# 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 the **base of the parallelepiped**.

It is usual to choose the **base** to be the one which is conceptually on the bottom.

In the above, $ABCD$ would conventionally be identified as being the **base**

### 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

In the words of Euclid:

*And the***bases**are the circles described by the two sides opposite to one another which are carried round.

(*The Elements*: Book $\text{XI}$: Definition $23$)

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): Entry:**base**:**3.**