Re: Math riddle involving line y=x rotating into cone?

On Aug 22, 9:10 am, Phil Powell <phillip.s.pow...@xxxxxxxxx> wrote:
Can someone either explain or point me to a visual example of this?

If you have an x-y axis and the line y=x and you rotate this line
along the y-axis, how do you get an upside-down cone? I can't picture
the result of that and it's been perplexing me for a very long time..

Thanks
Phil

Look at the picture of the cone here.
http://mathworld.wolfram.com/SurfaceofRevolution.html

Can you see that the surface is made of a bunch of
lines, all starting at the same point and going
down at the same angle? One such line in the x-y plane
is shown at the left of the cone.

Now turn that picture upside-down.

Another picture:
http://en.wikipedia.org/wiki/Conical_surface

That pair of cones is what you get when you rotate
the entire infinite straight line.

And another:
http://planetmath.org/?op=getobj&from=objects&name=ConicalSurface

- Randy

.

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