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Chinese knots come in a variety of shapes and sizes. They are made from a single cord and are often double-layered and symmetrical in all directions. [3] [4] [5] Satin cording is the most widely used material, especially when the knotting is done for clothing and jewellery; however, cotton, parachute cord, and other materials are frequently used as well.
Examples of different knots including the trivial knot (top left) and the trefoil knot (below it) A knot diagram of the trefoil knot, the simplest non-trivial knot. In topology, knot theory is the study of mathematical knots.
In the original Chinese myth, the thread is tied around both parties' ankles, while in Japanese culture it is bound from a male's thumb to a female's little finger. Although in modern times it is common across both these cultures to depict the thread being tied around the fingers, often the little finger.
Lào zi (simplified Chinese: 络子; traditional Chinese: 絡子), also called Tāo zi (Chinese: 绦子), is an ancient appellation for knots in China. [1] In ancient Chinese literature, the Lào zi actually refers to what is now known as zhongguo jie (simplified Chinese: 中国结; traditional Chinese: 中國結; Hanyu Pinyin: zhōngguó jié; Tongyong Pinyin: li; lit.
Knots and knotting have been used and studied throughout history. For example, Chinese knotting is a decorative handicraft art that began as a form of Chinese folk art in the Tang and Song Dynasty (960–1279 AD) in China, later popularized in the Ming. Knot theory is the recent mathematical study of knots.
Three-twist knot is the twist knot with three-half twists, also known as the 5 2 knot. Trefoil knot A knot with crossing number 3; Unknot; Knot complement, a compact 3 manifold obtained by removing an open neighborhood of a proper embedding of a tame knot from the 3-sphere. Notation used in knot theory: Conway notation
Many other familiar objects exhibit the same chiral symmetry of the human body, such as gloves, glasses (sometimes), and shoes. A similar notion of chirality is considered in knot theory, as explained below. Some chiral three-dimensional objects, such as the helix, can be assigned a right or left handedness, according to the right-hand rule.
A reduced diagram is one in which all the isthmi are removed. Tait came up with his conjectures after his attempt to tabulate all knots in the late 19th century. As a founder of the field of knot theory, his work lacks a mathematically rigorous framework, and it is unclear whether he intended the conjectures to apply to all knots, or just to alternating knots.