Register to reply

Is a cone the degenerate of a 4 dimensional hyperbola?

Share this thread:
JonDrew
#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
World's largest solar boat on Greek prehistoric mission
Google searches hold key to future market crashes
Mineral magic? Common mineral capable of making and breaking bonds
Tinyboss
#2
Jan31-13, 08:52 PM
P: 233
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
#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