# Pythagoras' theorem in engineering

A collection of resources to provide ideas for setting Pythagoras' theorem in the context of engineering, together with materials to support teaching of the topic.

**'Tunnelworks'** links mathematics and science to the Thames Tideway Tunnel project. There are two lessons, both of which have Pythagoras' theorem as their primary focus, but also involve work on gradients, units, grid references, and scale drawings.

**'Well placement between villages' **looks at the optimal placement of wells in a semi-dessert area. Pythagoras' theorem is used along with work on constructions.

**'****Circles with Whole Number Points'** provides an extension activity to support embedding Pythagoras' theorem, linking it with the equation of a circle. The **'Pythagoras' Theorem' **resource has enrichment activities and probing questions.

### Tunnelworks: Key Stage Three Mathematics

Tunnelworks is a series of resources linking mathematics and science to the Thames Tideway Tunnel project. Lesson one explores right-angled triangles and Pythagoras’ Theorem using simplified engineering drawings. Lesson two explores co-ordinates and uses Pythagoras' Theorem to calculate distances.

### Well placement between villages

This resource asks students to use Pythagoras' Theorem and geometric constructions to find the optimal place for a water well. The resource includes a presentation that introduces the task and a series of questions for students to explore.

### Circles with Whole Number Points

This resource investigates equations of a circle and Pythagoras’ theorem. The task makes use of Geogebra and involves finding the integer coordinates through which a given circle passes.

### Pythagoras' Theorem

This resource consists of 23 instant maths ideas, ideal for use as starter questions, extension questions or probing questions to assess understanding. Ideas include investigating tilted squares, a proof of the theorem, families of Pythagorean triples, and square pegs fitting in round holes.