The arithmetic rope, or knotted rope, was a widely used arithmetic tool in the Middle Ages that could be used to solve many mathematical and geometrical problems.
![](http://upload.wikimedia.org/wikipedia/commons/f/f4/Hortus_Deliciarum_-_Arithmetik.gif)
An arithmetic rope generally has at least 13 knots—therefore, it is often called thirteen-knot-rope—placed at equal intervals. More knots were beneficial, especially for multiplication and division.[1]
In medieval architecture, the knotted rope was indispensable for architects, because it allowed the construction of equilateral and right-angled triangles, as well as circles.[1]
In the depiction of the liberal arts in Hortus deliciarum, the allegory of arithmetics is a female figure with a knotted rope.[1]
Common Applications
editArithmetics[1] | |||
Addition | X + Y = Z | X knots are counted, then another Y. The total number of counted knots is Z. | e.g.: 5 + 4 = 9 |
Subtraction | X - Y = Z | X knots are counted, then Y knots are 'uncounted'. The total number of knots remaining counted is Z. | e.g.: 9 - 4 = 5 |
Multiplication | X * Y = Z | X knots are counted, and the resulting distance is put together Y times. The total number of counted knots is Z. | e.g.: 4 * 3 = 12 |
Division | X / Y = Z (remainder Q) | X knots are counted. From these knots, Y knots are taken and grouped together until all are used up. The number of groups is Z; the number of remaining knots represents the remainder, Q. | e.g.: 12 / 4 = 3 |
Geometrics[1] | |||
Right angle | The two ends of the knotted rope are nailed together, and 5 knots are counted for the base. For the perpendicular side, 4 knots are required. The right-angled triangle is generated by pulling the sides taut. | ||
Equilateral triangle | The two ends of the knotted rope are nailed together, and 5 knots are counted for each side. The sides are tautened to create an equilateral triangle. | ||
Circle | One end is nailed down, and a stylus is attached at the desired distance. With the rope pulled taut, the stylus is moved around, forming a circle. |