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Ein ungewöhnlicher Weg zu Jakob Steiners Umellipse eines Dreiecks und zur Steiner–Hypozykloide
Published:
2004-06-01
https://doi.org/10.5485/TMCS.2004.0039
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Keywords
projective geometry of triangles plane cubics circumscribed Steiner ellipse about a triangle Steiners hypocycloid
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Copyright (c) 2004 Oswald Giering
This work is licensed under a Creative Commons Attribution 4.0 International License.
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Oswald. (2004). Ein ungewöhnlicher Weg zu Jakob Steiners Umellipse eines Dreiecks und zur Steiner–Hypozykloide. Teaching Mathematics and Computer Science, 2(1), 49-65. https://doi.org/10.5485/TMCS.2004.0039
Abstract
In real projective geometry of triangles two problems of collinear points are discussed. The problems differ only from the running through the vertices of a given triangle ABC. Resolving the problems we find two cubic curves kS and kT . Affine specialization leads to the circumscribed Steiner ellipse about the triangle ABC and shows us this ellipse in more general surroundings. Euclidean specialization leads to Steiners three-cusped hypocycloid.