Arithmetic rope
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The arithmetic rope or knotted rope was a widely used arithmetic tool in Middle Ages, with its use one could solve different mathematical and geometrical problems.
In the depiction of the liberal arts the allegory of arithmetics is a female figure with the attribute of the knotted rope.
An arithmetic rope generally has at least 13 knots (therefore it is often called thirteen-knot-rope) placed with equal intervals. More knots were beneficial especially for multiplication and division.
In medieval architecture the knotted rope was indispensable for architects, because it gave the possibility to construct equilateral and rectangular triangles as well as circles.
[edit] Arithmetic functions
| Arithmetics | |||
| Addition | X + Y = Z | First X knots are counted, then another Y ones. The total number of counted knots is Z. | e.g.: 5 + 4 = 9 |
| Subtraction | X - Y = Z | First X knots are counted, then one goes back Y knots. The total number of counted knots is Z. | e.g.: 9 - 4 = 5 |
| Multiplication | X * Y = Z | X knots are counted and the resulting distance is put together for Y times. The total number of counted knots is Z. | e.g.: 4 * 3 = 12 |
| Division | X / Y = Z (Rest 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 is representing the remainder Q. | e.g.: 12 / 4 = 3 |
| Geometrics | |||
| Right angle | The two ends of the knotted rope are nailed together. 5 knots are counted for the base side and nailed down. For the perpendicular side 4 knots are required. The rectangular triangle is generated by stretching these two sides. |  |
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| Equilateral triangle | The two ends of the knotted rope are nailed together. 5 knots are counted for the base side. For each of the other two sides another 5 knots are required. The equilateral triangle is formed by stretching these sides. |  |
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| Circle | One end is nailed down and a stylus is attached at the desired distance. Then the stylus is moved around once with the stretched rope. | ||
