How was the area of a circle discovered?

The ancient Babylonians calculated the area of a circle by taking 3 times the square of its radius, which gave a value of pi = 3. Archimedes knew that he had not found the value of π but only an approximation within those limits. In this way, Archimedes showed that π is between 3 1/7 and 3 10/71.

Why do we use pi to find the area of a circle?

In basic mathematics, pi is used to find the area and circumference of a circle. Pi is used to find area by multiplying the radius squared times pi. Because circles are naturally occurring in nature, and are often used in other mathematical equations, pi is all around us and is constantly being used.

Who discovered the pi?

pi, in mathematics, the ratio of the circumference of a circle to its diameter. The symbol π was devised by British mathematician William Jones in 1706 to represent the ratio and was later popularized by Swiss mathematician Leonhard Euler.

How did Archimedes find 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 does pi r mean?

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.

Why is circumference 2pir?

Since the diameter is twice the radius, the circumference of a circle is a product of pi and 2r, i.e. 2(pi)*r. Hi! Now, the polygon will become a circle if n tends to infinity. hence, circumference of circle stands out to be 2.

How do you find the area of a circle using a=pi/r2?

A = π × r 2 ≈ 3.14… × r 2 ≈ 3 r 2 + 0.1 r 2 + 0.04 r 2 +… In other words you are summing smaller and smaller squares. These squares can be arranged to look ever more like the circle you want the area of. Note π has no dimension and r has units of, for example, cm so the units are correct namely square cm.

What does a = π r 2 mean?

What the formula A = π r 2 says is that the area of the circle is larger than the area of the square with side r (as you can clearly see by your drawing). More precisely, the area of the circle is the same as the area of the square with side π ⋅ r because ( π ⋅ r) 2 = π r 2.

How to find the area of a circle with 8 sides?

It is reasonable then to replace 8s by 2 × pi × r, which is the perimeter of the circle, to calculate the area of the polygon or the circle when the number of sides is very big. Doing so we get: Area of circle or polygon equal = 1/2 r × 2 × pi × r = pi × r2. Proof of the area of the circle has come to completion.

Is the formula for the area of a circle intuitively easy?

Although the formula for the area of ​​a circle was already known in Ancient Greece, its justification is not easy at all. So it’s a great topic to enrich the “Why?” series. As you can see above – a square and a circle of the same area are not “somehow intuitively easy” related.