answer is that the latter is pi times the former. It is not unreasonable for everyday purposes to say that pi constitutes that relationship.