Knot Theory 2D — Crossing Diagrams & Invariants

🪢 Knot Theory (2D)

The same knot, seen as a flat diagram: a 3D curve projected onto the canvas, with the strand broken wherever it passes underneath another.

🔵 Select Knot

🎛 Display

Strand thickness 4 Auto-rotate speed 0.6×

🔭 View

📐 Invariants

Crossing #

Writhe

Alexander Δ(t)

t−1+t⁻¹

Unknotting #

ℹ️ Theory

Drag the diagram to rotate it in 3D before it is flattened. Every time a strand crosses another, the one further from you (smaller depth) is drawn with a gap — the standard "over/under" convention of a knot diagram. Crossing signs (green + / red −) sum to the writhe.