Where did the formula for area of a circle come from?
One method of deriving this formula, which originated with Archimedes, involves viewing the circle as the limit of a sequence of regular polygons. The area of a regular polygon is half its perimeter multiplied by the distance from its center to its sides, and the corresponding formula (that the area is half the perimeter times the radius, i.e. ) holds in the limit for a circle.
Where and from who did the formula for area of a circle come from?
Archimedes
Area of a circle
One method of deriving this formula, which originated with Archimedes, involves viewing the circle as the limit of a sequence of regular polygons. The area of a regular polygon is half its perimeter multiplied by the distance from its center to its sides, and the corresponding formula (that the area is half the perimeter times the radius, i.e. ) holds in the limit for a circle.
Where did Archimedes derive the formula for area of a circle come from?
viewing the circle as the limit of a sequence of regular polygons method of exhaustion,
Area of a circle
No context provided
From what literary work did the formula for area of a circle first come from?
The Measurement of a Circle
Area of a circle
https://en.wikipedia.org/wiki/Area%20of%20a%20circle
In geometry, the area enclosed by a circle of radius r is πr2. Here the Greek letter π represents the constant ratio of the circumference of any circle to its diameter, approximately equal to 3.1416.

One method of deriving this formula, which originated with Archimedes, involves viewing the circle as the limit of a sequence of regular polygons. The area of a regular polygon is half its perimeter multiplied by the distance from its center to its sides, and the corresponding formula–that the area is half the perimeter times the radius–namely, A = 1/2 × 2πr × r, holds in the limit for a circle.
Area of a circle
Archimedes used the tools of Euclidean geometry to show that the area inside a circle is equal to that of a right triangle whose base has the length of the circle's circumference and whose height equals the circle's radius in his book Measurement of a Circle.
Area of a circle
In geometry, the area enclosed by a circle of radius r is πr2, where the Greek letter π represents the constant ratio of the circumference of any circle to its diameter, approximately equal to 3.1416. One method of deriving this formula, which originated with Archimedes, involves viewing the circle as the limit of a sequence of regular polygons, where the area of a regular polygon is half its perimeter multiplied by the distance from its center to its sides, and the corresponding formula–that the area is half the perimeter times the radius–namely, A = 1/2 × 2πr × r, holds in the limit for a circle. Archimedes showed the work for the formula for area of a circle in his book, The Measurement of a Circle.