Definition:Cylinder
Definition
A cylinder is a solid made by rotating a rectangle along one of its sides.
In the words of Euclid:
- When, one side of those about the right angle in a rectangular parallelogram remaining fixed, the parallelogram is carried round and restored again to the same position from which it began to be moved, the figure so comprehended is a cylinder.
(The Elements: Book $\text{XI}$: Definition $21$)
In the above diagram, the rectangle $ADHG$ has been rotated around the side $GH$ to produce the cylinder $ACBEFD$.
Axis of Cylinder
In the words of Euclid:
- The axis of the cylinder is the straight line which remains fixed and about which the parallelogram is turned.
(The Elements: Book $\text{XI}$: Definition $22$)
In the above diagram, the axis of the cylinder $ACBEFD$ is the straight line $GH$.
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 $DEF$.
Lateral Surface of Cylinder
The lateral surface of a cylinder is the curved surface between the bases
Height of Cylinder
The height of a cylinder is the length of a line segment drawn perpendicular to the base and its opposite plane.
In the above diagram, $h$ is the height of the cylinder $ACBDFE$.
Similar Cylinders
Let $h_1$ and $h_2$ be the heights of two cylinders.
Let $d_1$ and $d_2$ be the diameters of the bases of the two cylinders.
Then the two cylinders are similar if and only if:
- $\dfrac {h_1} {h_2} = \dfrac {d_1} {d_2}$
In the words of Euclid:
- Similar cones and cylinders are those in which the axes and the diameters of the bases are proportional.
(The Elements: Book $\text{XI}$: Definition $24$)
Also see
- Results about cylinders can be found here.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): cylinder
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): cylinder