198 Part 3: The Shape of the World
The Language of Circles
Take a piece of string and tie a pencil to one end. Pin the other end of the string to the center
of a sheet of paper, grab the pencil and pull it out as far as the string will go. With the pencil
point on the paper, move the pencil wherever you can, keeping the string taut. The pencil moves
around the point where you pinned the string, tracing a curve that comes around to meet itself.
That curve is a circle.
A circle is defined as the set of all points at a fixed distance from a given point. The point is called
the center of the circle. That’s the spot where you pinned down the string. The fixed distance that
determines the size of the circle is called the radius. That’s the length of the string. (The plural of
radius is radii.) All radii of a circle are the same length, because every point on the circle is the
same distance from the center.DEFINITION
The collection of all points that sit at a certain distance, called the radius, from a set
point, called the center, forms the shape called a circle.If you mark two or more points on a circle, you divide the circle into sections. Each portion or
part of the circle is called an arc. An arc that is less than half the circle is a minor arc. An arc that
is greater than half the circle is a major arc. A half circle is called a semicircle.DEFINITION
An arc is a portion of a circle. A semicircle is half a circle, a minor arc is smaller than
a semicircle, and a major arc is larger than a semicircle.