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单词 Fagnano's Theorem
释义

Fagnano's Theorem

If and are two points on an Ellipse

(1)

with Eccentric Angles and such that
(2)

and and . Then
(3)

This follows from the identity
(4)

where is an incomplete Elliptic Integral of the Second Kind, is a complete Elliptic Integralof the Second Kind, and is a Jacobi Elliptic Function. If and coincide, the point where they coincide is called Fagnano's Point.
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更新时间:2024/11/15 1:53:05