Publication:
On the Center of Surface Area of the Boundary of a Star-Shaped Region

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Issued Date

2023

Resource Type

Article

File Type

application/pdf

DOI

10.1080/07468342.2023.2240203

Rights Holder(s)

Scopus

Bibliographic Citation

College Mathematics Journal. Vol 54, No.4 (2023), p.326-336

Suggested Citation

Theerakarn T. On the Center of Surface Area of the Boundary of a Star-Shaped Region. College Mathematics Journal. Vol 54, No.4 (2023), p.326-336. doi:10.1080/07468342.2023.2240203 Retrieved from: https://hdl.handle.net/20.500.14740/10717

Title

On the Center of Surface Area of the Boundary of a Star-Shaped Region

Author(s)

Theerakarn T.

Other Contributor(s)

Srinakharinwirot University

Abstract

Every line passing through the center of a circular disk bisects its area. Not every planar region has a point with this property. It turns out that if a compact connected region is star-shaped at its center of area, then it must be centrally symmetric. However, there exists a non-centrally symmetric star-shaped region whose boundary has a center of length, which is a point where every line passing through this point cut its length in half. In this article, we characterize such regions and provide a method to create them. Additionally, we provide new examples and a method to generate analogous objects in higher dimensions. © 2023, THE MATHEMATICAL ASSOCIATION OF AMERICA.

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URI

https://hdl.handle.net/20.500.14740/10717

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Scopus: Year 2023

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