The Perimeter of an Ellipse or OvalDate: 9/5/96 at 10:7:58 From: Larry Friend Subject: The Perimeter of an Ellipse, or Oval What is the formula for calculating the perimeter of an elliptical oval? Date: 9/5/96 at 13:28:11 From: Doctor Tom Subject: Re: The Perimeter of an Ellipse, or Oval Hi Larry, This problem cannot be solved in terms of "elementary functions". The study of the problem led to many interesting discoveries in the field of complex variables, among them, elliptic integrals and the modular function. In their book on mathematical tables and formulas by Abramovitz and Stegun, there are a bunch of formulas to approximate the perimeter. Here's a chunk of C code that gives a good approximation: #define a1 .44325141463 #define a2 .06260601220 #define a3 .04757383546 #define a4 .01736506451 #define b1 .24998368310 #define b2 .09200180037 #define b3 .04069697526 #define b4 .00526449639 /* * ellipse_len returns the length of the ellipse: * x^2 + y^2/b^2 = 1; b < 1; */ float ellipse_length(float b) { float k; float m; k = 1 - (b*b); m = 1-k; return 4*((1 + m*(a1 + m*(a2 + m*(a3 + m*a4)))) + m*(b1 + m *(b2 + m*(b3 + m*b4)))*log(1/m)); } -Doctor Tom, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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