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Visualizing the 4d numbers Quaternions

A 32-minute video by 3Blue1Brown about linear algebra and geometry and number systems and proofs, on the Mathematics shelf. It came up in r/3Blue1Brown, in a thread called “Topic requests”. It is pitched at intermediate level.

3Blue1Brown, Video, 32 min, 2018, on the Mathematics shelf

Builds geometric intuition for quaternions by visualizing a four-dimensional number system in three-dimensional space.

Study notes

Intermediate, Visual intuition. Step 4 of 13 in The mathematics of change and signals

Helpful first

• Complex numbers
• Three-dimensional coordinates

What it builds

• Treat quaternions as a four-dimensional extension of complex numbers.
• Visualize their behaviour in three dimensions.
• Connect quaternion history and modern uses.

Useful moments

• 0:21Quaternions as four-dimensional numbers
• 1:42Hamilton’s push for quaternions

Check yourself: Why can a four-dimensional number system help describe three-dimensional rotations?

Next in the path: Differential equations, a tourist's guide | DE1

Notes are based on metadata, Reddit context and selected English caption passages. They are not a review of every claim in the video.

Builds geometric intuition for quaternions by visualizing a four-dimensional number system in three-dimensional space.