On Sequences of Nested Triangles |
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| Authors: | Dan Ismailescu Jacqueline Jacobs |
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| Affiliation: | (1) Hofstra University, Department of Mathematics, Hempstead, NY 11549, USA;(2) Hofstra University, Department of Mathematics, Hempstead, NY 11549, USA |
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| Abstract: | Summary For a given triangle, we consider several sequences of nested triangles obtained via iterative procedures. We are interested in the limiting behavior of these sequences. We briefly mention the relevant known results and prove that the triangle determined by the feet of the angle bisectors converges in shape towards an equilateral one. This solves a problem raised by Trimble~[5]. |
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| Keywords: | geometric iterations limiting point limiting shape |
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