I have a ellipse, that i want to clip in equal sized (Area) parts. In a circle it´s simply taking 2 Pi and devide it by the wanted numbers.. At an ellipse it´s more complicated. And I am sure I got the result, but i don´t know how to set my Mathematica to do it... To simplify i set one radius to 1, the other one to 2. I want 30 parts of the ellipse.
The function for the ellipse is: ell=b/Sqrt[1 - ((a^2 - b^2)*Cos[phi]^2)/a^2]
So the Area for a part of the ellipse is (from "start" to "x" in rad): 1/2Integrate[ell^2, {phi, start, x}]
I don´t know, why following code doesn´t work:
a = 1;
b = 2;
step = 30;
start = 0;
ell = b/Sqrt[1 - ((a^2 - b^2)*Cos[phi]^2)/a^2];
For [i = 1, i < step+1, i++,
Solve[1/2 Integrate[ell^2, {phi, start, x}] == a*b*Pi/step, {x}];
start = x
]
I would appreciate every help!