Extremal problems on triangle areas in two and three dimensions
Adrian Dumitrescu, Micha Sharir, Csaba D. Tóth · 2008
The study of extremal problems on triangle areas was initiated in a series of papers by Erdös and Purdy in the early 1970s. Here we present new results on such problems, concerning the number of triangles of the same area that are spanned by finite point sets in the plane and in 3-space, and the number of distinct areas determined by the triangles.