Computing rope

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Allegory of arithmetic with arithmetic rope (from the Hortus Deliciarum around 1180)

The arithmetic rope or knot rope was a common arithmetic aid of the Middle Ages , with the help of which one could solve and demonstrate simple numerical and geometric problems.

A female figure with the attribute of the knotted rope served as an allegorical personification of arithmetic in the representation of the liberal arts .

A computing rope had several knots a hand's breadth apart. It is often incorrectly called a twelve-knot cord . However, a twelve-knot cord is always a closed (ring) cord. More knots in the arithmetic rope were especially beneficial for multiplication and division.

Arithmetic functions

arithmetic
addition X + Y = Z You first count off X nodes, then Y more. The total number of nodes counted is Z. E.g .: 5 + 4 = 9
13node add.png
subtraction X - Y = Z You first count off X nodes and then go back Y. The total number of nodes counted is Z. E.g .: 9 - 4 = 5
13node sub.png
multiplication X × Y = Z You count X nodes and put this line Y times together. The total number of nodes counted is Z. E.g .: 4 * 3 = 12
13knoten mul.gif
division X / Y = Z (remainder Q) Count off X nodes. From this you take Y and put them together until they are all used up. The number of merges is Z. The remaining nodes are the remainder Q. E.g .: 13/4 = 3 remainder 1
13knoten div.png
geometry
Right angle 4 2 + 3 2 = 5 2

16 + 9 = 25
( Pythagoras )

You nail the beginning and end of the computing rope together. For the base side, count down 5 (4 sections) and nail it down. For the vertical on it you need 4 knots (3 sections). Tensioning these sides creates a right-angled triangle (principle of the Pythagorean triple ). If you now fix 3 sections of the right-angled sides (7 nodes) and pull the remaining 5 nodes symmetrically outwards, a square is created. 13node rw.png
Equilateral triangle You nail the beginning and end of the computing rope together. Count 5 for the base side. For the sides on it you need 5 knots each. Tensioning these sides creates an equilateral triangle. 13node gs.png
Circle , hexagon One end is nailed down and a stylus is attached to the desired location. Then you lead the stylus around once on the taut rope. With the set radius, the arc can easily be divided into a hexagon.

Individual evidence

  1. ↑ Archived copy ( Memento from March 31, 2010 in the Internet Archive )
  2. ↑ Archived copy ( Memento from October 23, 2008 in the Internet Archive )
  3. ↑ Archived copy ( Memento from October 23, 2008 in the Internet Archive )

Web links