EUREKA! PYTHAGOREAN TRIPLES FROM THE MULTIPLICATION TABLE

It is important that teachers of mathematics encourage open, imaginative investigations that give students an opportunity to probe, find patterns and relations, and derive new patterns and relations from others. Activities of this kind foster analytic and creative thinking, and so they involve students in problem solving of the highest order. They also generate enthusiasm. stimulate interest, and can give considerable insight into the nature and the underlying unity and beauty of mathematics.