Delving Deeper: Triangulating Polygonal Numbers

Abstract

Like touring an old city, exploring classical topics from school mathematics allows us to make discoveries and enjoy knowing that other like-minded travelers have been in the same place before. There are few better areas for rediscovering formerly well-traveled mathematical pathways than the roads opened up by polygonal numbers. Polygonal numbers were revered by the Pythagoreans, were studied thoroughly by Euler, and are used as motivating examples in many contemporary textbooks. Despite their long history and frequent mention, our guidebooks—the student texts—leave 20016out many of their interesting features, making them an ideal area for mathematical tourism.