Making a Strip of Isosceles Trapezoids

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Suppose the angle measures . The line bisects , so . The line bisects , so triangle is isosceles and is congruent to , which measures . Then and . So the angles converge to . In this way the trapezoids converge to an isosceles trapezoid congruent to the trapezoid consisting of three sides and of a diagonal of a regular pentagon. Isosceles trapezoids are obtained immediately when . Otherwise, the isosceles condition is approached as the number of repeats, . Visually, however, the result appears to be satisfied with . Use the bottom scroll bar to view extended regions of the diagram.

Contributed by: Izidor Hafner (January 2016)
Open content licensed under CC BY-NC-SA


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Reference

[1] P. Hilton and J. Pedersen, Build Your Own Polyhedra, Boston: Addison-Wesley, 1994, pp. 18–23.



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