Good question. Similarly, why is the length of a sine wave not a simple formula? Actually, they are the same. If you wrap a sheet of paper around a cylinder and cut it diagonally, the edge of the cut is an ellipse. When you unroll the paper, its edge is a sine wave. The two edges are, clearly, the same length.
Regards Chris 51.4N 1.3W "Frans W. MAES" wrote: > Hi all, > > Just to relieve the recent boredom of this list, how about this one: > > As some of you may know, I have an analemmatic sundial in my > garden (story on my homepage). The person who did the actual > work had to know how much material (tiles, bricks etc.) he would > need. Then I found out that there is no 'simple' formula for the > circumference of an ellipse. (I also found out that this led to a lot of > interesting mathematics, called 'elliptic integrals'. I knew the term, > but never realized where it came from.) > > The formula for the area of a circle generalizes simply to the area of > an ellipse (pi x r x r -> pi x a x b ; a and b being half the major and > minor axes, resp.). What puzzles me since is, why the > circumference of a circle does NOT generalize simply (actually, not > at all) to an ellipse. > > My question thus is: does anyone of you happen to know of a NON- > mathematical, intuitively convincing explanation for the fact that > there is no 'simple' formula for the circumference of an ellipse? > > Regards, > Frans Maes > > ===================================== > Frans W. Maes > Peize, The Netherlands > 53.1 N, 6.5 E > www.biol.rug.nl/maes/ > =====================================
