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.
Show health and safety information
Please be aware that resources have been published on the website in the form that they were originally supplied. This means that procedures reflect general practice and standards applicable at the time resources were produced and cannot be assumed to be acceptable today. Website users are fully responsible for ensuring that any activity, including practical work, which they carry out is in accordance with current regulations related to health and safety and that an appropriate risk assessment has been carried out.