Triangles in a Spiral

This activity is based upon a practical task to fit a set of similar triangles into a spiral. It is in two parts, the first of which is more accessible.

In Part 1 students are presented with a series of different sized similar triangles. These fit together to form a spiral and students look at how many are needed to make one complete turn.

Students are asked to investigate other sets of similar triangles which also make a complete turn when fitted together in a spiral. Some understanding of scale factor of enlargement is required but the main focus of the investigation is about angles at a point.

The second part of this activity is much more challenging. Students need to be able to find the nth term of various sequences as they investigate the length of the spirals and the area of the series of triangles. An understanding of indices, surds and Pythagoras' Theorem is needed. Students are encouraged to pose their own questions and this may lead to the use of trigonometry.

This resource has student handouts and teachers' notes with answers. It is part of the Churchill Maths Activities collection.