Circle is a closed curve on a plane. All points of the curve are the same distance from a point that lies within the curve. This point is called the center. There are 360 degrees in a circle.
Many common objects have a circular shape, including rings, hoops, and wheels. You can easily draw a circle with an instrument called a compass. A compass looks like a pair of scissors with a pencil where one point should be. To draw a circle, place one point of the compass at the point chosen as the center, and rotate the pencil around it.
Parts of a circle.
Sometimes people use the words disc or circle to mean the area inside the curve. They call the curve itself the circumference. The length of the curve is also called the circumference. An arc is any connected part of the circumference.
A chord is a straight line between two points on the circumference of a circle. If a chord goes through the center, it forms a diameter. A diameter is the longest chord of a circle, and divides the circle into two equal parts called semicircles.
The radius is the distance from the center to the circumference. It equals half the length of a diameter. The word radius is also used to mean any line that joins the center to the circumference.
A secant is a straight line that intersects a circle at two points. A line that just touches the circle, or meets the circle at just one point, is called a tangent. If you move a secant away from the center of the circle so that it always lies parallel to its previous position, the two points at which it touches the circle will get closer to each other. When the points come together, the secant has reached the position of a tangent. The point where the tangent touches the circle is the point of tangency. The radius at the point of tangency makes a right angle with the tangent.
The use of pi.
The Greek letter pi stands for the number by which the diameter of a circle (d) must be multiplied to obtain the circumference (c). That is, c equals pi times d or 2pi times r, where r is the radius. The area of a circle (A) is given by the formula A equals pi times r-squared.
You cannot write pi exactly as a decimal. But by increasing the number of digits, you can get a number as near to it as you want. Common estimates used for pi include 22/7, 3.14, 3.1416, and 3.14159.
History.
The ancient Chinese used 3 as the value of pi. About 1650 B.C., the Egyptians improved on the approximation. During the A.D. 100’s, the astronomer Ptolemy of Alexandria calculated an even more precise value of pi. The decimal system did not come into use until the 1600’s, but Ptolemy’s value was the equivalent of 3.1416. After the introduction of decimals, mathematicians sought an exact value for pi–either a repeating decimal or a value with a limited number of decimal places. Mathematicians now know that there is no such value.
