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Exhibition · projection · dimensions

Rotation in Four Dimensions

What does an object look like when no single projection can contain the event?

One state, several synchronized shadows.

A four-dimensional object rotates in two independent planes. Its lower-dimensional projections change differently, so the event becomes legible only when the views are kept synchronized to one underlying mathematical state.

Animated three-dimensional projection of a rotating four-dimensional objectAnimated two-dimensional projection of the same rotating four-dimensional objectProjection signature chart comparing invariant four-dimensional edge length to changing lower-dimensional projections
Everyday analogy. Think of turning an unfamiliar object behind a screen. Its shadow changes dramatically as it rotates, but no single shadow is the whole object. Several coordinated projections tell you more than any one view.

Pre-rendered from executable mathematics and generated visualization. The public page contains no runtime or interactive execution.