MATHEMATICS AND ORIGAMI

Mathematics and Origami

As Ang. EBC = 108, it is: Ang. ABC = 72 ; 180 – Ang. EBC = 72
Therefore, angles ABC and EBC are supplementary.
Fig. 4 adds to Fig. 3 the ∆ABC of Fig. 1, both, seated on the pentagonal face, and revolved
around BC to form ∆A ́BC. Consequently A ́ is the wanted center of homothecy: the vertex of two
pentagonal pyramids having parallel bases. Of course AB = A ́B.

Interlude