Leonardo da Vinci wanted to "square the circle" and solve quadrature problems.
He also wanted to avoid taking square roots and doing tedious computations.
Here is his ingenious method for finding the areas of some curvy shapes.

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The Lune-Easy of

EONARDO da INCI

Leonardo was not very good at arithmetic especially finding square roots. To avoid doing many
tedious calculations (by hand), he devised an ingenious method for finding the areas of
certain curvilinear shapes. He starts with a semi-circle (above, left). By folding down the lune
on the right (in orange), he effectively subtracts that area from the triangle. Then, by moving the
lune on the left over to the empty space, he now has built a simple triangle.

Next, Leonardo uses a related shape, a full circle, to create the pendulum shape in the middle.
He substracts the lunes on the right. Then he moves the two on the left over to create a square.
It's fairly easy to find the area of a square, but not the pendulum shape.

Leonardo de-lunes the ax and ...voila! a square.

More LUNE-EASY problems

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