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

Full-text PDF Free Access

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]**Miloš Zlámal,*On some finite element procedures for solving second order boundary value problems*, Numer. Math.**14**(1969/1970), 42–48. MR**0256588****[2]**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****[3]**J. F. RANDOLPH,*Calculus and Analytic Geometry*, Wadsworth, Belmont, Calif., 1961.

Retrieve articles in *Mathematics of Computation*
with MSC:
50B15,
65M10

Retrieve articles in all journals with MSC: 50B15, 65M10

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