Carved Torus Knots in Wood & Stone

A torus is a basic geometrical shape in mathematics, known more commonly as a doughnut. It is topologically distinct from a sphere because there are two circles on its surface, neither of which can be contracted to a point, one going around the hole, & one going through it. Any circle on a sphere can be continuously contracted to a point. A torus knot is a closed curve not crossing itself on the surface of a torus, & any such knot is topologically determined by an ordered pair of integers, (m,n), where m is the number of times the curve goes around the outside of the hole, & n is the number of times it goes through the hole. When making such a torus knot by carving or casting, it can be emphasized by making a valley in the surface of the torus so that the knot consists of the topmost points, the crest of two adjacent valley regions. The torus knots I like best to carve are the (3,5) & the (4,5), but I have sometimes carved torus links, which consist of more than one knot, intertwined with each other. For the (3,5) knots, I carve the valley so that the cross-section perpendicular to the circle going around the hole of the torus is a hypocycloid. All the carvings shown here were handmade by me, that is, using a hand held shaping tool like a Dremel, but larger & more powerful. Different kinds of wood were used (cocobolo, black palm, timborana, cherry, maple burl, sirari rosewood) & two examples are here shown carved of alabaster stone. The smallest size wooden carving is 3.75 in diameter & 1.75 deep, then next larger is 5.75 in diameter & 2.75 deep. The alabaster stone pieces are approximately 10 in diameter & 4 deep. It is a much longer & harder process to polish the stone than the wood. Each piece is unique because of the grain of wood or color of the stone. Carved Torus Knots in Wood & Stone