An Incircle, Circumcircle, Excircle and Apollonius Circle of a Triangle in the Maximum Plane

Authors : Özcan Gelişgen, Aylin Palazoğlu

Pages : 29-45

View : 77 | Download : 559

Publication Date : 2025-12-29

Article Type : Research Paper

Abstract :Classical Euclidean geometry places significant emphasis on circles related to triangles, such as the incircle, circumcircle, excircle, and Apollonius circles. Each of these circles shows important features of the triangle. As new types of geometry were developed, these classic shapes were looked at again in different ways, leading to new mathematical ideas. One of these new geometries is called maximum plane geometry, which uses a different way to measure distances. In this geometry, circles take the form of axes-aligned squares. This creates both similarities and differences compared to circles in regular Euclidean geometry. This paper investigates the existence and uniqueness of these types of circles in maximum plane geometry and analyzes their properties. By clearly defining them and looking at their effects, the paper tries to build on old results, show how they are different, and find uses in areas like computational geometry and discrete mathematics.
Keywords : Maksimum düzlem, maksimum iç teğet çember, maksimum çevrel çember, maksimum dış teğet çember, maksimum Apollonius çember

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