Inequalities for the Perimeter of an Ellipse
نویسندگان
چکیده
منابع مشابه
On The Perimeter of an Ellipse
Let E be the ellipse with major and minor radii a and b respectively, and Pbe its perimeter, then P = lim 4 tan(p/n)(a + b + 2) Σ a2 cos2 (2k-2)Pi/n+ sin2 (2k-2)Pi/n; where n = 2m. So without considering the limit, it gives a reasonable approxi-mation for P, it means that we can choose n large enough such that the amountof error be less than any given small number. On the other hand, the form...
متن کاملOn the Perimeter of an Ellipse
Computing accurate approximations to the perimeter of an ellipse is a favourite problem of mathematicians, attracting luminaries such as Ramanujan [1, 2, 3]. As is well known, the perimeter, , of an ellipse with semimajor axis a and semiminor axis b can be expressed exactly as a complete elliptic integral of the second kind, which can also be written as a Gaussian hypergeometric function, (1) ...
متن کاملon the perimeter of an ellipse
let e be the ellipse with major and minor radii a and b respectively, and pbe its perimeter, then p = lim 4 tan(p/n)(a + b + 2) σ a2 cos2 (2k-2)pi/n+ sin2 (2k-2)pi/n; where n = 2m. so without considering the limit, it gives a reasonable approxi-mation for p, it means that we can choose n large enough such that the amountof error be less than any given small number. on the other hand, the formul...
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چکیده ندارد.
Inequalities for the Probabilitycontent of a Rotated Ellipse
Let X i and Y i follow noncentral chi-square distributions with the same degrees of freedom i and noncentrality parameters 2 i and 2 i , respectively, for i = 1; : : : ; n, and let the X i 's be independent and the Y i 's independent. A necessary and suucient condition is obtained under which P n i=1 i X i is stochastically smaller than P n i=1 i Y i for all nonnegative real numbers 1 n. Reform...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2001
ISSN: 0022-247X
DOI: 10.1006/jmaa.2000.7128