Tangent Circles on the Plane Using Variable Compass
Publication: Journal of Architectural Engineering
Volume 23, Issue 2
Abstract
The present study analyzes how to trace a circle packing using a variable compass. Several of these circle packings have been used by artisans and designers to make ornamental patterns in architecture and arts. The present paper begins by analyzing tangent circles between secant straight lines based on the Archimedes theorem and then studies other ways to trace tangent circles between secant straight lines, showing how craftsmen applied this knowledge to their artistic or architectural creations. Packing circles with different diameters has led to analyzing various geometric constructions used to design Gothic rosettes and is how craftsmen were forced to face new geometric and mathematical problems, such as the Apollonius problem. Geometric constructions of rosettes led to the knowledge and design of different spiral patterns, which involved a new relationship with mathematicians. Similar to a previous study, this paper is limited to geometric constructions developed on the plane, leaving three-dimensional analysis for further study.
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Acknowledgments
The author especially thanks Antonio Casas for support in multiple issues on geometry and mathematics and Manuela Arzola for the revision of the translation of this manuscript.
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Information & Authors
Information
Published In
Journal of Architectural Engineering
Volume 23 • Issue 2 • June 2017
Copyright
© 2017 American Society of Civil Engineers.
History
Received: Feb 10, 2016
Accepted: Sep 12, 2016
Published online: Jan 19, 2017
Published in print: Jun 1, 2017
Discussion open until: Jun 19, 2017
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