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Hofstadter Triangle


For a nonzero real number r and a triangle DeltaABC, swing line segment BC about the vertex B towards vertex A through an angle rB. Call the line along the rotated segment L. Construct a second line L^' by rotating line segment BC about vertex C through an angle rC. Now denote the point of intersection of L and L^' by A(r). Similarly, construct B(r) and C(r). The triangle having these points as vertices is called the Hofstadter r-triangle (Kimberling 1994; 1998, pp. 176-178 and 241-242). For r=1/3, the resulting triangle is the first Morley triangle.

Kimberling (1994) showed that the Hofstadter triangle is perspective to DeltaABC, and calls perspective center the Hofstadter point.


See also

First Morley Triangle, Hofstadter Point

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References

Kimberling, C. "Hofstadter Points." Nieuw Arch. Wisk. 12, 109-114, 1994.Kimberling, C. "Triangle Centers and Central Triangles." Congr. Numer. 129, 1-295, 1998.Kimberling, C. "Hofstadter Points." http://faculty.evansville.edu/ck6/tcenters/recent/hofstad.html.

Referenced on Wolfram|Alpha

Hofstadter Triangle

Cite this as:

Weisstein, Eric W. "Hofstadter Triangle." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HofstadterTriangle.html

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