Definition For Cylinder without Big WordsDate: 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/ |
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