Interactive Applet |
You can move the points A, B and C (click on the point and drag it).
Press the keys “+” and “−” to zoom in or zoom out the visualization window and use the arrow keys to translate it.
You can also construct all centers related with this one (as described in ETC) using the “Run Macro Tool”. To do this, click on the icon _{}, select the center name from the list and, then, click on the vertices A, B and C successively.
Information from Kimberling's Encyclopedia of Triangle Centers |
Trilinears f(A,B,C) : f(B,C,A) : f(C,A,B), where f(A,B,C) = cos A/3 + 2 cos B/3 cos C/3
Barycentrics (sin A)f(A,B,C) : (sin B)f(B,C,A) : (sin C)f(C,A,B)X(356) is the centroid of the Morley equilateral triangle. For a discussion of the theorem and extensive list of references, see
C. O. Oakley and J. C. Baker, "The Morley trisector theorem," American Mathematical Monthly 85 (1978) 737-745.
For a sketch of the Morley cubic and list of centers on it, including X(356), X(357), X(358), visit Bernard Gibert's site.
For a biographical sketch, including details about Morley's famous theorem on angle trisectors, with history and references, see Frank Morley (1860-1937) geometer.
X(356) lies on this line: 357,358