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Triangle Centers in the 2D, 3D, Spherical and Hyperbolic

Posted 1 year ago
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At Wolfram Demonstrations, I perused the greater triangle center material that we had, including a new one.

Fate of the Euler Line and the Nine-Point Circle on the Sphere by Paolo Maraner

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Non-Euclidean Triangle Continuum by Robert A. Russell

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Tetrahedron Centers by Ed Pegg Jr

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Also items like Triangle Calculator and Spherical Triangle Solutions, along with many recent submissions by Izidor Hafner. After writing the third demo above, I was surprised to rediscover the second, and astounded by the discussions in the first. In 2D euclidean space, these points in a triangle are known as Kimberling Centers. In 3D euclidean space, spherical geometry and hyperbolic geometry; many of these same points exist, but exact areal coordinates for them are not yet known. It seems like they should be findable, though, with this much interplay.

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Posted 1 month ago

My paper at https://arxiv.org/abs/1608.08190 has non-Euclidean coordinates for many triangle centers.

That's very nice. Thank you for bringing it to my attention.

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