Cristiano 0 Posted July 20, 2018 Share Posted July 20, 2018 I know that the area of an ellipse is 1403761773.43497 and its circumference is 145485.418131498. Is there any way to calculate from those numbers that the semi-major axis is 26534.9039306654? Link to post Share on other sites

YaDinghus 49 Posted July 20, 2018 Share Posted July 20, 2018 (edited) There is no straightforward method for calculating the circumference of an ellipse from the two semiaxes, so there is also no straightforward method for determining the length of any semi-axis from the area and the circumference. Given the area and the suspected size of the major semiaxis, the small semiaxis would be 16839.3769767847. Wikipedia suggests that at this proportion of the major to the minor semiaxis the circumvmference U = pi*(a+b) yields an error of 1%. So for the current assumed configuration, U should be 136264.322253585, which is more than 1% outside the originally stated circumference For clarity: close, but no cigar Edited July 20, 2018 by YaDinghus 1 Link to post Share on other sites

Cristiano 0 Posted July 20, 2018 Author Share Posted July 20, 2018 (edited) Supposing that I correctly calculate the integral to obtain the circumference and the area (I'm not sure right now), is there any numerical method that I can try? EDIT: I used the formula C= pi * (a + b) [ 1 + sum... to calculate the circumference and my above result (145485.418131498) is good, while the area is wrong. Edited July 20, 2018 by Cristiano formula image link not working Link to post Share on other sites

YaDinghus 49 Posted July 20, 2018 Share Posted July 20, 2018 15 minutes ago, Cristiano said: Supposing that I correctly calculate the integral to obtain the circumference and the area (I'm not sure right now), is there any numerical method that I can try? That depends on how precise you need the results to be. As I've said, up to a ratio of 3:2 for the major to the minor semiaxis, the error is smaller than 1% for U = pi*(a+b). Since pi appears in both formulae for circumference and area, then A/U = ab/(a+b). This is the most I can offer right now... Link to post Share on other sites

Cristiano 0 Posted July 20, 2018 Author Share Posted July 20, 2018 I meant a recursive formula like: a = A/U * (a + b) (I wrote just an example for clarification). Link to post Share on other sites

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