median
don steward
mathematics teaching 10 ~ 16

Monday, 13 February 2012

semicircles in a square

this puzzle by Peter Grabarchuk appears on the 'Mathsisfun' website as 'double hearts ratio'



a square with semicircles

which area is larger

the purple

the gold yellow







this could be posed with a grid as a simple 'area of a circle' question
inviting students to make an initial estimate of which looks larger


















however it is more challenging to pose the problem without a grid
various relationships are not too difficult to establish




what is the relationship between
R and r?











then the areas (in the right angled triangle version) are:

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