Euclidean geometric description of radial centers of a triangle
Volume 170 / 2022
Colloquium Mathematicum 170 (2022), 275-288
MSC: Primary 51N20; Secondary 51M04, 26B05, 26E99.
DOI: 10.4064/cm8493-12-2021
Published online: 26 May 2022
Abstract
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)].
