This clip is from the 1970's television show Cosmos. Some of you might have seen the remake from a few years ago that was shown on FOX and is now available on Netflix. In this clip, well-known scientist and author Carl Sagan talks about how higher dimensions can be projected in 2D and 3D. I chose this as the first item in my list because it does a good job of relating higher dimensions to their projections. Though the video is a little bit dated, it helps the viewer understand how higher dimensions are hard for us to visualize.
This is a short story by science fiction author Robert Heinlein to help you understand how higher dimensions relate to the plane and solid geometry we have studied. The story illustrates what a four dimensional house would look like if you tried to go on a tour of it. .
This video contains computer animations to help you visualize the movement of 4D solids in a 3D projection, particularly rotations. I found it particularly interesting to imagine some of these objects as being present in the house described in the Heinlein story.
This video contains some 3D computer models of a tesseract. It shows more stereographic projections (mentioned by Dr. Sagan in the first video). Rotations of a tesseract are also shown. After seeing references to a tesseract in science fiction and comics, looking at the figure's geometric properties is intriguing.
In this clip, mathematician Carlo Seguin talks about some relationships between the platonic solids and higher dimensions. There are some good visuals in this video that connect four dimensional objects to the Platonic solids.
