“Fagnano's Theorem”的概念、定义、习题解题方法及翻译-数学辞典

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

. 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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