Geometry · Foundation · 9 min

Rotations

Rotation turns every point through the same angle around a fixed center.

WHAT HAPPENS IF…Where does (2.5,0) go after a 90° turn?
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Connect the picture to the ideaRθ(x,y)=(xcos⁡θ−ysin⁡θ, xsin⁡θ+ycos⁡θ)R_\theta(x,y)=(x\cos\theta-y\sin\theta,\ x\sin\theta+y\cos\theta)

The columns of the rotation matrix are perpendicular unit vectors. Therefore dot products and distances are preserved. Its determinant is 1, so area and orientation are preserved as well.

A detail that matters

Rotation about a different center requires translating to that center and translating back.

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One idea leads to another.

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