Calculation of Perimeter and Area of Ellipse.

Keyword

Ellipse,Complete elliptic integral of the second kind,Perimeter,Area,Long radius,Short radius.

Reference

[1]:『ケンブリッジ物理公式ハンドブック』(Graham Woan).

Remarks

・P=4*a*E(π/2,e).(Reference[1]).
・E(π/2,e)=∫[0~π/2](1-e^2*(sinθ)^2)^0.5・dθ.(Reference[1]).
・A=π*a*b.(Reference[1]).
・e=1-b^2/a^2.(Reference[1]).
・To calculate the value of integral,Simpson's rule is applied.Therefore,it contains error.
・Simpson's rule:∫[x0~x2]f(x)≈h/3*[f(x0)+4*f(x1)+f(x2)].h=(x2-x0)/2.x1=(x0+x2)/2.

History

・2014/08/06:layout change.
・2009/09/24:Revise Reference.
・2009/08/30:Upload.