Hi, Zoya Popova for About.com, and today going to show you how to measure circles.A circle is a geometrical shape consisting of points which lie at an equal distance from a given point, called the center of a circle. This distance between the center and any of the points on the circle is called a radius. The radius is very important in calculating all the other characteristics of a circle, such as its diameter, circumference, and area. The diameter is a line segment passing through the center of a circle and having its endpoints on the circle.The circumference of a circle is the length around it. If we start at point A, and go all the way around the clock until we arrive back at point A, this will be our circumference. Finally, every circle has an area. The area is the number of square units inside that circle.So how does the radius of a circle help us determine its diameter, circumference, and area? Well, the relationship between the radius and the diameter is pretty self-evident. Because the diameter passes through the center, it consists of two radii. So the diameter is two times the radius:d=2rSo what about the relationship between the radius and the circumference? The larger the radius of a circle, the greater it is, and the more its circumference. Ancient Greeks actually realized that the relationship between the circle diameter and its circumference is a constant, which means, that in any circle, big or small, C – circumference, divided by d – diameter, is always the same number. They called that constant number (Pi), but they didn't actually know what the value of is. = C/dArchimedes was the first one to find out that equals approximately 3.14, and he was right. In our time, we know that is an irrational number, which means it has an infinite amount of digits after its decimal point and those digits never end and never repeat. For most calculations and measurements in geometry, we use rounded to 3.14, or simply write it down as. So now we know that the circumference of a circle equals its diameter times PiIt was also Archimedes who came up with the formula for the area of a circle, and it also involves. Archimedes proved that the area of a circle equals pi times the radius squared.And these are the basics for measuring circles. Thank you for watching, and for more information, please visit us at About.com.

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