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Knot Theory - 3D Mathematical Visualizations next

Mathematical Knots

Mathematical knots are closed curves in 3D space that cannot be untangled. Each knot has unique topological invariants that distinguish it from others.

Trefoil Knot

The simplest non-trivial knot, with crossing number 3

Crossing #

Alexander Δ

t²-t+1

Genus

Chirality

Chiral

Knot Types

Trefoil

Figure-8

Torus (3,2)

Torus (5,1)

Hopf Link

Borromean

Stevedore

Pretzel

Geometric Parameters

Tube Thickness 0.15

Scale 3.0

Curve Resolution 300

Tube Detail 16

Visualization

Coloring Method

Auto Rotation 0.008

Show Wireframe

Cast Shadows

Animation & Interaction

Morphing Speed 0.02

Scan with Phone

Knot Theory

Mathematical Knots

Knot Types

Geometric Parameters

Visualization

Animation & Interaction

Export Options