Isotomic conjugate

Isotomisch conjugate points are considered in the triangle geometry. They are defined as follows:

Given a triangle ABC. The midpoints are denoted with D, E, and F. Next are X1, Y1 and Z1 on pages [BC ], [ CA ] or [DOWN] three points, with the straight lines AX1, BY1 and CZ1 ( in the sketch blue) intersect at a point P1. Denoting the mirror points of X1, Y1 and Z1 on the respective side midpoints (D, E or F) with X2, Y2 and Z2, it follows from the theorem of Ceva, that the straight line AX2, BY2 and CZ2 (red drawn ) at a point P2 intersect. Is defined as the points P1 and P2 to one another as conjugated isotomisch.

Examples

  • The center of gravity of a triangle is conjugated isotomisch to himself.
  • The nail - point and point - Gergonne are conjugate to each other isotomisch.

Properties

  • Has a point P1, the trilinear coordinates, the isotomisch conjugate point P2 has the trilinear coordinates. And thereby represent the side lengths of the given triangle.
  • Has a point P1, the barycentric coordinates, the isotomisch conjugate point P2 has the barycentric coordinates or equivalent.
Ceva's theorem Nagel point Isogonal conjugate Wolfram Research
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