Counting Triples, Triangles, and Acute Triangles

Activities involving counting triples, triangles, and acute triangles enrich the curriculum with excursions into modular arithmetic, the greatest-integer function, and summation notation. In addition, more advanced students can apply difference-equation techniques to find closed forms and can use mathematical induction to prove the formulas. Students may be learning about these topics for the first time, or they may be reviewing familiar ideas in different problem-solving contexts. In either situation, personal arsenals of problem-attacking skills are strengthened.