# Introduction to the Sphere

A sphere is a solid figure bounded by a curved surface, where every point of which is equidistant from a fixed point called its center.

A straight line starting at the surface, passing through the center and ending at the surface is called a diameter. The radius of a sphere is a straight line connecting its center with any point on the surface. Obviously, all radii of the same sphere are equal.

The sphere may be considered as generated by the complete rotation of a semi-circle about its diameter. A tennis ball is an example of a sphere.

The section of a sphere made by a plane is a circle. If the plane passes through the center of the sphere, the circle is known as a great circle. Other sections made by a plane not passing through the center are small circles. As shown in the figure, circles $ACB$ and $NCS$ are great circles while $MER$ is a small circle. Clearly, any plane passing through the center of a sphere contains a diameter. Hence, all great circles of a sphere are equal, have for their common center the center of the sphere and have their radii as the radius of the sphere.

A great circle bisects the surface of a sphere. One of the two equal parts into which the sphere is divided by a great circle is called a hemisphere.