Back in the 70's, Martin Gardner published an article in his Mathematical Games column in the SciAm, about visualising rotating hyperspheres and hypercubes. The way I remember it, his imaginary friend Dr. Morpheus (or something) had shown him colour animations of these rotating objects. There were a couple of stills in the article. The 4D objects were of course projected down to 2D.
I've played with an animation of a wireframe hypercube that you could rotate around different axes. It was quite mind-boggling. But Gardner particularly raved about the mind-altering effect of viewing a rotating hypersphere. I've always wanted to view that, but I never heard anything about it again. It seems to me that a 2D projection of a hypersphere must look to all intents and purposes like a sphere.
Does anyone know where that article might be archived? Or where I can view an animation of a rotating hypersphere?
I've played with an animation of a wireframe hypercube that you could rotate around different axes. It was quite mind-boggling. But Gardner particularly raved about the mind-altering effect of viewing a rotating hypersphere. I've always wanted to view that, but I never heard anything about it again. It seems to me that a 2D projection of a hypersphere must look to all intents and purposes like a sphere.
Does anyone know where that article might be archived? Or where I can view an animation of a rotating hypersphere?