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realitybugll
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perimeter of an elipse -- exact formula
I found an exact formula for the perimeter of an ellipse in terms of its major and minor axis
a = 1/2(major axis)
b=1/2(minor axis)
my equation for the perimeter of an ellipse:
[tex]4{\frac{\frac{(a^2+b^2)\frac{1}{b}\pi}{4}}{\frac{2({\sin^{-1}(\frac{a}{\sqrt{a^2+b^2}})-45)}}{90-2{(\sin^{-1}(\frac{a}{\sqrt{a^2+b^2}})-45)}}+1}[/tex]
I tested it against this formula a couple times:
for a =3, b =1
the formula: 12.808
my formula:12.870
for a=7 b=2
the formula:29.462
my formula:29.499
for a=84 b = 9
the formula:339356
my formula:338.56555
on cabri II plus i drew a proof that shows how i got this -- if u want that tell me.
any insight is greatly appreciated![Big Grin :biggrin: :biggrin:](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
I found an exact formula for the perimeter of an ellipse in terms of its major and minor axis
a = 1/2(major axis)
b=1/2(minor axis)
my equation for the perimeter of an ellipse:
[tex]4{\frac{\frac{(a^2+b^2)\frac{1}{b}\pi}{4}}{\frac{2({\sin^{-1}(\frac{a}{\sqrt{a^2+b^2}})-45)}}{90-2{(\sin^{-1}(\frac{a}{\sqrt{a^2+b^2}})-45)}}+1}[/tex]
The perimeter of an ellipse with semi-major axis a and eccentricity e is given by 4aE(pi/2,e), where E is the complete elliptic integral of the second kind. This can be calculated to great precision instantly on any mathematics program like mathematica
I tested it against this formula a couple times:
for a =3, b =1
the formula: 12.808
my formula:12.870
for a=7 b=2
the formula:29.462
my formula:29.499
for a=84 b = 9
the formula:339356
my formula:338.56555
on cabri II plus i drew a proof that shows how i got this -- if u want that tell me.
any insight is greatly appreciated
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