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Point Alrescha


PointAlrescha

Point Alrescha is the triangle center obtained, when the following operations are defined, from the Parry reflection point by taking its isogonal conjugate, applying inversion in the circumcircle, and taking the isogonal conjugate of the result. Both conjugations use the original triangle. It is Kimberling center X_(1117) (Kimberling). The point takes its name from the star Alrescha, also called Alpha Piscium (SkyEye), following Kimberling's convention of using star names for some triangle centers (Kimberling).

Bernard Gibert discovered that Point Alrescha lies on the Lester circle of a scalene triangle whenever the point and circle are both defined (Grozdev and Dekov 2016). The other four labeled centers on the circle are the circumcenter X_3, nine-point center X_5, first Fermat point X_(13), and second Fermat point X_(14).


See also

Inversion, Isogonal Conjugate, Parry Reflection Point

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References

Grozdev, S. and Dekov, D. "Computer Discovered Mathematics: Lester Circles." Internat. J. Comput. Discovered Math. 1, 15-25, 2016. https://journal.bulgarian-kangaroo.eu/2016-1/Grozdev-Dekov-Lester-Circles-pp.15-25.pdf.Kimberling, C. "Constellations." In Encyclopedia of Triangle Centers. https://faculty.evansville.edu/ck6/encyclopedia/links.html.Kimberling, C. "Encyclopedia of Triangle Centers: X(1117)=Point Alrescha." https://faculty.evansville.edu/ck6/encyclopedia/ETCPart2.html#X1117.SkyEye. "(Un)Common Star Names." https://www.obliquity.com/skyeye/misc/name.html.

Cite this as:

Weisstein, Eric W. "Point Alrescha." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/PointAlrescha.html

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