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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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On the bisection method for triangles
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by Andrew Adler PDF
Math. Comp. 40 (1983), 571-574 Request permission

Abstract:

Let UVW be a triangle with vertices U, V, and W. It is "bisected" as follows: choose a longest edge (say VW) of UVW, and let A be the midpoint of VW. The UVW gives birth to two daughter triangles UVA and UWA. Continue this bisection process forever. We prove that the infinite family of triangles so obtained falls into finitely many similarity classes, and we obtain sharp estimates for the longest jth generation edge.
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Additional Information
  • © Copyright 1983 American Mathematical Society
  • Journal: Math. Comp. 40 (1983), 571-574
  • MSC: Primary 51M15; Secondary 51M20, 65L50, 65N50
  • DOI: https://doi.org/10.1090/S0025-5718-1983-0689473-5
  • MathSciNet review: 689473