Abstract
In this paper, we introduce the notion of an elliptical segment as some analogy of the circular segment and we focus on the problem of calculation of its area. Based on the analytical method, we derive the formulas, which can be used for the numerical approximation of the area of the given segment.
Highlights
We present the problem of calculation of the area of elliptical segment
The notion elliptical segment is a generalization of the term circular segment
In accordance with this analogy, we consider the elliptical segment as a set of points surrounded by a given elliptical arc and its chord
Summary
We present the problem of calculation of the area of elliptical segment. The notion elliptical segment is a generalization of the term circular segment. There exist a few formulas about how to calculate the area A of the given circular segment. Their proving is based on the idea of subtraction of the area of the circular sector and the area of the subsistent triangle portion [1]. In this concept, the term central angle is crucial, but it is undefined for the ellipse [2]. The Gauss–Green formula is used to determine an elliptical sector area.
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