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Locus problems concerning centroids of a cyclic quadrilateral and two classic cubic curves
Published online by Cambridge University Press: 22 June 2022
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On his website dedicated to questions and investigations arising out of dynamic geometry technology, Michael de Villiers has a series called Geometry Loci Doodling [1]. These are locus problems connected to the centroids of cyclic quadrilaterals – ‘centroids’ in the plural, for there are three different kinds of centroid depending whether one understands the quadrilateral in terms of its vertices, perimeter or area. The corresponding centroids are the point-mass centroid, the perimeter-centroid, and the lamina-centroid. In each case, de Villiers keeps three vertices of the quadrilateral fixed on the circumcircle, and then traces the locus of the different centroids as the fourth point moves round the circle. In this paper, I shall take a brief look at the point-mass centroid and then a lingering view of the lamina-centroid.
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This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/) which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.- Copyright
- © The Authors, 2022 Published by Cambridge University Press on behalf of The Mathematical Association
References
de Villiers, Michael, Geometry Loci Doodling, accessed December 2021 at http://dynamicmathematicslearning.com/geometry-loci-doodling.html
Google Scholar
Yaglom, I. M., Geometric transformations (vol.2), translated by Shields, Allen, House, Random (1968).Google Scholar
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