2010/03/24 by Dimitrios Kodokostas · 1 citation
Computer Science · Mathematics · #Mathematics, Computing, and Information Processing #Mathematics and Applications #Mathematics #Trigonometry #Interval (graph theory) #Perimeter #Trigonometric functions #Line (geometry) #Spherical trigonometry #Equalizer #Mathematical analysis #Geometry #Combinatorics #Computer science #Telecommunications #Channel (broadcasting)
paper · doi:10.4169/002557010x482916
openalex publication_date 2010/03/24 · openalex created_date 2025/10/10 · openalex updated_date 2025/11/06
SummaryA triangle equalizer is a line bisecting both its area and perimeter. We provide a detailed account of equalizer locations, showing that there exist triangles with exactly one, two, or three equalizers, but no more. Triangles with exactly two equalizers are quite rare: Their smallest angle is less or equal to a particular angle of approximately 49 degrees, and the angle next in size is the unique root of a trigonometric equation in a specific interval depending on the smallest angle.