Running the machines backwards
So far the area was the answer. Now it's a GIVEN, and a side is hiding. Working backwards is division: a rectangle's width is ; a triangle's height is , the ½ un-halving into a 2 on top, exactly as last lesson promised.
Circles add one more move. reversed gives — r equals the square root of A over pi: divide the away first, then un-square with the root. Dividing by leaves , and is not yet — stopping there is this lesson's favourite trap. The draws are kind: every root lands on a perfect square.
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