What did Archimedes discover?

Archimedes found that the volume of a sphere is two-thirds the volume of a cylinder that encloses it. He also discovered a law of buoyancy, Archimedes’ principle, that says a body in a fluid is acted on by an upward force equal to the weight of the fluid that the body displaces.

How far did Archimedes calculate pi?

He went from a 6-sided polygon, to a 12-sided polygon, to a 24-sided polygon, to a 48-sided polygon, and ended up with a 96-sided polygon. This final estimate gave a range for π between 3.1408 and 3.1428, which is accurate to two places.

What shape did Archimedes find pi?

Archimedes computed upper and lower bounds of π by drawing a regular hexagon inside and outside a circle, and successively doubling the number of sides until he reached a 96-sided regular polygon. By calculating the perimeters of these polygons, he proved that 22371 < π < 227 (that is 3.1408 < π < 3.1429).

How did Archimedes come up with Pi?

Mathematics. Archimedes is credited to have estimated the value of pi, a factor used in calculating the area of circles and volume of spheres and cylinders. He was able to prove that the area of a circle is actually equal to pi multiplied by the square of the circle’s radius.

How did Archimedes prove his theory?

Archimedes. Archimedes came upon the solution on how to prove this as he was taking a bath. Upon entering a full tub of water, he noticed that the weight of his body displaced a certain amount of water. Knowing that this same principle could be used on the crown, he forgot himself with excitement.

What shape did Archimedes use to approximate pi?

Archimedes’ method finds an approximation of pi by determining the length of the perimeter of a polygon inscribed within a circle (which is less than the circumference of the circle) and the perimeter of a polygon circumscribed outside a circle (which is greater than the circumference).

What did Archimedes use to approximately Pi?

Archimedes used the method of exhaustion to approximate the value of pi. He did this by drawing a larger regular polygon outside of a circle and a smaller regular polygon inside the circle. Doubling the number of sides of each regular polygon and calculating the length of each side.