Tuesday, April 28, 2015

Unizor - Geometry3D - Elements - Cylinders

Unizor - Creative Minds through Art of Mathematics - Math4Teens

Consider a plane α that we will call a base plane and a circle c with a center at point O and radius R on this plane. This circle c will be used as a directrix of a cylindrical surface we will construct.
Also assume there is another plane β parallel to a plane α that we will also call a base plane. To differentiate between two base planes, we will call one of them "bottom" and another - "top".
Finally, assume that we have a straight line d that is not parallel to base planes.

Let's construct a cylindrical surface σ using circle c as a directrix and line d as a generatrix.

Circular cylinder is an object in solid geometry formed by a part of a cylindrical surface σ between base planes α and β (called its side surface) and parts of the base planes inside that cylindrical surface - circle c on the "bottom" base plane α and a corresponding circle c' with center O' and the same radius R on the "top" base plane β.
In most cases, when we use a term cylinder, we mean circular cylinder.

Cylinders have no vertices, edges or sides.
The segment connecting centers of base circles OO' is called an axis of a cylinder.
Radius of a base circle is considered as a radius of a cylinder.

It's easy to prove (and we will do it in one of the future lectures) that the top base of a cylinder is also a circle and it is congruent to the bottom circle.

If a generatrix is perpendicular to bases then a cylinder is called a right cylinder. All cylinders that do not have this characteristic, that is if a generatrix is not perpendicular to bases, are called oblique cylinders.
In most cases we will be dealing with right circular cylinders and call them just cylinders.

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