“Soddy Line”的概念、定义、习题解题方法及翻译-数学辞典

单词

Soddy Line

释义

Soddy Line

A Line on which the Incenter , Gergonne Point Ge, and inner and outer Soddy Points and lie (the latter two of which are the Equal Detour Point and the Isoperimetric Point). The Soddy linecan be given parametrically by

where

is a parameter. It is also given by

where cyclic permutations of

, and

are taken and the sum is over Trilinear Coordinates

,and

	Center
	Outer Griffiths Point
	Outer Oldknow Point
	Outer Rigby Point
	Outer Soddy Point
0	Incenter
1	Inner Soddy Point
	Inner Rigby Point Ri
2	Inner Oldknow Point Ol
4	Inner Griffiths Point Gr
	Gergonne Point

, , , and Ge are Collinear and form a Harmonic Range (Vandeghen 1964, Oldknow 1996). There are atotal of 22 Harmonic Ranges for sets of four points out of these 10 (Oldknow 1996).

The Soddy line intersects the Euler Line in the de Longchamps Point, and the Gergonne Line in theFletcher Point.

See also de Longchamps Point, Euler Line, Fletcher Point, Gergonne Point, Griffiths Points,Harmonic Range, Incenter, Oldknow Points, Rigby Points, Soddy Points

References

Oldknow, A. ``The Euler-Gergonne-Soddy Triangle of a Triangle.'' Amer. Math. Monthly 103, 319-329, 1996.

Vandeghen, A. ``Soddy's Circles and the De Longchamps Point of a Triangle.'' Amer. Math. Monthly 71, 176-179, 1964.

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