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- Title
Exploring the Dynamics of the Circumcenter Map.
- Authors
McDonald, Nicholas; Garcia, Ronaldo; Reznik, Dan
- Abstract
Let HT <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mrow><mi mathvariant="script">M</mi></mrow><mi>k</mi></msup></math> ht denote I k i successive applications of the Miquel map. As shown above, HT <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="script">R</mi><mn>3</mn></msub></math> ht is similar to HT <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="script">R</mi></math> ht . The circumcenter map can be generalized to the HT <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>X</mi><mi>k</mi></msub></math> ht -map, where HT <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>X</mi><mi>k</mi></msub></math> ht is some triangle center (see [[3]]). A question not addressed here is whether a certain HT <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>X</mi><mi>k</mi></msub></math> ht -map is integrable in the sense of [[1], [5]].
- Subjects
TRIANGLES; SPHERICAL projection; PLANE curves
- Publication
Mathematical Intelligencer, 2023, Vol 45, Issue 3, p232
- ISSN
0343-6993
- Publication type
Article
- DOI
10.1007/s00283-022-10223-9