Abstract
The bisection method is the consecutive bisection of a triangle by the median of the longest side. This paper introduces a taxonomy of triangles that precisely captures the behavior of the bisection method. Our main result is an asymptotic upper bound for the number of similarity classes of triangles generated on a mesh obtained by iterative bisection, which previously was known only to be finite. We also prove that the number of directions on the plane given by the sides of the triangles generated is finite. Additionally, we give purely geometric and intuitive proofs of classical results for the bisection method.
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© 2004 Springer-Verlag Berlin Heidelberg
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Gutierrez, C., Gutierrez, F., Rivara, MC. (2004). A Geometric Approach to the Bisection Method. In: Farach-Colton, M. (eds) LATIN 2004: Theoretical Informatics. LATIN 2004. Lecture Notes in Computer Science, vol 2976. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24698-5_21
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DOI: https://doi.org/10.1007/978-3-540-24698-5_21
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-21258-4
Online ISBN: 978-3-540-24698-5
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