don steward
mathematics teaching 10 ~ 16

Tuesday, 1 March 2011

circle and parts of circle packing

a ppt is here

this is based on an OCR, GCSE question:

in a similar vein:


this is from 'mental gymnastics' by dick hess

this is from an article by DP Eperson [in Mathematics in School, January 1992]

a square has touching circles, semicircles, quadrants drawn inside them:

intended to be practice in calculating areas of circles and bits of circles
[although several of the designs can be viewed as a scaling up, or down, of a part of another diagram]

this is from a John Mason session:

not needed to find the answer of this problem (by using the carpet's theorem)
but solutions to how to find the area of overlap are found here

this next question requires an understanding of similar triangles:
[from a problem by Peter Grabarchuk here]

this is one of Paul Lockhart's problems (in 'measurement')
I think pythagoras is needed
the orange area is slightly bigger than the circle radius R

tan (22.5) =
(square root 2) - 1

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