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

单词

Menelaus' Theorem

释义

Menelaus' Theorem

For Triangles in the Plane,

(1)

For Spherical Triangles,

(2)

This can be generalized to

-gons

, where a transversal cuts the side

for

, ...,

, by

(3)

Here,

and

(4)

is the ratio of the lengths

and

with a Plus or Minus Sign depending ifthese segments have the same or opposite directions (Grünbaum and Shepard 1995). The case

is Pasch'sAxiom.

See also Ceva's Theorem, Hoehn's Theorem, Pasch's Axiom

References

Beyer, W. H. (Ed.) CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, p. 122, 1987.

Coxeter, H. S. M. and Greitzer, S. L. Geometry Revisited. Washington, DC: Math. Assoc. Amer., pp. 66-67, 1967.

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

Pedoe, D. Circles: A Mathematical View, rev. ed. Washington, DC: Math. Assoc. Amer., p. xxi, 1995.

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