Power Point
PowerPoints
Triangle centers with triangle center functions of the form alpha=a^n are called nth power points. These points lie along the trilinear curve a^n:b^n:c^n that passes through vertices B and C of the triangle DeltaABC. The following table summarizes special named power points, where X_n denotes the nth center in Kimberling's numbering scheme.
n symbol Kimberling
center triangle center
-3 Omega^('') X_(76) third Brocard point
-2 X_(75) isotomic
conjugate of the incenter
-1 G X_2 triangle centroid
0 I X_1 incenter
1 K X_6 symmedian
point
2 X_(31) second power point
3 X_(32) third
power point
See also
Incenter, Second Power Point, Symmedian Point, Third Power Point, Triangle Center Function, Triangle CentroidExplore with Wolfram|Alpha
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References
Groenman, J. T. and Eddy, R. H. "Problem 858 and Solution." Crux Math. 10, 306-307, 1984.Kimberling, C. "Problem 865." Crux Math. 10, 325-327, 1984.Kimberling, C. "Central Points and Central Lines in the Plane of a Triangle." Math. Mag. 67, 163-187, 1994.Referenced on Wolfram|Alpha
Power PointCite this as:
Weisstein, Eric W. "Power Point." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/PowerPoint.html