“π is wrong!” by Bob Palais
appeared in
The Mathematical Intelligencer Springer-Verlag New York Volume 23, Number 3, 2001, pp. 7-8.
The author gratefully acknowledges Dr. Chandler Davis, for his encouragement and editorial input.
(See also the Wikipedia entry on Dr. Davis.) The most amusing letter to the editor in response stated:
``I agree with Bob Palais' pi-ous article, but it may be 2-pi-ous.''
The article has been discussed in several places since then, including:
A couple of my own observations since the article. It seems to me that you can't have it both ways on area A= πr2 and circumference C= πd. If you believe diameter is fundamental, then it should be A= πd2/4. As noted in the last page of the pdf, I suggest calling the alternate constant 2π=6.283... `1 turn', so that 90 degrees is `a quarter turn', just as we would say in natural language. The main point is that the historical choice of the value of π obscures the benefit of radian measure. It is easy to see that 1/4 turn is more natural than 90° , but π/2 seems almost as arbitrary. It is apparent that we can't eliminate π but it is to be aware of its pitfalls, and introduce an alternative for those who might wish to use one.
The following \TeX macro which produces the symbol \newpi
used in the article was created by Richard Palais.
\def \newpi{{\pi\mskip -7.8 mu \pi}}