Topics on Pedal Polygons
Chia-An Hsu, Hsin-Chuang Chou, Chen-Rui Liu, Chih-Hsuan Liang, Yu-Wei, Chang
TL;DR
This paper explores properties of pedal polygons, including a new proof of pedal centers' existence, an invariance property related to polygon areas, and conditions for a polygon to be a pedal of another.
Contribution
It introduces a novel proof for pedal centers' existence and uncovers area invariance and characterization conditions for pedal polygons.
Findings
New proof of pedal centers' existence
Area sum invariance under rotation
Conditions for a polygon to be a pedal polygon
Abstract
In this paper, we study several topics on pedal polygons. First, we prove the existence for pedal centers of triangles in a new way. From its proof, we find that the sum of area of outer and inner polygons is invariant under rotation. Finally, we investigate when a polygon will be a pedal polygon of another one.
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Taxonomy
TopicsMathematics and Applications · History and Theory of Mathematics · Advanced Materials and Mechanics