Twelve-knot cord

The twelve-knot cord and the merchet were measuring instruments for the field measurement of angles in ancient Egypt. The twelve-knot cord was used for horizontal angle measurements and the merchet for vertical angle measurements. The angles were measured in setback (as a slope). The unit of measurement is the Seked . Both measuring instruments are based on the reverse of the Pythagorean theorem. In the original version, the twelve-knot cord is a closed cord (ring) with a division into 12 royal cells ( Meh ). The cord is stretched as the first Pythagorean triple . The short cathetus is used as the standard base. The usual division of 7 hand-widths per royal place is made on the three royal places of the base. The return is read from this division. Four hand widths are a seced. By extending the base beyond the length of the adjacent cathetus (three royal cells), it was possible to measure the angle of inclination over the Seked. ${\ displaystyle (3,4,5)}$ ${\ displaystyle 5 + 1/4}$

normal clamping

inverse clamping

In contrast to the twelve-knot cord, a computing rope is used to illustrate simple numerical and geometrical problems and is not a measuring instrument.

Rope tensioner in ancient Egypt

When temples were founded in ancient Egypt , the priestly professional group of the harpedonapten used measuring cords. Many books state that they used twelve-knot cords to construct angles.

The starting point for the assumption was the first volume of Moritz Cantor's "Lectures on the History of Mathematics". Cantor writes there: “Let us think, currently without any justification, that the Egyptians had known that the three sides of length 3, 4, 5 connected to form a triangle formed one with a right angle between the two smaller sides , ... "

Web links

R. Moosbrugger: Cord measurement: simple-minded - simple. ( Memento of March 5, 2016 in the Internet Archive ). Society for the History of Geodesy 2006.

literature

Moritz Cantor : About the oldest Indian mathematics. Archive of Mathematics and Physics. 3rd series, Volume 8 (1905) pp. 63-72.

Individual evidence

^ Frank Müller-Römer: The construction of the pyramids in Ancient Egypt, Herbert Utz Verlag, 2011, p. 133
↑ Eli Maor : The Pythagorean Theorem. A 4,000-year history. University Presses of CA, 2007, ISBN 978-0-691-12526-8 .
^ Moritz Cantor : Lectures on the history of mathematics. First volume. From the oldest times to the year 1200 AD. 2nd edition. P. 64.

[1] Frank Müller-Römer: The construction of the pyramids in Ancient Egypt, Herbert Utz Verlag, 2011, p. 133

[2] Eli Maor : The Pythagorean Theorem. A 4,000-year history. University Presses of CA, 2007, ISBN 978-0-691-12526-8 .

[3] Moritz Cantor : Lectures on the history of mathematics. First volume. From the oldest times to the year 1200 AD. 2nd edition. P. 64.