Searching for Extra Dimensions by Don V Black, PhD 
My research into the visualization of multiple spatial
dimensions has lead to a PhD in Computer Graphics and Visualization
and the following dissertation: 

The following videos are cited in the above dissertation. Click the YouTube™ logo to play those videos on YouTube at a lower resolution. Otherwise there is a mirror copy at UCI that may be downloaded for your personal use. The videos© and dissertation© are copyright 2010, Don V Black.  
Figure 2.9  Two 4D Objects Crossing at 0.866c.  
Figure 6.2  Twotorus in 4D and sliced orthogonal to W by a threeflat.  
Figure 6.3  Twotorus in 4D and projected obliquely onto a threeflat.  
Figure 6.8  A 4D Sphere sliced along the Waxis by a 3D hyperplane.  
Figure 6.9  A 4D Torus sliced along the Waxis by a 3D hyperplane.  
Figure 6.10  A 5D Torus Shown in 15 3D Viewports.  
Figure 7.2  Spacetrace showing Three Viewports.  
Figure 8.1  Slice of a 4D Torus in a nonEuclidean 4space.  
Figure 8.2  Slice of a 4D Torus in Euclidean 4space..  
Figure 0.0  This is a concatentation of the above videos into one stream.  
Recent Papers  
Visualizing flat spacetime: Viewing optical versus relativistic effects.,
Black, Don V.; Gopi, M.; Wessel, Frank; Pajarola, Renato; Kuester, Falko
American Journal of Physics, Volume 75, Issue 6, pp. 540545 (2007).


A visual representation of Minkowski spacetime appropriate for a student with a background in geometry and algebra is presented. Minkowski spacetime can be modeled with a Euclidean fourspace to yield accurate visualizations as predicted by special relativity. The contributions of relativistic aberration, as compared to classical prerelativistic aberration, to the geometry are discussed in the context of its visual representation  
Viewing Classical and Relativistic Spacetime  Click here for accompanying Animated Videos  
Master of Science in Information and Computer Sciences  
Visualization of Classical and Relativistic Spacetime Geometry  
Herein we devise, explore, and test an elegant theoretical spacetime model to enable realistic visualization of special relativistic effects. Images and animated videos are provided.  
BackLight Software Package Animations  Click here for accompanying Animated Videos  
Viewing Classical and Relativistic Spacetime  Click here for accompanying Animated Videos  
Two early examples of interactive 4D models, follow. The first is a straightforward Euclidean 4D space depicted by a display similar to that of a 3D CAD pacakge. The second is a 4D Minkowski spacetime displayed the same way, showing relativistic distortions and infinities at lightspeed.  
Euclidean 4D Viewer (sin & cos)  Minkowski 4D Viewer (sinh & cosh) 
My Erdös Number  5:
The Paul Erdös number represents
the separation of a scientist from the famous mathematician Paul Erdös in
terms of coauthoring mathematical research articles, and is an easy way
to lose a lot of time browsing bibliographies and the Internet (there are
tools). I determined my Erdös number to be 5 as follows:
Don V Black > Renato Pajarola > Peter Widmayer > Emo Welzl > Boris Aronov / Paul Erdos 

You are welcome to explore my various websites: 
Go here for Physics & Education:  http://www.GravityWaves.com 
or here for Business:  http://www.dcgFX.com 
or here to learn about Special Relativity & Visualization:  http://www.HyperVisualization.com 
or here to explore another Dimension:  http://www.HyperDimensia.com 
or here to learn about Flying:  http://www.PilotAge.com 
I calculated my Erdös
number to be 5 as follows:
Boris Aronov, Paul Erdös, Wayne Goddard, Daniel J. Kleitman, Michael Klugerman, János Pach, and Leonard J. Schulman. Crossing families. In Proceedings Symposium on Computational Geometry, pages 351–356. ACM, 1991.
