mathematics of turks head knots

Working with the black 3 mm cord to create a 19 bight 13 part 2 strand knot on a large mold. The weave is worked to a firm finish on the tube where there are no gaps between parts.

The knot it is eased off the mold and relaxed which lets the parts open up the small diamond shaped openings in the weave.

Edge tensioning the piece produces this rather pleasing shape with the ends flared out and the center tucked in. The individual cords become straighter across the center as the knot moves toward a low energy state (all the cords as relaxed as possible)

Did you know that curves can be created using straight lines?

Who knew that math could be a "soft" science?

The loose ends wrapped around the narrow section in the center.
Art imitates nature (again) and the universe remains an orderly place.

check your slip-on size click here then select your favorite from one of these three online shops:

Etsy: http://www.etsy.com/shop/WhatKnotShop
ArtFire: http://www.artfire.com/users/WhatKnotShop
Zibbet: http://www.zibbet.com/WhatKnotShop

Mathematically this is described as a hyperboloid of one sheet. You can see this and other 3D models here: http://math.asu.edu/~nbrewer/Fall2007/MAT267/section10.6.html