Curvy Areas
Curvy Areas printable sheet
Curvy Areas downloadable slides
Take a look at the image below:
Can you see how the image was created?
Try to recreate it using a ruler and compasses.
Here are two images created in a similar way.
Can you work out the proportion of the 3-colour, 4-colour and 5-colour circles which is shaded red?
Can you make any generalisations?
Can you prove your ideas?
Extension
What about the proportion which is shaded orange? Yellow? ...
Can you make any generalisations?
Can you prove your ideas?
You may also like
Giant Holly Leaf
Find the perimeter and area of a holly leaf that will not lie flat (it has negative curvature with 'circles' having circumference greater than 2πr).
Quadarc
Given a square ABCD of sides 10 cm, and using the corners as centres, construct four quadrants with radius 10 cm each inside the square. The four arcs intersect at P, Q, R and S. Find the area enclosed by PQRS.
Get Cross
A white cross is placed symmetrically in a red disc with the central square of side length sqrt 2 and the arms of the cross of length 1 unit. What is the area of the disc still showing?