Cool Movie Links
Sphere eversions
Did you know it is possible to turn a sphere inside out? Imagine taking a tennis ball and manipulating it so that the outside becomes the inside, and the inside becomes the outside. If you think about this, you quickly notice that the surface of the tennis ball must be allowed to intersect and pass through itself.
The Optiverse is a six minute
RealPlayer video with an excellent narration that illustrates a technique of
sphere eversion called "minimal energy". It is well worth watching.
Another method of sphere eversion is shown in this MPEG video created at the
Geometry Center at the University of Minnesota. The same video
is also available in
quicktime format.
Read about history of sphere eversions as well
as a detailed explanation of how the eversion
works, mirrored from the Geometry Center .
Visualizing strange geometries and the fourth dimensions
Discover hyperbolic geometry and other strange spaces in this seven minute
narrated RealPlayer movie entitled Post-Euclidean Walkabout.
Our mirror of Olaf Holt's tesseract site provides a demonstration of how to
visualize four dimensional shapes. The site includes MPEG video illustrations. You can access the original site here.
What is the four dimensional equivalent of a cube? Check out this MPEG video depiction of a four-dimensional die with 3D faces and dots.
A Klein bottle is a two-dimensional surface that lives in four-dimensional space. Think of a soda bottle whose neck has been passed back through its body -- but in the fourth dimension so that there are no intersections! Here is an MPEG video visualizing its construction.
Dynamical Systems and Fractal movies
Check out how a double pendulum displays sensitivity to initial conditions in this narrated ram video.
This six-and-a-half minute narrated ram video shows how chaotic dynamical systems like severe storms can be numerically modeled.
The von Koch snowflake is a
self-similar curve with a dimension of (ln 4)/(ln 3) -- yes, that is a
fractional dimension which is a little over 1.26. This MPEG video
demonstrates its self-similarity. Set your player to loop and you will see
what we mean.
The dynamical systems and technology project at Boston University has developed a number of quicktime movies featuring fractal patterns. Check out the one-eyed starfish , a dancing sierpinksi , and this one called spiral mania.
The math department at the University of East
Anglia developed two MPEG videos of zooms on the Mandelbrot set:
animation the first and
animation the second.
 If you want to
generate more images of the Mandelbrot Set and Julia Sets, take a look at
David Joyce's Geometric Pix Gallery, which not
only lets you generate images, it explains what they are.
Knot Movies
John Sullivan has made an excellent narrated 3 minute RealPlayer video discussing knot theory and knot energies.
Wanna see an MPEG video which demonstrates that a seemingly complicated knot is not
(no pun intended)? If you like this video, check out our mirror of Robert
Scharein's Knotplot site. There are hundreds of knot images,
lots of movies, and all sorts of other stuff. The
original
site is here.
Sites with lots of movies
A virtual spacetime travel machine has over 800 still pictures and animations describing many interesting mathematical and physical situations.
The CSC has a page of mathematical visualizations and animations.
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