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Can 3 Rings Be Locked Without Ever Touching?
Dimensions & topology

Can 3 Rings Be Locked Without Ever Touching?

BEHIND THE WORK

Can 3 rings be locked together without ever touching or linking in pairs? In knot theory, the Borromean rings are a famous Brunnian link: no two rings are linked together (pairwise linking number Lk = 0), yet all three are collectively inseparable (Milnor triple invariant μ = ±1). Cut any single ring, and the other two instantly fall completely apart.

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#MathArt #BorromeanRings #Topology #Geometry #Mathematics #KnotTheory #Blender3D

THE MATHEMATICAL RULE

Ring components before connecting splines\text{Ring components before connecting splines}r1(t)=(acos⁡t,bsin⁡t,ccos⁡2t)\mathbf r_1(t)=(a\cos t,b\sin t,c\cos 2t)r2(t)=(ccos⁡2t,acos⁡t,bsin⁡t)\mathbf r_2(t)=(c\cos 2t,a\cos t,b\sin t)r3(t)=(bsin⁡t,ccos⁡2t,acos⁡t)\mathbf r_3(t)=(b\sin t,c\cos 2t,a\cos t)
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