## pantograph

A pantograph is a type of linkage that draws enlargements of images. Below are pictures of one I made that enlarges shapes by scale factor 2 (or scale factor 1/2). The kids love playing with it!

Only the point at the bottom left is fixed. All other points are free to move. Moving one of the pencils moves the other one.

To see how it works, consider a line drawn through the fixed point and the two pencils, making a large triangle. The parallelogram in the centre has side lengths half the size of the large triangle. Therefore the large triangle is similar and twice as large as the triangle from the fixed point to the first pencil (on the left). So when you draw an image with the pencil on the right, the pencil on the left makes an image half as big, and vice versa.

There's plenty of maths here. Along with enlargement (including centre of enlargement and fractional scale factors), there are corresponding and alternate angles in action here. You could experiment with different scale factors.

Or perhaps you could make a giant one like Nick Sayers. He showed us his giant pantograph at a conference for maths teachers in Brighton, and then showed us how to make some using only card and a few paper fasteners - see slide show below! He has inspired me to make one with metre rulers and people as hinges - watch this space!

To see how it works, consider a line drawn through the fixed point and the two pencils, making a large triangle. The parallelogram in the centre has side lengths half the size of the large triangle. Therefore the large triangle is similar and twice as large as the triangle from the fixed point to the first pencil (on the left). So when you draw an image with the pencil on the right, the pencil on the left makes an image half as big, and vice versa.

There's plenty of maths here. Along with enlargement (including centre of enlargement and fractional scale factors), there are corresponding and alternate angles in action here. You could experiment with different scale factors.

Or perhaps you could make a giant one like Nick Sayers. He showed us his giant pantograph at a conference for maths teachers in Brighton, and then showed us how to make some using only card and a few paper fasteners - see slide show below! He has inspired me to make one with metre rulers and people as hinges - watch this space!