Sphere

sfer, a geometrical solid, bounded by a surface every point of which is equally distant from a point within called the center. The sphere is the most interesting and perfect geometrical form. It attracted the attention of the ancients. It is one of the gifts given to children by the kindergartner. Euclid, in Greek mathematics, defined a sphere as a solid figure generated by the revolution of a semi-circle about its diameter. The particles of a liquid, as drops of rain, molten lead, etc., if left free to act naturally, arrange themselves in the form of a sphere. Some of the more important mathematical facts may be mentioned:

Every section of a sphere made by a plane is a circle.

Any section made by a plane passing through the center is a great circle.

Every great circle bisects the surface of the sphere.

The diameter is obtained most readily by placing the sphere between two parallel surfaces or blocks and then measuring the distance between them.

Using the numbers abstractly, we may say that the surface of a sphere equals the circumference multiplied by the diameter. The result may be obtained by multiplying the square of the diameter by 3.1416.

The area of the surface equals the area of four great circles.

The volume equals the surface multiplied by one-third of the radius or by one-sixth of the diameter. This result may be obtained by multiplying the cube of the diameter by 5236.

The surfaces of two spheres are to each other as the squares of their radii, or as the cubes of their diameters, etc.

The surface of a sphere is equal to the concave surface of a circumscribed cylinder.

The volume of the sphere is equal to two-thirds of that of the circumscribing cylinder.

The volume of a sphere is equal to 5236 of the circumscribing cube.