Exploring and Solving Feynman's Triangle Through Multiple Approaches

Abstract

It has long been recognized that using multiple approaches to solve problems is essential for students to obtain understanding of mathematical concepts. In view of this, we consider an interesting plane geometry problem with a straightforward formulation, known as the one-seventh area triangle or Feyman's triangle problem. We present solutions using GeoGebra constructions and manipulation, coordinate geometry, Euclidean geometry and linear algebra. This allows students to apply many of the tools they acquired at the secondary level and to make important and crucial connections between them. The linear algebra section can be used as an introduction to the subject. This section can also reinforce the close relationship between linear algebra and geometry which might not receive enough emphasis at the undergraduate level. GeoGeobra diagrams, constructions and computer algebra are used throughout the paper. All explanations are done through questions and answers which allows instructors to easily format the sections into inquiry-based lessons.