Part 7/10:
The introduction of hyperplanes—three-dimensional objects slightly offset from our existing universe—serves as a foundational concept for understanding spatial relationships in four dimensions.
Extruding into the Fourth Dimension
To build our understanding, we must conceptualize higher-dimensional objects through geometric operations. For example, we can begin with a line segment and extrude it to form a square, generating a two-dimensional shape. Continuing this process, we would then take a square and extrude it along a perpendicular direction to realize a three-dimensional cube.