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I was going through a definition about cylinder which states that :

A cylinder is a surface generated by a variable straight line which moves parallel to a fixed line and intersects a fixed curve not lying in a plane parallel to the fixed line or touches a given surface . The given curve is called the guiding curve or directrix and the variable line is known as generator. If the guiding curve is a circle and the fixed line is normal to the plane of the circle through the centre of it, then the cylinder is right cylinder and the fixed line is called the axis of this cylinder.

This is a very lengthy definition given, (or maybe a long information but either way,) I am not getting what are they trying to mean ? Can anyone explain what are they trying to mean ? Also,what's the difference between right cylinder and a normal cylinder?I am not getting which is the guiding curve and directrix and wha's the generator ? Also, I have just started an elementary course in analytical geometry so ,I dont know much about this , so I need a "simplified" or rather an "elementary level explanation "(if that's possible at all ) ...But I am not quite getting this...

Arthur
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  • See here a correct definition of a (generalized) cylinder. – Jean Marie Nov 30 '22 at 13:05
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    @JeanMarie Thank you! But that's highly complicated and not at all elementary level(atleast for me)...a simplified explanation if provided may be of great help ...Thank you! – Arthur Nov 30 '22 at 13:47
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    Take any base curve, say in horizontal plane (this curve can be a circle, an ellipse, a spiral, etc.) then take a stick and let the base of this stick follow the base curve keeping always the stick in a same orientation (like fixing a remote star): you will get in this way a generalized cylinder (coinciding with an ordinary cylinder if the base curve is a circle and the stick stays in a vertical position). – Jean Marie Nov 30 '22 at 13:51
  • When you read a novel, you read a paragraph once and then you move on. To read a piece of mathematics, you read it repeatedly, breaking it up into different pieces and building the connections between them as you re-read. Some of that paragraph introduces new words ("is called the"); other parts contain the actual content. Don't give up so easily. – JBL Nov 30 '22 at 15:39
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    @JeanMarie Thank you! Your way of defining really simplifies that down immensely...but somehow I feel the definition given above in my post is not quite complete..This is in the sense (from your explanation as I made out, if I'm correct) that the variable straight practically follows the curve and moves along it thus generating the whole cylinder...but in the definition its given "intersects a fixed curve not lying in a plane parallel to the fixed line or touches a given surface " is not sufficient as it seems as the variable line must follow the "trajectory " of the curve. What do you think? – Arthur Dec 01 '22 at 16:14
  • The verbal form "intersects" is in fact a static way to say the same thing ; my "moves along" brings a cinematic view which has its didactic merits but isn't compulsory in a definition :) – Jean Marie Dec 01 '22 at 17:31
  • @JeanMarie Thank you! That may be the case ...but I do get it now...Thank you!... – Arthur Dec 02 '22 at 01:48

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