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Euclidean geometric description of radial centers of a triangle

Volume 170 / 2022

Shigehiro Sakata Colloquium Mathematicum 170 (2022), 275-288 MSC: Primary 51N20; Secondary 51M04, 26B05, 26E99. DOI: 10.4064/cm8493-12-2021 Published online: 26 May 2022


We consider the convolution of a radially symmetric function and the characteristic function of a triangle. We describe the location of a critical point of the convolution in the Euclidean geometric manner. The description slightly shortens the proof of the analytic characterizations of equilateral triangles shown in [S. Sakata, Ann. Mat. Pura Appl. 200 (2021)].


  • Shigehiro SakataDepartment of Applied Mathematics
    Fukuoka University
    8-19-1 Nanakuma, Jonan
    814-0180 Fukuoka, Japan

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