1. Hypercube, VT 360
Just as Australian aborigines reportedly had a hard time seeing the two-dimensional representation of a cube as a cube, so you will enjoy seeing how aboriginal your four dimensional perception is!
2. Newton’s Equal Areas VT 378
Newton used beautiful ideas from geometry to show how his theory of gravitational force is leads to Kepler’s Second Law (that planets sweep out equal area in equal time). Three times in the video the essential idea of calculus appears; can you spot them?
3. Dragon Fold VT 377
A simple closed curve is a continuous curve that begins and ends at the same point without crossing (or tangentially touching) itself. Note that every such curve has an inside and an outside. Can you determine which is the inside of the Sierpinski curve? The dragonfold curve is made by walking along the curve and bending it right, then left, then right, etc. A very simple idea, but a beautifully complicated curve!
4. Powers of Ten: Films of Charles and Ray Eames, VT 3096
This classic is somewhat out of date, now that we have dark matter and dark energy, but still thought-provoking. Please note that the video begins with biographical material on the Eames that you can skip.
5. Turning a sphere inside out, VT 3544
This low budget film interviews some mathematicians, with an intriguing view of their views on abstract versus real mathematical structure. It shows how chicken wire can make an abstract idea concrete, and ends with computer animations of a sphere turning inside out.
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