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- Title
Chess Billiards.
- Authors
Nogueira, Arnaldo; Troubetzkoy, Serge
- Abstract
These results also hold with HT <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi> </mi><mn>1</mn></msub></math> ht and HT <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi> </mi><mn>2</mn></msub></math> ht interchanged. To see this, we think of HT <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi> </mi><mn>1</mn></msub></math> ht and HT <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi> </mi><mn>2</mn></msub></math> ht as oriented directions. The sides of I P i divide the set of directions into open sectors HT <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>C</mi><mi>i</mi></msub></math> ht . Each line intersects the boundary HT <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi> </mi><mi>P</mi></mrow></math> ht in either no point, one point, two points, or a segment.
- Subjects
BILLIARDS; SYMMETRIC domains; CHESS; IRRATIONAL numbers; ARC length; CIRCLE; TRIANGLES
- Publication
Mathematical Intelligencer, 2022, Vol 44, Issue 4, p331
- ISSN
0343-6993
- Publication type
Article
- DOI
10.1007/s00283-021-10150-1