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Title: | On the Center of Surface Area of the Boundary of a Star-Shaped Region |
Authors: | Theerakarn T. |
Issue Date: | 2023 |
Publisher: | Taylor and Francis Ltd. |
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. |
URI: | https://www.scopus.com/inward/record.uri?eid=2-s2.0-85172765987&doi=10.1080%2f07468342.2023.2240203&partnerID=40&md5=170b7a038b833938944823626a9d979d https://ir.swu.ac.th/jspui/handle/123456789/29473 |
Appears in Collections: | Scopus 2023 |
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