Re:A mathematician's guided tour through higher dimensions
by wruza on Monday September 20, 2021 @08:48PM
(#28600850)
You may try to imagine 3d objects (shadows of 4d) in consecutive slices. E.g. the foreground 3d scene contains a dot, middle scenes contain bigger and then again smaller spheres down to the background scenewith a dot. By looking at the entire setup from the side you’ll notice that spheres grow and shrink in the same fashion the 2d sphere’s x/y’s do. Similar to this, but in 3d: https://www.google.ru/search?q=sphere+slices&tbm=isch
A 4-cube would look like just few identical 3-cubes from the side, if oriented face-to-3-space. If not, it will be series of prisms or platonic solid alikes.
It doesn’t help much with shapes that have complex 4d-edges, or with higher dimensions, but may give an idea. Also, open two gifs from this link http://www.math.union.edu/~dpvc/math/4D/folding/welcome.html side by side and you’ll quickly get the concept of rotation of a solid around 4th axis.
A 4-cube would look like just few identical 3-cubes from the side, if oriented face-to-3-space. If not, it will be series of prisms or platonic solid alikes.
It doesn’t help much with shapes that have complex 4d-edges, or with higher dimensions, but may give an idea. Also, open two gifs from this link http://www.math.union.edu/~dpvc/math/4D/folding/welcome.html side by side and you’ll quickly get the concept of rotation of a solid around 4th axis.