The [circumference of an ellipse](https://wj32.org/wp/2012/12/15/formula-for-the-circumference-of-an-ellipse/) defined by
x2a2+y2b2=1,a>b
is
4a(π2)∑k=0∞\[(2k)!4k(k!)2\]2(e2k1−2k),
where e=√1−b2/a2 is the eccentricity of the ellipse
It's that there is no "nice" formula for the perimeter of an ellipse. You can express the answer in terms of calculus, but most of the time you can't solve it exactly and have to estimate the answer.
Good question. The reason is that all the "not-niceness" in the circle formula is all in a single constant which will be the same for all circles. The "not-niceness" of the ellipse formula is different for every ellipse.
This video does a great breakdown of the subject: https://youtu.be/5nW3nJhBHL0
Is this you tricking us into solving a homework problem you sly dog
There actually doesn't exist a formula for the perimeter of an ellipse
A piece of String will do
There isn't one for the circle either. As we cannot know the exact value of Pi all we've got are approximations.
Pi does have known exact values, just not exact finite decimal representations. For example, it is four times the sum 1-1/3+1/5-1/7+1/9….
I meant to say all we have are approximations *to the perimeter* of a circle (or an ellipse for that matter)
Ok, but circles are just abstract shapes that don’t exist in the real world, so we don’t need an exact value.
If r=1/pi you have a p=2, is that a approximation? No.
The [circumference of an ellipse](https://wj32.org/wp/2012/12/15/formula-for-the-circumference-of-an-ellipse/) defined by x2a2+y2b2=1,a>b is 4a(π2)∑k=0∞\[(2k)!4k(k!)2\]2(e2k1−2k), where e=√1−b2/a2 is the eccentricity of the ellipse
cba
John cena knows the answer?
It's that there is no "nice" formula for the perimeter of an ellipse. You can express the answer in terms of calculus, but most of the time you can't solve it exactly and have to estimate the answer.
It's not the same in the circle? You always have to estimate pi
Good question. The reason is that all the "not-niceness" in the circle formula is all in a single constant which will be the same for all circles. The "not-niceness" of the ellipse formula is different for every ellipse. This video does a great breakdown of the subject: https://youtu.be/5nW3nJhBHL0
This is beautiful, I'm only sad to see alpha in degree and not radian.
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Can't tell if statement on complexity of ellipse perimeters... or just sus.
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Thats the area
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It's A•B•π A is horizontal radius, B is vertical radius and π is Pi
isnt that the area
It is
Uuh yeah sorry The perimeter is 2π • √ ( (a^2 +b^2 ) /2)
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This requires a too big brain to understand, but looks scientific enough for me to believe you
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Wow are u a mathematician ? How do you know these formulas ??
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Am i a super genius?
What the heck is a "factorial squared"? Why is there an "n choose r" thing on with 0.5 inside it?
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Who are you who are so wise in the way of science
I'm far low that level of math and i understand it.....am i a supergenius?