Problem

Describe this image to someone who cannot see it. What information do you need to provide in order for them to accurately reconstruct it?

Four sectors of radius 1, 2, 4 and 8, and angle 45 degrees centred on the origin to create a 'spiral'

Assuming the four sectors are of equal angle, calculate the arc length and area of each sector.

What do you notice?


What features of the original image are preserved if it is adapted to create each of these?

Four sectors of radius 1, 2, 4 and 8, and angle 90 degrees centred on the origin to create a 'spiral'
Four unequal sectors of radius 1, 2, 4 and 8, centred on the origin to create a 'spiral

What can you say about the arc length and area of each sector in each case?