Cut a cake 1/5

Visually cut a cake 1/5 portions of equal size:

1) divide into half:

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2) divide 1/5 of the right half:

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3) divide half, obtain 1/5 = right of (3)

\frac{1}{5}= \frac{1}{2} (\frac{1}{2}(1- \frac{1}{5}))= \frac{1}{2} (\frac{1}{2} (\frac{4}{5}))=\frac{1}{2}(\frac{2}{5})

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4) By symmetry another 1/5 at (2)=(4)

20130513-174541.jpg

5) divide left into 3 portions, each 1/5

\frac{1}{5}= \frac{1}{3}(\frac{1}{2}+ \frac{1}{2}.\frac{1}{5}) = \frac{1}{3}.\frac{6}{10}

20130513-174742.jpg

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