Editing Cylinder (section)

===Cylindric sections===
[[Image:Cylindric section.svg|thumb|left|120px|Cylindric section]]

A cylindric section is the intersection of a cylinder's surface with a [[Plane (geometry)|plane]]. They are, in general, curves and are special types of [[cross section (geometry)|''plane sections'']]. The cylindric section by a plane that contains two elements of a cylinder is a [[parallelogram]].{{sfn|Wentworth|Smith|1913|p=354}} Such a cylindric section of a right cylinder is a [[rectangle]].{{sfn|Wentworth|Smith|1913|p=354}}

A cylindric section in which the intersecting plane intersects and is perpendicular to all the elements of the cylinder is called a ''{{dfn|right section}}''.{{sfn|Wentworth|Smith|1913|p=357}} If a right section of a cylinder is a circle then the cylinder is a circular cylinder. In more generality, if a right section of a cylinder is a [[conic section]] (parabola, ellipse, hyperbola) then the solid cylinder is said to be parabolic, elliptic and hyperbolic, respectively.
[[File:Blue cut-cylinder.gif|thumb|Cylindric sections of a right circular cylinder]]
For a right circular cylinder, there are several ways in which planes can meet a cylinder. First, planes that intersect a base in at most one point. A plane is tangent to the cylinder if it meets the cylinder in a single element.  The right sections are circles and all other planes intersect the cylindrical surface in an [[ellipse]].<ref>{{cite web |mode=cs2 |title=Cylindric section |website= [[MathWorld]] |url=http://mathworld.wolfram.com/CylindricSection.html }}</ref> If a plane intersects a base of the cylinder in exactly two points then the line segment joining these points is part of the cylindric section. If such a plane contains two elements, it has a rectangle as a cylindric section, otherwise the sides of the cylindric section are portions of an ellipse. Finally, if a plane contains more than two points of a base, it contains the entire base and the cylindric section is a circle.

In the case of a right circular cylinder with a cylindric section that is an ellipse, the [[Eccentricity (mathematics)|eccentricity]] {{math|''e''}} of the cylindric section and [[semi-major axis]] {{math|''a''}} of the cylindric section depend on the radius of the cylinder {{math|''r''}} and the angle {{math|''α''}} between the secant plane and cylinder axis, in the following way:
<math display="block">\begin{align}
e &= \cos\alpha, \\[1ex]
a &= \frac{r}{\sin\alpha}.
\end{align}</math>