Gauss notation (original) (raw)
Un code de Gauss, du nom du mathématicien Carl Friedrich Gauss est une liste de nombres codant une courbe plane fermée présentant des croisements. Il a été étendu au codage d'un nœud, et même d'un entrelacs.
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| dbo:abstract | Gauss notation (also known as a Gauss code or Gauss word) is a notation for mathematical knots. It is created by enumerating and classifying the crossings of an embedding of the knot in a plane. It is named for the mathematician Carl Friedrich Gauss (1777–1855). Gauss code represents a knot with a sequence of integers. However, rather than every crossing being represented by two different numbers, crossings are labeled with only one number. When the crossing is an overcrossing, a positive number is listed. At an undercrossing, a negative number. For example, the trefoil knot in Gauss code can be given as: 1,−2,3,−1,2,−3. Gauss code is limited in its ability to identify knots by a few problems. The starting point on the knot at which to begin tracing the crossings is arbitrary, and there is no way to determine which direction to trace in. Also, Gauss code is unable to indicate the handedness of each crossing, which is necessary to identify a knot versus its mirror. For example, the Gauss code for the trefoil knot does not specify if it is the right-handed or left-handed trefoil. This last issue is often solved by using the extended Gauss code. In this modification, the positive/negative sign on the second instance of every number is chosen to represent the handedness of that crossing, rather than the over/under sign of the crossing, which is made clear in the first instance of the number. A right-handed crossing is given a positive number, and a left handed crossing is given a negative number. (en) Un code de Gauss, du nom du mathématicien Carl Friedrich Gauss est une liste de nombres codant une courbe plane fermée présentant des croisements. Il a été étendu au codage d'un nœud, et même d'un entrelacs. (fr) Un código de Gauss, del nombre del matemático Carl Friedrich Gauss es una lista de números que codifica una curva plana cerrada que presenta lazos. Ha sido extendido a la codificación de un nudo, e incluso de un enlace. (es) ドウカーの表示法（ドウカーのひょうじほう、Dowker notation）とは、位相幾何学の一分野である結び目理論において、結び目を表示する方法のひとつ。名前は数学者のに由来する。元となる、結び目の射影図を偶数の数列で表すアイデアはカール・フリードリヒ・ガウスが考案したもので、その後改良が加えられた。 結び目の表示法には、ほかにや組み紐の群による表示法などがある。 (ja) |
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| rdfs:comment | Un code de Gauss, du nom du mathématicien Carl Friedrich Gauss est une liste de nombres codant une courbe plane fermée présentant des croisements. Il a été étendu au codage d'un nœud, et même d'un entrelacs. (fr) Un código de Gauss, del nombre del matemático Carl Friedrich Gauss es una lista de números que codifica una curva plana cerrada que presenta lazos. Ha sido extendido a la codificación de un nudo, e incluso de un enlace. (es) ドウカーの表示法（ドウカーのひょうじほう、Dowker notation）とは、位相幾何学の一分野である結び目理論において、結び目を表示する方法のひとつ。名前は数学者のに由来する。元となる、結び目の射影図を偶数の数列で表すアイデアはカール・フリードリヒ・ガウスが考案したもので、その後改良が加えられた。 結び目の表示法には、ほかにや組み紐の群による表示法などがある。 (ja) Gauss notation (also known as a Gauss code or Gauss word) is a notation for mathematical knots. It is created by enumerating and classifying the crossings of an embedding of the knot in a plane. It is named for the mathematician Carl Friedrich Gauss (1777–1855). Gauss code represents a knot with a sequence of integers. However, rather than every crossing being represented by two different numbers, crossings are labeled with only one number. When the crossing is an overcrossing, a positive number is listed. At an undercrossing, a negative number. (en) |
| rdfs:label | Código de Gauss (es) Gauss notation (en) Code de Gauss (fr) ドウカーの表示法 (ja) |
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