Is a cone the degenerate of a 4 dimensional hyperbola?


by JonDrew
Tags: cone, degenerate, higher dimensions, hyperbola
JonDrew
JonDrew is offline
#1
Jan30-13, 10:48 PM
P: 83
Is a cone a the degenerate of a 4 dimensional hyperbola?

I only ask because I think it is and I am not sure. I am trying to get better at higher dimensional visualizations.

My analogy being that a point is the degenerate of a 3 dimensional cone. With that logic wouldn't that make a cone the degenerate of a 4 dimensional hyperbola?
Phys.Org News Partner Science news on Phys.org
Internet co-creator Cerf debunks 'myth' that US runs it
Astronomical forensics uncover planetary disks in Hubble archive
Solar-powered two-seat Sunseeker airplane has progress report
Tinyboss
Tinyboss is offline
#2
Jan31-13, 08:52 PM
P: 234
Sort of, though not 4 dimensions, but 3.

x^2+y^2-z^2=C is a hyperboloid of two sheets if C<0, one sheet if C>0, and a cone when C=0.
JonDrew
JonDrew is offline
#3
Jan31-13, 09:05 PM
P: 83
Aren't degenerates usually at least one dimension less than what they degenerate from? and If not could it still be the degenerate of a 4 dimensional hyperbola?

Because I don't think a cone can exist in 4 dimensions, it would be too many axes going through a single point, right?


Register to reply

Related Discussions
Hyperbola and cone General Math 0
dimensional analysis and frustum of a cone Introductory Physics Homework 4
Non-degenerate and degenerate perturbation theory Quantum Physics 13
parameterization of hyperbola intersecting cone Calculus & Beyond Homework 5
non-degenerate Poisson bracket and even-dimensional manifold Differential Geometry 1