Definition:Base of Geometric Figure
Definition
The base of a geometric figure is a specific part of that figure which is distinguished from the remainder of that figure and placed (actually or figuratively) at the bottom of a depiction or visualisation.
In some cases the base is truly qualitiatively different from the rest of the figure.
In other cases the base is selected arbitrarily as one of several parts of the figure which may equally well be so chosen.
Base of Polygon
For a given polygon, any one of its sides may be temporarily distinguished from the others, and referred to as the base.
It is immaterial which is so chosen.
The usual practice is that the polygon is drawn so that the base is made horizontal, and at the bottom.
Base of Segment of Circle
The base of a segment of a circle is the straight line forming one of the boundaries of the seqment.
In the above diagram, $AB$ is the base of the highlighted segment.
Base of Solid Figure
The base of a solid figure is one of its faces which has been distinguished from the others in some way.
The solid figure is usually oriented so that the base is situated at the bottom.
Base of Parallelepiped
One of the faces of the parallelepiped is chosen arbitrarily, distinguished from the others and called a base of the parallelepiped.
The opposite face to that face is also referred to as one of the bases.
It is usual to choose one of the bases to be the one which is conceptually on the bottom.
In the above, $ABCD$ and $EFGH$ would conventionally be identified as being the bases.
Base of Pyramid
The polygon of a pyramid to whose vertices the apex is joined is called the base of the pyramid.
In the above diagram, $ABCDE$ is the base of the pyramid $ABCDEQ$.
Base of Prism
The bases of a prism are the two parallel polygons which form the faces at either end of the prism.
In the above diagram, the faces $ABCDE$ and $FGHIJ$ are the bases of the prism.
Base of Cone
The plane figure $PQR$ is called the base of the cone.
Base of Right Circular Cone
Let $\triangle AOB$ be a right-angled triangle such that $\angle AOB$ is the right angle.
Let $K$ be the right circular cone formed by the rotation of $\triangle AOB$ around $OB$.
Let $BC$ be the circle described by $B$.
The base of $K$ is the plane surface enclosed by the circle $BC$.
In the words of Euclid:
- And the base is the circle described by the straight line which is carried round.
(The Elements: Book $\text{XI}$: Definition $20$)
Base of Cylinder
The $2$ parallel planes which form a cylinder by intersecting a cylindrical surface are called the bases.
In the above diagram, the bases of the cylinder $ACBEDF$ are the faces $ABC$ and $DEF$.
Also see
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): base: 3.
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): base: 3.