What would a 3D ball look like if it were partially in 4D space when none of the 4th dimension is visible to the 3D observer?(adsbygoogle = window.adsbygoogle || []).push({});

The equivalent question in flatland is: What would a 2D filled circle look like in flatland if it was partially in 3D?

I think that there the answer would be a line, but the direction and length of the line would vary depending upon how the filled circle was tilted in 3D. The endpoints of the line would always be somewhere on the circumference of the circle. A 3D tilt angle could be constructed for any two points on the circle's circumference.

Dynamically, a filled 2D circle in 3D passing through a different 2D space would appear as a growing then shrinking line. The line would grow to be the diameter of the filled circle and begin and end as a single point. The rate of growth and shrinkage of the line would depend on both the angle between the planes and the relative velocity of the planes. Trying to think about this in terms of volumes makes my head hurt.

All I got from Google was that I really want to talk about a ball rather than a sphere. (In flatland, for a circle we'd only be talking about the endpoints of the line in 2D rather than the entire line.)

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# What would a 3D ball look like (in 3D) if it were partially in 4D space?

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