“Area Principle”的概念、定义、习题解题方法及翻译-数学辞典

单词

Area Principle

释义

Area Principle

The ``Area principle'' states that

(1)

This can also be written in the form

(2)

where

(3)

is the ratio of the lengths

and

for

with a Plus or Minus Signdepending on if these segments have the same or opposite directions, and

(4)

is the Ratio of signed Areas of the Triangles. Grünbaum and Shepard show thatCeva's Theorem, Hoehn's Theorem, and Menelaus' Theorem are the consequences of this result.

See also Ceva's Theorem, Hoehn's Theorem, Menelaus' Theorem, Self-Transversality Theorem

References

Grünbaum, B. and Shepard, G. C. ``Ceva, Menelaus, and the Area Principle.'' Math. Mag. 68, 254-268, 1995.

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