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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

On the bisection method for triangles


Author: Andrew Adler
Journal: Math. Comp. 40 (1983), 571-574
MSC: Primary 51M15; Secondary 51M20, 65L50, 65N50
MathSciNet review: 689473
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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

DOI: http://dx.doi.org/10.1090/S0025-5718-1983-0689473-5
PII: S 0025-5718(1983)0689473-5
Article copyright: © Copyright 1983 American Mathematical Society