A cyclic Kepler quadrilateral & the golden ratio

VILLIERS, MICHAEL DE (2018) A cyclic Kepler quadrilateral & the golden ratio. At Right Angles, 7 (1). pp. 91-94.

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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.

Item Type: Articles in APF Magazines
Uncontrolled Keywords: Dynamic geometry, Kepler triangle, Kepler quadrilateral
Subjects: Natural Sciences > Mathematics
Divisions: Azim Premji University > University publications > At Right Angles
Depositing User: Mr. Sachin Tirlapur
Date Deposited: 15 Sep 2018 07:45
Last Modified: 15 Sep 2018 07:45
URI: http://publications.azimpremjifoundation.org/id/eprint/1328
Publisher URL:

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