A lower bound on the angles of triangles constructed by bisecting the longest side

Authors:
Ivo G. Rosenberg and Frank Stenger

Journal:
Math. Comp. **29** (1975), 390-395

MSC:
Primary 50B15; Secondary 65M10

DOI:
https://doi.org/10.1090/S0025-5718-1975-0375068-5

MathSciNet review:
0375068

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a triangle with vertices at and . The process of "bisecting " is defined as follows. We first locate the longest edge, of where , set , and then define two new triangles, and .

Let be a given triangle, with smallest interior angle . Bisect into two new triangles, . Next, bisect each triangle , to form four new triangles , and so on, to form an infinite sequence *T* of triangles. It is shown that if , and is any interior angle of , then .

**[1]**M. ZLÁMAL, "On some finite element procedures for solving second order boundary value problems,"*Numer. Math.*, v. 14, 1969/70, pp. 42-48. MR**41**#1244. MR**0256588 (41:1244)****[2]**C. HARVEY & F. STENGER, "A two dimensional extension of the method of bisections for solving nonlinear equations,"*Quart. Appl. Math.*(to appear.) MR**0455361 (56:13600)****[3]**J. F. RANDOLPH,*Calculus and Analytic Geometry*, Wadsworth, Belmont, Calif., 1961.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1975-0375068-5

Keywords:
Triangulation,
bisection,
finite element method

Article copyright:
© Copyright 1975
American Mathematical Society