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Only three of his treatises on plane geometry have survived, these are; Measurement of a Circle, Quadrature of a Parabola, and On the Sphere and Cylinder. In his book Measurement of a Circle Archimedes shows that the ratio between the circumference of a circle and its diameter can be calculated as he calls it the method for calculating Pi. He correctly determined that the value of Pi is somewhere between 3.1408 and 3.1428. Along the same plane he determined that a circle's area could be determined by using the formula PI( r^2 ).
In the book On the Sphere and Cylinder Archimedes dealt with the topic of solid geometry contains several famous discoveries, including his theory that the volume of a sphere is equal to 4/3Pi( r^3)...
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