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The proof in question proceeds by dissecting the square of side a+b in two different ways. In the first way, the square is broken into four right triangles, congruent to the given one, and two squares of sides a and b respectively. The second dissection breaks the square of side a+b into four right triangles, congruent to the given one, and one square of side c.

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Tangrams are a 4000 year old activity that allows you to cut a square piece of paper into various shapes, and reform them into images.

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You can dissect shapes into smaller pieces in order to make the architecture visually appealing as well as intricate.

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In geometry, a dissection problem is the problem of partitioning a geometric figure (such as a polytope or ball) into smaller pieces that may be rearranged into a new figure of equal content.

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Dissection can be seen in art, especially in cubism.

"Weeping Woman" by Pablo Picasso

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Any rectilinear objects with the same area can be cut up and then be reshaped to form each other.