LINKS TO INTERACTIVE DEMOS OF

QUATERNIONS IN THREE DIMENSIONS

Equivalent Ordered Pairs of Vectors in R³ that Represent a Quaternion

Merging Two Ordered Pairs of Vectors in R³ Through a Common Intermediate Multiplies Quaternions Geometrically

Interpolating The Second Elements ofTwo Ordered Pairs of Vectors in R³ that Share a Common First (or Last) Element Interpolates Quaternions Geometrically

Ordered Pairs of Reflections that Implement the same Rotation

Continuous Deformation (Homotopy) u(s,t) the path u(s,0)=u₀(s) from e₁ to e₁ around the e_1-e₂ Equator to the Constant Path u(s,1)=u₁(s)=e₁ on S²

Mathematical Belt Trick and Plate Trick Homotopies on SO(3) Arising from the Homotopy on S² by R(s,t)=ρ(u(s,t))ρ(e₁), where ρ(v) reflects across v

Mathematical Plate Trick Obtained by Preceding a Mathematical Belt Trick by a Two-turn Wind-Up

Mathematical Tangle Trick Obtained by Reflecting theWind-up + Belt Trick Plate Trick Across the Plate

Physical Belt Trick, Plate Trick, and Tangle Trick (.mov)

The Rotation Hall of Fame Historical Material