322 Answers- THE CRESCENT AND THE STAR
Though we cannot square a circle, certain portions of a circle may be
squared, as Hippocrates first discovered. If we draw the circle in the diagram
and then, with the point of the compasses at E, draw the arc BA, the area ofAc
B
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, •the lune or crescent is exactly the same as the area of the triangle ABE. As we
know the line AB to be 12 in., the area of the triangle (and therefore of the
crescent) is obviously 36 sq. in. Also, as the triangle D is known to contain
3 sq. in., the star, which is built up of twelve such triangles, contains 36 sq. in.
Therefore the areas of the crescent and the star were exactly the same.
- THE PATCHWORK QUILT
Except for my warning the reader might have supposed that the dark zig-
zag line from A to B would solve the puzzle. But it will not, because the pieces
are not of the same size and shape. It would be all right if we could go along
the dotted line D instead of C, but that would mean cutting a piece. We must
cut out all the shaded portion in one piece, which will exactly match the other.