Forma, Vol. 22 (No. 1), pp. 75-91, 2007
Original Paper

Shapes of Knot Patterns

Katsumi Morita

Junior College of Sapporo Otani University, Hokkaido 065-8567, Japan
E-mail address:

(Received November 3, 2006; Accepted September 5, 2007)

Keywords: Knot, Crossing Number, Components, Combination, Pattern

Abstract. In the mathematical knot theory, knot can be defined as an embedding of a circle in the three dimensional Euclidean space. In the plastic sense, as 3-dimensional objects, knots represent a very interesting phenomenon. This paper focuses on shapes of knots, using computer graphics, and attempts to present variations of the form of knot patterns. At the first stage, we constructed only alternating knots. At the second stage knot patterns are formed by using combinations of similar shapes. At the third stage knot patterns are formed as combinations of different shapes. The basis for the study of these designs is the mathematical knot theory.

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