Hi All At risk again of exposing my limited math skills, I was wondering if it would be possible to get an approximation of the area of an elipse by the following method:
Average the length of the major an minor axises and then apply the formula for the area of a circle to this value, treating it as the diameter of a circle. example: If the major axis equals 4 cm. and the minor axis equals 2 cm. then their average length is 3 cm. The area of a circle is pi times the diameter. So , 3 times pi = 9.42 square cms. Would somebody check to see how close this is to the actual value? (p.s. I'm thinking that you could use the formula for the circumference of a circle in the same way to get the circumference of an elipse. ) Thanks John L. Carmichael 925 E. Foothills Dr. Tucson Arizona 85718 USA e-mail: [EMAIL PROTECTED] Tel: 520-696-1709 ----- Original Message ----- From: "Frans W. MAES" <[EMAIL PROTECTED]> To: "Sundial Mail List" <[email protected]> Cc: "Tony Moss" <[EMAIL PROTECTED]> Sent: Friday, March 16, 2001 5:51 AM Subject: Circumference of ellipse > 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/ > =====================================
