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Puzzle 57.  DISSECTING A SQUARE

Cut the square below into 4 smaller pieces and rearrange them into 2 smaller squares, each having half the area of the original square.

 

 

 

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Bits and Beyond...

ARCHIMEDES

Archimedes (298-212 B.C.) was a great mathematician of the ancient times.  He was a native of Syracuse, Sicily.   He spent some time in Egypt, where he invented a mechanical water pump, now called Archimedes' screw.  His greatest contributions were in the field of geometry.  In his work, Measurement of the Circle, he approximated the value of pi by inscribing and circumscribing a circle with a 96-sided regular polygon.  Archimedes made many contributions to geometry with his work on the areas and volumes of plane figures and curved surfaces.  His methods provided the framework for calculus, which was introduced later by Sir Isaac Newton.  Archimedes showed that the volume of an inscribed sphere is two-thirds the volume of the cylinder circumscribing it.  He requested that this formula and the corresponding diagram be inscribed on his tomb.  Some of his known works include:  The Measurement of a Circle, On the Sphere and Cylinder, On Spirals, and The Sand Reckoner.

 

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