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Constructing the Analytic Solution of Fuss Relation of Bicentric Pentagon Based on Projective Mapping
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A bicentric polygon is a polygon that possesses both a circumscribed circle and an incircle. Constructing bicentric pentagons remains a challenging problem. This paper presents a novel geometric discovery that establishes a constructive link between two classical families of polygons: bicentric polygons and polygons inscribed in a parabola while tangent to an incircle. Based on this theory, the solution of the Fuss relation of a bicentric pentagon can be expressed in a parametric form, which provides an effective method for constructing bicentric pentagons.
Title: Constructing the Analytic Solution of Fuss Relation of Bicentric Pentagon Based on Projective Mapping
Description:
A bicentric polygon is a polygon that possesses both a circumscribed circle and an incircle.
Constructing bicentric pentagons remains a challenging problem.
This paper presents a novel geometric discovery that establishes a constructive link between two classical families of polygons: bicentric polygons and polygons inscribed in a parabola while tangent to an incircle.
Based on this theory, the solution of the Fuss relation of a bicentric pentagon can be expressed in a parametric form, which provides an effective method for constructing bicentric pentagons.
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