An Extension of Heron's Formula
Zohreh Shahbazi
TL;DR
This paper extends Heron's formula to approximate the area of cyclic n-gons with a guaranteed maximum error bound of rac{c0}{e}-1, providing a new mathematical tool for polygon area estimation.
Contribution
It introduces a novel extension of Heron's formula applicable to cyclic n-gons with a proven error bound, advancing geometric approximation methods.
Findings
The extended formula accurately estimates cyclic n-gon areas.
Maximum error of the approximation is bounded by rac{c0}{e}-1.
The method applies to polygons with any number of sides.
Abstract
This paper introduces an extension of Heron's formula to approximate area of cyclic n-gons where the error never exceeds
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Taxonomy
TopicsMathematics and Applications · History and Theory of Mathematics · Advanced Mathematical Theories and Applications