The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » sci.math.* » sci.math

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Arbitrariness of pi
Replies: 7   Last Post: Mar 8, 2013 1:48 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Brian Chandler

Posts: 1,899
Registered: 12/6/04
Arbitrariness of pi
Posted: Mar 3, 2013 5:29 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

There's an exceedingly tedious argument going on at
about the "tauist" movement, which argues that if only we used a
symbol for 2pi instead of pi, the world would become numerate,
textbooks would be thinner and everything would be free. Well, this is
all a bit silly.

But it seems to me that there is an important point somewhere: it is
rather arbitrary to use a symbol for periphery/diameter, rather than
periphery/radius, or the ratio of the curved arc of a 60-degree 'fan'
to its side. In other words, using a symbol for any reasonable "small
fraction"** of pi would give us exactly the same mathematical
expressiveness, with only notational changes, and for many of these
variants there would be cases (formula for the volume of a sphere,
anyone?) in which the different symbol gave a simpler form.

This does not seem to be true of e, for example, and obviously isn't
true of i. (I suppose we could have a name for the fourth root of -1,
and square it all the time?) I have an intuition that the
transcendence of pi is related to this, because in algebraic terms,
extending the rationals (or the algrebraic numbers for that matter) by
any rational multiple of pi gives exactly the same structure. (I can't
give a simple justification why this shouldn't also imply that e could
be similarly known as f/2, except that in practice e doesn't keep
appearing with small fractional multiples.)

Can anyone help me write this more precisely, and (optimally) as
understandable as possible to people who have no idea what a field is?

I want to add a dispassionate bit about how the choice of 'pi' is
rather arbitrary, even though historically it seems to have arisen at
least twice (?? I think) independently, in Babylonia or whatever, and
in China. Any suggestions appreciated.

Brian Chandler

(** What is the word for a rational number with small numerator and

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.