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

单词

Routh's Theorem

释义

Routh's Theorem

If the sides of a Triangle are divided in the ratios , , and , the Cevians form a central Triangle whose Area is

(1)

where

is the Area of the original Triangle. For

(2)

For

, 2, 3, ..., the areas are 0, 1/7, 4/13, 3/7, 16/31, 25/43, .... The Area of the Triangle formed byconnecting the division points on each side is

(3)

Routh's theorem gives Ceva's Theorem and Menelaus' Theorem as special cases.

See also Ceva's Theorem, Cevian, Menelaus' Theorem

References

Coxeter, H. S. M. Introduction to Geometry, 2nd ed. New York: Wiley, pp. 211-212, 1969.

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