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math.MG2022
The relation between symmetries and coincidence and collinearity of polygon centers and centers of multisets of points in the plane
Luis Felipe Prieto-Martínez
There are several remarkable points, defined for polygons and multisets of points in the plane, called centers (such as the centroid). To make possible their study, there exists a…
math.MG2022
-gon centers and central lines
Marta Farré Puiggalí, Luis Felipe Prieto-Martínez
In this paper we provide a review of the concept of center of a -gon, generalizing the original idea given by C. Kimberling for triangles. We also generalize the concept of cent…
math.MG2022
Circular arcs are the only analytic Jordan curves with an exterior power point
Luis Felipe Prieto-Martínez
In 1946, J. Rosenbaum proposed a family of problems asking how many power points are needed to ensure that the boundary of a given convex body is a disk. In this paper, we use…