Archimedes was an ancient Greek mathematician and physicist known for his work in geometry, calculus, and fluid mechanics. He laid the groundwork for integral calculus through his method of exhaustion.
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Archimedes introduced the method of exhaustion to find areas under curves, which is a precursor to integral calculus.
He calculated the area of a circle by inscribing polygons within it and increasing the number of sides.
Archimedes' principle involves the concept of buoyancy, stating that an object submerged in fluid experiences an upward force equal to the weight of the fluid displaced.
His work on approximating pi involved using polygons with many sides to get closer to the true value.
The Archimedean property states that for any two positive numbers, there exists a multiple of one that exceeds the other.
Review Questions
What mathematical technique did Archimedes use that is considered a precursor to integral calculus?
How did Archimedes approximate the value of pi?
Explain Archimedes' principle related to buoyancy.
Related terms
Method of Exhaustion: An ancient mathematical technique used by Archimedes to find areas and volumes by inscribing shapes within shapes.
Integral Calculus: A branch of calculus focused on finding areas under curves and accumulation functions.
\$\pi\$ (Pi): The ratio of a circle's circumference to its diameter, approximately equal to 3.14159; used extensively in geometry and calculus.