Hornbein
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I programmed a perspective projection of a transparent unit hypercube and noticed that the image was the same as that Gamow one. The inner cube appears smaller because it is further away.DaveC426913 said:Citation? I would like to read more about this.
I didn't think this would attract this kind of attention so I didn't do the math. You can tell where the viewpoint is via this calculation.
Measure the height of the outer cube, divide by the height of the inner cube. You get 2.4. That's the magnification you get from being so close to the cube. This is the same as ratio of the distance to the far face divided by the distance to the near face. Let d be the distance to the near face. The distance between the near face and far face is one so 2.4 = (d+1)/d. We get d = 1/1.4 = 0.7. The distance to the near face is that, to the far face it is 1.7.
It so happens that I have a plastic food container that is a transparent rectangloid so I performed an experiment. With one eye at a distance of 5cm from the 12x12cm container the near wall appears to be 2.4 times the height of the far wall. It looks as much like that diagram as a 3D cube possibly could.
Kids! Explore the fourth dimension with common household items!
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