“Nature does not consist entirely, or even largely, of problems designed by a Grand Examiner to come out neatly in finite terms, and whatever subject we tackle the first need is to overcome timidity about approximating.”
H. and B. S. Jeffreys, Methods of Mathematical Physics, 2nd ed., Cambridge University Press, 1950, p. 8.
Related post: Just an approximation
4 thoughts on “Timidity about approximating”
And why stop there? Good approximations are hard; start simple. Begin, at first, to assume the answer is about 2.7. Then improve things from there.
I’m reminded from one of the best things a lecturer ever said in a physics class: “Pi is about 10.”
@Pseudonym: In some cases pi = 10 is good enough. The next refinement would be pi = sqrt(10), which is not bad.
I think in most contexts where pi=10 is good enough, pi=1 is both simpler and better.