Arithmetic Polygons and Sums of Consecutive Squares
Abstract
We introduce and study arithmetic polygons. We show that these arithmetic polygons are connected to triples of square pyramidal numbers. For every odd N≥3, we prove that there is at least one arithmetic polygon with N sides. We also show that there are infinitely many arithmetic polygons with an even number of sides.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.