# What kind of 3D object is this/what is it's parameterisation?

• May 14th 2012, 02:07 PM
babushka
What kind of 3D object is this/what is it's parameterisation?
Hello, I am trying to work out the function of this 3D object and it's parametrisation but after searching the web I have had no luck. Does anybody have any clue what it may be? I was thinking it could be some sort of inverse hyperboloid.

http://www.ikeamarketplace.com/produ...69357_zoom.JPG

Thank you
• May 14th 2012, 02:24 PM
HallsofIvy
Re: What kind of 3D object is this/what is it's parameterisation?
That looks like a variation on the "bell shaped curve", rotated around the x-axis. You can write it most easily as parametric equations using "x" and the angle of rotation as parameters:

$x= t$
$y= e^{-t^2}cos(\theta)$
$z= e^{-t^2}sin(\theta)$
• May 14th 2012, 02:34 PM
babushka
Re: What kind of 3D object is this/what is it's parameterisation?
Thank you!

I am attempting to integrate this, do you know what the determinant of the Jacobian matrix would be?
You say that this is a variation of the bell shaped curve, is there a significant change or would it be ok to use those equations in finding the volume?
• May 16th 2012, 05:28 AM
HallsofIvy
Re: What kind of 3D object is this/what is it's parameterisation?
If you are only given a picture, it is impossible to give an exact formula- we don't know the exact shape!