Does any convex quadrilateral have circumscribed ellipses?

• Autorzy: Jia Hui Li , Zhuo Qun Wang , Yi Xi Shen , Zhong Yuan Dai
• Języki publikacji: EN

Abstrakty

EN

The past decades have witnessed several well-known beautiful conclusions on four con-cyclic points. With highly promising research value, we profoundly studied circumscribed ellipses of convex quadrilaterals in this paper. Using tools of parallel projective transformation and analytic geometry, we derived several theorems including the proof of the existence of circumscribed ellipses of convex quadrilaterals, the properties of its minimal coverage area, and locus center, respectively. This simple approach lays a solid foundation for its application to three-dimensional situations, which is namely the circumscribed quadric surface of a solid figure and its wide-range utility in construction engineering. Meanwhile, we have a new insight into innate connection of conic sections as well as a taste of beauty and harmony of geometry.

Słowa kluczowe

EN

Convex quadrilateral; Circumscribed ellipse; Parallel projective transformation; Analytical geometry; Conic section

Kategorie tematyczne

• 51M09: Elementary problems in hyperbolic and elliptic geometries
• 51N20: Euclidean analytic geometry
• 51N15: Projective analytic geometry
• 51M05: Euclidean geometries (general) and generalizations
• 51M04: Elementary problems in Euclidean geometries

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2017
• Tom: 15
• Numer: 1
• Strony: 1463-1476

Daty

wydano

2017-01-01

otrzymano

2016-07-18

zaakceptowano

2017-11-02

online

2017-12-16

Twórcy

autor

Jia Hui Li

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autor

Zhuo Qun Wang

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autor

Yi Xi Shen

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autor

Zhong Yuan Dai

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Identyfikatory

DOI

10.1515/math-2017-0117