Mathematical Analysis of Circum-inscribed Polygons: Circum-inscribed (C-I) Trapezium and Right Kite
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| Natura: | Recurso digital |
| Lingua: | inglese |
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Zenodo
2022
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| _version_ | 1866901179242381312 |
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| author | Rajpoot, Harish Chandra |
| author_facet | Rajpoot, Harish Chandra |
| contents | <p>The circumscribed and the inscribed polygons are well known and mathematically well defined in the context of 2D geometry. The term ‘Circum-inscribed Polygon’ has been proposed by the author and used as a new definition of the polygon that satisfies the conditions of a circumscribed polygon and an inscribed polygon together. In other words, the circum-inscribed polygon is a polygon that has both the inscribed and circumscribed circles. The newly defined circum-inscribed polygon has each of its sides touching a circle and each of its vertices lying on another circle. The most common examples of circum-inscribed polygon are triangle, regular polygon, trapezium with each of its non-parallel sides equal to the Arithmetic Mean (AM) of its parallel sides (called circum-inscribed trapezium), and a right kite. This paper describes the new definitions of circum-inscribed (C-I) polygon and the mathematical derivations of the analytic formula to find out the different parameters in terms of AM and GM of known sides, such as radii of circumscribed & inscribed circles, unknown sides, interior angles, diagonals, perimeter, and area of circum-inscribed trapezium and right kite. Like an inscribed polygon, a circum-inscribed polygon always has all of its vertices on an infinite number of spherical surfaces. All the analytic formulae have been derived using simple trigonometry and 2-dimensional geometry, which can be used to analyse the complex 2D and 3D geometric figures such as cyclic quadrilaterals and trapezohedra, and other polyhedra such as trapezohedra/deltohedra.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18056809 |
| institution | Zenodo |
| language | eng |
| publishDate | 2022 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Mathematical Analysis of Circum-inscribed Polygons: Circum-inscribed (C-I) Trapezium and Right Kite Rajpoot, Harish Chandra Mathematics Geometry Circum-inscribed (CI) polygons Circum-inscribed (CI) Trapezium <p>The circumscribed and the inscribed polygons are well known and mathematically well defined in the context of 2D geometry. The term ‘Circum-inscribed Polygon’ has been proposed by the author and used as a new definition of the polygon that satisfies the conditions of a circumscribed polygon and an inscribed polygon together. In other words, the circum-inscribed polygon is a polygon that has both the inscribed and circumscribed circles. The newly defined circum-inscribed polygon has each of its sides touching a circle and each of its vertices lying on another circle. The most common examples of circum-inscribed polygon are triangle, regular polygon, trapezium with each of its non-parallel sides equal to the Arithmetic Mean (AM) of its parallel sides (called circum-inscribed trapezium), and a right kite. This paper describes the new definitions of circum-inscribed (C-I) polygon and the mathematical derivations of the analytic formula to find out the different parameters in terms of AM and GM of known sides, such as radii of circumscribed & inscribed circles, unknown sides, interior angles, diagonals, perimeter, and area of circum-inscribed trapezium and right kite. Like an inscribed polygon, a circum-inscribed polygon always has all of its vertices on an infinite number of spherical surfaces. All the analytic formulae have been derived using simple trigonometry and 2-dimensional geometry, which can be used to analyse the complex 2D and 3D geometric figures such as cyclic quadrilaterals and trapezohedra, and other polyhedra such as trapezohedra/deltohedra.</p> |
| title | Mathematical Analysis of Circum-inscribed Polygons: Circum-inscribed (C-I) Trapezium and Right Kite |
| topic | Mathematics Geometry Circum-inscribed (CI) polygons Circum-inscribed (CI) Trapezium |
| url | https://doi.org/10.5281/zenodo.18056809 |