Form Study

The sphere, the cube, the cylinder, the square prism, the hemisphere and the right-angled triangulared prism. These may be considered in the following order:

1. The surfaces and faces.
2. The edges.
3. The corners.

The surface is the outside of any object.

In the case of the cube, for instance, we find the surface limited and broken up by edges and faces. The face is a limited part of a surface. An edge is formed by the meeting of two faces.

When passing the fingers over the surface of one of the solids, the pupil discovers decided differences. He notes a plain or flat surface, a curved surface and a round surface. He finds that all are not the same shape, and learns that
Edges may be curved or straight.

Corners will be noted, as well as the difference in shape, if he is shown how to study them. Having familiarized himself by a study of each, it is well for the pupil to take the sphere and cube together, in order that he may observe their resemblances and their differences. Explain to him carefully the meaning of dimension.

Dimension is an extent in one direction.

Considered as to surfaces, their differences are notable. The surface of the sphere is curved equally in all its parts, while the cube’s surface has six equal plane faces.

Two of these six faces coming in contact form an edge, which is the subject of a second topic in the study of solids.

While the cube has twelve edges, the sphere has none.

As to Corners – The sphere has none; there can be no corners where there are no edges. The cube has eight corners.

Three or more faces must come in contact to form a corner. The angles of the plane faces of a cube are right angles, therefore on each cube twenty-four right angles are found.

Cylinder and Square Prism – Considered as a whole, the points of resemblance are these: The dimensions are the same in each.

As to Surface and Faces – The cylinder has both curved and plane surfaces; a square prism has only plane surfaces.

Considered as to their edges, the cylinder has curved edges; the square prism, straight edges. Considered as to corners, the square prism has the same number of corners as the cube; the cylinder has no corners.

Two cubes will make one square prism.
Faces are parallel to each other when they extend in the same direction.

Faces are perpendicular when they are at right angles to each other. A square corner would be formed by the intersection of three.

Faces are oblique to each other when they form angles other than right angles.

The solids are considered, first, as “wholes”; second, as “to surfaces and faces,” and, third, “as to edges.”

An edge is formed by the meeting of two faces.

Edges may be curved or straight. The surface of the sphere is curved equally in all parts, while the surface of the cube is composed of six equal plane faces. When any two of these faces come in contact an edge is formed.

A profile limits the part that we see of any round or curved surface. Profiles and edges limit and give visible shape to the faces and parts of faces.