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### Definition For Cylinder without Big Words

Date: 11/03/98 at 21:58:28
From: Teresa Bowden
Subject: Geometry Definition

I just need to know a good definition for cylinder that I can
UNDERSTAND.  The ones that I find are all impossible and use huge words
that make no sense to me.

Date: 11/04/98 at 13:01:47
From: Doctor Peterson
Subject: Re: Geometry Definition

Hi, Teresa. There are a lot of different answers I could give you,
depending on what you are going to do with the definition. A young
child will be satisfied by just being told that a cyclinder is a "can
shape." Later in math you use more precise definitions of the same
shape. Then you may learn a more general definition that allows it to
be "tilted" (an oblique cylinder, rather than a right cylinder), or
even to have some other shape than a circle. Another way the definition
can vary is by whether you want to work with a cylinder that has a top
and bottom, or just the lateral (side) surface of an infinitely tall
cylinder with no top or bottom. The more general you want it to be, the
more complicated the definition is.

Our FAQ on cylinders gives a relatively complicated, general
definition, which defines most of the terms involved, but requires you
to understand the ideas of "generating" a surface:

http://mathforum.org/dr.math/faq/formulas/faq.cylinder.html

My dictionary says the same thing without the big words, defining a
circle as:

(a) A surface generated by a straight line moving parallel to a
fixed straight line and intersecting a plane curve.
(b) The portion of such a surface bounded by two parallel planes
and the regions of the planes bounded by the surface.

For a normal "right circular cylinder," I can rephrase this to say

A cylinder is the surface formed by the set of lines perpendicular
to a plane, which pass through a given circle in that plane.

|
|
|
| ------>
|
|
|
|
***|****************
******   |                ******
**         |                      **
*         |                      *
******   |                ******
***+****************
|
|

This says that you make a cylinder by dragging a line around in a
circle. The "generatrix" is the axis, and the "directrix" is the circle
forming the base, around which you move a line parallel to the axis to
form the cylinder.

Here's a page that gives a more restricted definition of a circular
cylinder:

http://www.astro.virginia.edu/~eww6n/math/Cylinder.html

"In common usage, the term 'cylinder' refers to a Solid of circular
Cross-Section in which the centers of the Circles all lie on a
single Line. In mathematical usage, 'cylinder' is commonly taken to
refer to only the lateral sides of this solid, excluding the top
and bottom caps. ... A cylinder is called a right cylinder if it is
'straight' in the sense that its cross-sections lie directly on top
of each other; otherwise, the cylinder is called oblique."

I can rewrite this for a right circular cylinder to say

A cylinder is the surface formed by all circles of a given radius,
in planes perpendicular to a given line (the axis), whose centers
are on that line.

|
|
*********|**********
******         |          ******
**               +                **
*               |                *
******         |          ******
********************
|               ^
|               |
|               |
*********|**********
******         |          ******
**               +                **
*               |                *
******         |          ******
********************
|
|
|

This says that you make a cylinder by dragging a circle in a straight
line.

- Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/

Associated Topics:
High School Definitions
High School Geometry
High School Higher-Dimensional Geometry
Middle School Definitions
Middle School Geometry
Middle School Higher-Dimensional Geometry

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