Fourier transforms? (This use of pi, sqrt(pi) can be forgiven, due to the *circles*/*cycles* involved in Fourier analysis.) n-dimensional volumes involve pi^(n/2). Why the "1/2" ? (These formulae also involve gamma(n+1/2)). Is there a relationship between your integration of the Gaussian and n-dimensional volumes? (Google "Gaussian integrals" and wikipedia.) At 06:58 AM 3/1/2020, James Propp wrote:
I've written a new essay, which I hope to post on March 10th (rather than the 17th).
http://faculty.uml.edu/jpropp/mathenchant/059-draft1.pdf
Suggestions for improvements of all kinds are welcome, including other cool facts about the square root of pi, and good references for writeups and videos that evaluate the integral of exp -x^2.
Jim Propp