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Morley Centers

The geometric centroid of the first Morley triangle, which is also the center of Morley's circle, is called the first Morley center. It has triangle center function

alpha_(356)=cos(1/3A)+2cos(1/3B)cos(1/3C)

and is Kimberling center X_(356).

The perspector of the first Morley triangle with reference triangle DeltaABC is called the second Morley center. The triangle center function is

alpha_(357)=sec(1/3A),

which is Kimberling center X_(357).

See also

First Morley Center, First Morley Triangle, Geometric Centroid, Morley's Circle, Morley's Theorem, Perspector, Second Morley Center

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References

Kimberling, C. "Central Points and Central Lines in the Plane of a Triangle." Math. Mag. 67, 163-187, 1994.Kimberling, C. "1st and 2nd Morley Centers." http://faculty.evansville.edu/ck6/tcenters/recent/morley.html.Oakley, C. O. and Baker, J. C. "The Morley Trisector Theorem." Amer. Math. Monthly 85, 737-745, 1978.

Referenced on Wolfram|Alpha

Morley Centers

Cite this as:

Weisstein, Eric W. "Morley Centers." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MorleyCenters.html

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