Area of a circle can be calculated by using the formulas:
- Area = π × r2, where ‘r’ is the radius.
- Area = (π/4) × d2, where ‘d’ is the diameter.
- Area = C2/4π, where ‘C’ is the circumference.
Who discovered the formula for finding the area of a circle?
Archimedes of Syracuse
1650 BC) gives us insight into the mathematics of ancient Egypt. The Egyptians calculated the area of a circle by a formula that gave the approximate value of 3.1605 for π. The first calculation of π was done by Archimedes of Syracuse (287–212 BC), one of the greatest mathematicians of the ancient world.
Why area of circle is pir2?
The usual definition of pi is the ratio of the circumference of a circle to its diameter, so that the circumference of a circle is pi times the diameter, or 2 pi times the radius. This give a geometric justification that the area of a circle really is “pi r squared”.
How do you prove the circumference of a circle?
It follows that the ratio circumference : radius, which is equivalent to saying the ratio circumference : diameter is constant for any circle. If this constant is equal to some number π, then circumference = π × diameter, or circumference = 2π × radius. Hence proved.
How did Archimedes discover 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 is meant by area of circle?
Area of a circle is the region occupied by the circle in a two-dimensional plane. It can be determined easily using a formula, A = πr2, (Pi r-squared) where r is the radius of the circle. The unit of area is the square unit, such as m2, cm2, etc.
How are the formulas for circumference and area of a circle derived?
We start knowing that the circumference of a circle is C = 2π • r, and that the area of a rectangle is A = bh.
How did Archimedes determine the area of a circle?
Archimedes presented the proof in The Measurement of a Circle dating back to 260 BCE. To get the area, he ruled out possibilities for circles and corresponding right-angled triangles to be not equal. For it, he used the method of exhaustion to eliminate the possibilities of being greater and lesser, leaving equality as the only possibility.
How do you find the area of a circle with circumference?
In an algebraic formulation, we say that the area of a circle is πr2 π r 2 and its circumference is 2πr 2 π r. These are consistent with Archimedes’ claim: πr2 = (1/2)⋅r⋅(2πr). π r 2 = (1 / 2) ⋅ r ⋅ (2 π r). But the ancient Greeks did not have algebra, and they did not have the notion of a real number that we do.
What is Archimedes’ theorem?
The statement of Archimedes’ Theorem. In an algebraic formulation, we say that the area of a circle is πr2 and its circumference is 2πr. These are consistent with Archimedes’ claim: πr2 = (1/2)⋅r⋅ (2πr). But the ancient Greeks did not have algebra, and they did not have the notion of a real number that we do.
What is the difference between Euclid’s proof and Archimedes’ proof?
In Euclid’s proof the area of a circle is bounded above and below by the areas of circumscribed and inscribed polygons with an increasing number of sides, while in that of Archimedes the circumference is similarly also bounded.
