The theorem of Pythagoras

Pythagoras's theorem has made an immense contribution to mathematics. It gives us a simple relationship between the lengths of any right angled triangle. This has many important applications, such as in navigation in 2-D, where the theorem can be used to find the shortest distance between two lengths. This can be used by painters to calculate the length of ladder needed against a wall or to calculate the side lengths of a TV (where the screen size is always given as a diagonal length). Pythagoras's theorem can be extended into the sine and cosine rules in trigonometry and to find if a triangle is right angled or not. In construction and design the Pythagorean theorem is fundamental.

In this activity we explore Pythagoras's theorem through drawing with Mathomat. Doing this, while working algebraically using the theorem as a number scheme in our heads, builds confidence and understanding of this fundamental theorem in mathematics. It's also fun to do! Michelle Du Toit explores how the squares on the sides of a right triangle drawn using Mathomat can be decomposed into triangles.

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