0

I have a function for the calculation of the perimeter of an ellipse based on the inputs a and b. So far tested, it act similar to testing tools in the internet; example https://www.mathsisfun.com/geometry/ellipse-perimeter.html#tool
Has anybody some numerical precise examples of ellipse (perimeter, a and b) where the precision is quite high? (at least the first 10 digits after "," should be "correct" or should have been calculated with high and long computational power). I will make a python script on a 64bit PC later then compare the data I will receive from here, from where the data diverge after the ",".

Example

a= 0.1234567890123456 b= 2.345678901234567 Perimeter = 9.4xxxxxxxxxxxxx

After I will use my python script, I will numerically evaluate my result on my 64bit PC and the Perimeter above. (I have not started the mathematical proof phase of the precision of the function; I just want to have few numerical examples to "quick and dirty" check my function before I spend the next days working).

floppy_molly
  • 11

1 Answers1

0

With $a=0.1234567890123456$ and $b=2.345678901234567$

The exentricity is $\quad e=\sqrt{1-\frac{a^2}{b^2}}$

The perimeter is $\quad p=4 * b * EllipticE(e)$ $$p=9.4098873248446338450884417196493252931085343348684439058378...$$

You can use WolframAlpha, for example : https://www.wolframalpha.com/input/?i=4*2.345678901234567*EllipticE%28sqrt%281-%280.1234567890123456%2F2.345678901234567%29%5E2%29%29

For large number of digits clik on the button "More digits".

JJacquelin
  • 66,221
  • 3
  • 37
  • 87