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

单词

Kiepert's Parabola

释义

Kiepert's Parabola

Let three similar Isosceles Triangles , , and be constructed on the sides of a Triangle . Then the Envelope of the axis of the Triangles and is Kiepert's parabola, given by

(1)

(2)

where

are the Trilinear Coordinates for a line tangent to the parabola. It is tangent to the sides ofthe Triangle, the line at infinity, and the Lemoine Line. The Focus has Triangle CenterFunction

(3)

The Euler Line of a triangle is the Directrix of Kiepert's parabola. In fact, theDirectrices of all parabolas inscribed in a Triangle pass through theOrthocenter. The Brianchon Point for Kiepert's parabola is the Steiner Point.

See also Brianchon Point, Envelope, Euler Line, Isosceles Triangle,Lemoine Line, Steiner Points

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