Archimedes
Mathematical Genius
The ancient Greek mathematician who anticipated calculus, calculated π, and revolutionized geometry
Calculation of π (Pi)
Archimedes developed an ingenious method to approximate π by calculating the perimeters of inscribed and circumscribed polygons around a circle. Using a 96-sided polygon, he proved that:
His approximation of 3.1418 was the most accurate for nearly 1,000 years. This method established the foundation for later developments in calculus.
Geometric Breakthroughs
Archimedes made profound discoveries about spheres, cylinders, and other geometric shapes. In his work "On the Sphere and Cylinder," he proved that:
He demonstrated that the volume and surface area of a sphere are exactly two-thirds that of the circumscribed cylinder. These were among the most sophisticated results in ancient mathematics.
Anticipation of Calculus
Archimedes' "Method of Exhaustion" was a precursor to modern integral calculus. He used it to:
• Calculate the area under a parabola
• Find the volume of a sphere
• Determine the center of gravity of various shapes
His work contained concepts that wouldn't be formalized until Newton and Leibniz 18 centuries later.
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