“Pedal Triangle”的概念、定义、习题解题方法及翻译-数学辞典

单词

Pedal Triangle

释义

Pedal Triangle

Given a point , the pedal triangle of is the Triangle whose Vertices are the feet ofthe perpendiculars from to the side lines. The pedal triangle of a Triangle with Trilinear Coordinates and angles , , and has Vertices with Trilinear Coordinates

	(1)
	(2)
	(3)

The third pedal triangle is similar to the original one. This theorem can be generalized to: the th pedal -gon of any-gon is similar to the original one. It is also true that

(4)

(Johnson 1929, pp. 135-136). The Area

of the pedal triangle of a point

is proportional to the Power of

with respect to the Circumcircle,

(5)

(Johnson 1929, pp. 139-141).

See also Antipedal Triangle, Fagnano's Problem, Pedal Circle, Pedal Line, Schwarz's TriangleProblem

References

Coxeter, H. S. M. and Greitzer, S. L. Geometry Revisited. Washington, DC: Math. Assoc. Amer., pp. 22-26, 1967.

Johnson, R. A. Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle. Boston, MA: Houghton Mifflin, 1929.

随便看

数学辞典收录了8975条数学词条，基本涵盖了常用数学知识及数学英语单词词组的翻译及用法，是数学学习的有利工具。