HYPERBOLIC AND SPHERICAL POWER OF A CIRCLE

Young Wook Kim; Sung Eun Koh; Hyung Yong Lee; Heayong Shin; Seong Deog Yang

doi:10.4134/BKMS.b220246

HYPERBOLIC AND SPHERICAL POWER OF A CIRCLE

Young Wook Kim, Sung Eun Koh, Hyung Yong Lee, Heayong Shin, Seong Deog Yang

Research output: Contribution to journal › Article › peer-review

Abstract

Suppose that a line passing through a given point P intersects a given circle C at Q and R in the Euclidean plane. It is well known that |P Q||P R| is independent of the choice of the line as long as the line meets the circle at two points. It is also known that similar properties hold in the 2-sphere and in the hyperbolic plane. New proofs for the similar properties in the 2-sphere and in the hyperbolic plane are given.

Original language	English
Pages (from-to)	507-514
Number of pages	8
Journal	Bulletin of the Korean Mathematical Society
Volume	60
Issue number	2
DOIs	https://doi.org/10.4134/BKMS.b220246
Publication status	Published - 2023 Mar

Bibliographical note

Funding Information:
Received April 7, 2022; Revised June 17, 2022; Accepted June 21, 2022. 2000 Mathematics Subject Classification. 53A35. Key words and phrases. Power of a circle, hyperbolic plane, sphere, conformal metric. Heayong Shin was supported by NRF 2014R1A2A2A01007324, Sung-Eun Koh by NRF 2020R1A2C1A01003666 and Seong-Deog Yang by NRF 2012-042530.

Publisher Copyright:
© 2023 Korean Mathematical Society.

Keywords

conformal metric
hyperbolic plane
Power of a circle
sphere

ASJC Scopus subject areas

General Mathematics

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10.4134/BKMS.b220246

Cite this

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title = "HYPERBOLIC AND SPHERICAL POWER OF A CIRCLE",

abstract = "Suppose that a line passing through a given point P intersects a given circle C at Q and R in the Euclidean plane. It is well known that |P Q||P R| is independent of the choice of the line as long as the line meets the circle at two points. It is also known that similar properties hold in the 2-sphere and in the hyperbolic plane. New proofs for the similar properties in the 2-sphere and in the hyperbolic plane are given.",

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note = "Funding Information: Received April 7, 2022; Revised June 17, 2022; Accepted June 21, 2022. 2000 Mathematics Subject Classification. 53A35. Key words and phrases. Power of a circle, hyperbolic plane, sphere, conformal metric. Heayong Shin was supported by NRF 2014R1A2A2A01007324, Sung-Eun Koh by NRF 2020R1A2C1A01003666 and Seong-Deog Yang by NRF 2012-042530. Publisher Copyright: {\textcopyright} 2023 Korean Mathematical Society.",

year = "2023",

month = mar,

doi = "10.4134/BKMS.b220246",

language = "English",

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AU - Kim, Young Wook

AU - Koh, Sung Eun

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AU - Shin, Heayong

AU - Yang, Seong Deog

N1 - Funding Information: Received April 7, 2022; Revised June 17, 2022; Accepted June 21, 2022. 2000 Mathematics Subject Classification. 53A35. Key words and phrases. Power of a circle, hyperbolic plane, sphere, conformal metric. Heayong Shin was supported by NRF 2014R1A2A2A01007324, Sung-Eun Koh by NRF 2020R1A2C1A01003666 and Seong-Deog Yang by NRF 2012-042530. Publisher Copyright: © 2023 Korean Mathematical Society.

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N2 - Suppose that a line passing through a given point P intersects a given circle C at Q and R in the Euclidean plane. It is well known that |P Q||P R| is independent of the choice of the line as long as the line meets the circle at two points. It is also known that similar properties hold in the 2-sphere and in the hyperbolic plane. New proofs for the similar properties in the 2-sphere and in the hyperbolic plane are given.

AB - Suppose that a line passing through a given point P intersects a given circle C at Q and R in the Euclidean plane. It is well known that |P Q||P R| is independent of the choice of the line as long as the line meets the circle at two points. It is also known that similar properties hold in the 2-sphere and in the hyperbolic plane. New proofs for the similar properties in the 2-sphere and in the hyperbolic plane are given.

KW - conformal metric

KW - hyperbolic plane

KW - Power of a circle

KW - sphere

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DO - 10.4134/BKMS.b220246

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JF - Bulletin of the Korean Mathematical Society

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ER -

HYPERBOLIC AND SPHERICAL POWER OF A CIRCLE

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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