Definition:Right Circular Cylinder
Definition
Definition 1
A right circular cylinder is the solid of revolution 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 right circular cylinder $ACBEFD$.
Definition 2
A right circular cylinder is a right cylinder whose bases are circles.
Axis of Right Circular 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 Right Circular 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 known as
A right circular cylinder is usually known in common parlance as a cylinder.
This is also the usage in Euclid's The Elements.
However, on $\mathsf{Pr} \infty \mathsf{fWiki}$ a cylinder is a more general object, so right circular cylinder will be used when that is what is meant.
Also see
- Results about right circular cylinders can be found here.