Knots as a Principle of Form in Modern Art and Architecture

The article reviews the origin and development of the theme of knots in the contemporary art and architecture of 20th and 21st centuries. Knots are known from the very origin of the human material culture and for many millennia have become not only convenient and perfect tools and instruments, but also an integral part of traditional arts and crafts. Today, artists, sculptors and architects turn to knots as an effective means of expressiveness and perception of unusual curvilinear forms generated by curved and closed lines in space. Because of their close connection with modern mathematics, knots become one of the leading directions in a new and quick-growing school of mathematical art (math-art). The newest applications of the knot principle in art and architecture include the kinematic form-finding structures proposed by the author, where the knots are used to build transformable surfaces of arbitrary shape.