cylinder (original) (raw)
When a straight line moves in the space without changing its direction, the ruled surface it sweeps is called a cylindrical surface
(or, in some special cases, simply a cylinder). Formally, a cylindrical surface S is a ruled surface with the given condition:
If p,q are two distinct points in S, and l and m are the rulings passing through p and q respectively, then l∥m (this includes the case when l=m).
If the moving line returns to its starting point, the cylindrical surface S is said to be . In other words, if we take any plane π perpendicular to any of its rulings, and observe the curve c of intersection
of π and S, then S is if c is a closed curve.
Figure 1: A closed cylindrical surface
The solid cylindrical surface and two parallel planes is a cylinder. The portion of the surface of the cylinder belonging to the cylindrical surface is called the lateral surface or the mantle of the cylinder and the portions belonging to the planes are the bases of the cylinder.
The bases of any cylinder are congruent. The line segment of a generatrix between the planes is a of the cylinder. All side lines are equally long. If the side lines are perpendicular to the planes of the bases, one speaks of a right cylinder, otherwise of a skew cylinder.
For any integer n≥3, the following are equivalent statements about a prism P:
- P has a base that is an n-gon;
- P has n+2 faces;
- P has 2n vertices;
- P has 3n edges.