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
MathSciNet review: 0375068
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 .
-  Miloš Zlámal, On some finite element procedures for solving second order boundary value problems, Numer. Math. 14 (1969/1970), 42–48. MR 0256588, https://doi.org/10.1007/BF02165098
-  Charles Harvey and Frank Stenger, A two-dimensional analogue to the method of bisections for solving nonlinear equations, Quart. Appl. Math. 33 (1975/76), no. 4, 351–368. MR 0455361, https://doi.org/10.1090/S0033-569X-1976-0455361-7
-  J. F. RANDOLPH, Calculus and Analytic Geometry, Wadsworth, Belmont, Calif., 1961.
- 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)
- 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)
- J. F. RANDOLPH, Calculus and Analytic Geometry, Wadsworth, Belmont, Calif., 1961.
Keywords: Triangulation, bisection, finite element method
Article copyright: © Copyright 1975 American Mathematical Society