VILLIERS, MICHAEL DE
(2018)
A cyclic Kepler quadrilateral & the golden ratio.
At Right Angles, 7 (1).
pp. 9194.
Abstract
Proceeding to construct such a ‘Kepler quadrilateral’ ABCD with sides in geometric progression as
indicated by the first figure in Figure 1 produces a flexible quadrilateral with a changing shape. No
interesting, invariant properties seemed immediately apparent. However, if ABCD is dragged so that the
perpendicular bisectors of the sides become concurrent (i.e., so that it becomes cyclic), as indicated by the
second figure in Figure 1, it was observed as shown by measurements that not only did it seem that
diagonal AC appeared to be bisected by diagonal BD, but also that DG : AG = φ.
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