Trefoil
Steve Trettel
| Medium | Computer generated using a custom-built shader material and THREEjs. |
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| The Art | A parameterization of a tubular neighborhood of the trefoil knot, embedded in the 3-sphere. Viewed in 3 dimensional space via stereographic projection through a point on the knot, so that the negative space in the image is homeomorphic to the trefoil complement. | The Math | Knot theory is the study of closed loops in 3-dimensional spaces, often in the 3-dimensional sphere. The trefoil knot is the simplest nontrivial knot, and the negative space surrounding the knot, known as the knot complement, is surprisingly ubiquitous in low dimensional topology. |
| Categories | Knot Theory, Computer Graphics, Math Illustration, Stereographic Projection |
