A knotted cord was a primitive

surveyor Surveying or land surveying is the technique, profession, art, and science of determining the terrestrial two-dimensional or three-dimensional positions of points and the distances and angles between them. A land surveying professional is ca ...

's tool for measuring distances. It is a length of cord with knots at regular intervals. They were eventually replaced by surveyor's chains, which being made of metal were less prone to stretching and thus were more accurate and consistent. Knotted cords were used by many ancient cultures. The Greek schoenus is referred to as a rope used to measure land. Ropes generally became cables and chains with

Pythagoras Pythagoras of Samos ( grc, Πυθαγόρας ὁ Σάμιος, Pythagóras ho Sámios, Pythagoras the Samos, Samian, or simply ; in Ionian Greek; ) was an ancient Ionians, Ionian Ancient Greek philosophy, Greek philosopher and the eponymou ...

making the Greek agros a chain of 10 stadia equal to a nautical mile c 540 BC. The Romans used a waxed cord for measuring distances. A knotted cord 12 lengths long (the units do not matter) closed into a loop can be used to lay out a

right angle In geometry and trigonometry, a right angle is an angle of exactly 90 Degree (angle), degrees or radians corresponding to a quarter turn (geometry), turn. If a Line (mathematics)#Ray, ray is placed so that its endpoint is on a line and the ad ...

by forming the loop of cord into a 3–4–5 triangle. This could be used for laying out the corner of a field or a building foundation, for instance.

Ancient Egypt

Knotted cords were used by

rope stretcher In ancient Egypt, a rope stretcher (or harpedonaptai) was a surveyor who measured real property demarcations and foundations using knotted cords, stretched so the rope did not sag. The practice is depicted in tomb paintings of the Theban Necropol ...

s, royal

s who

measure Measure may refer to: * Measurement, the assignment of a number to a characteristic of an object or event Law * Ballot measure, proposed legislation in the United States * Church of England Measure, legislation of the Church of England * Mea ...

d out the sides of fields (

Egyptian Egyptian describes something of, from, or related to Egypt. Egyptian or Egyptians may refer to: Nations and ethnic groups * Egyptians, a national group in North Africa ** Egyptian culture, a complex and stable culture with thousands of years of ...

''3ht''). The knotted cords (Egyptian ''ht'') were 100 royal

cubit The cubit is an ancient unit of length based on the distance from the elbow to the tip of the middle finger. It was primarily associated with the Sumerians, Egyptians, and Israelites. The term ''cubit'' is found in the Bible regarding No ...

s in length, with a knot every ''hayt'' or 10 royal cubits. The rope stretchers stretched the rope in order to take the sag out, as well as to keep the measures uniform. Since land in ancient Egypt was measured using several different units, there would have been knotted cords with the knots spaced in each unit. Among these were the ''mh t3'' or land cubits, remen royal cubits, rods or ''ha3t'', generally the lengths in multiples of 100 units. The longest measured length listed in the Rhind Mathematical Papyrus is a circumference of about a Roman mile with a diameter of 9 khet. Despite many popular claims, there is no surviving evidence that the 3-4-5 triangle, and by implication the

Pythagoras' theorem In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposite ...

, was used in Ancient Egypt to lay out right angles, such as for the

pyramid A pyramid (from el, πυραμίς ') is a structure whose outer surfaces are triangular and converge to a single step at the top, making the shape roughly a pyramid in the geometric sense. The base of a pyramid can be trilateral, quadrilat ...

s. The historian

Moritz Cantor Moritz Benedikt Cantor (23 August 1829 – 10 April 1920) was a German historian of mathematics. Biography Cantor was born at Mannheim. He came from a Sephardi Jewish family that had emigrated to the Netherlands from Portugal Portugal, off ...

first made the conjecture in 1882. Right angles were certainly laid out accurately in Ancient Egypt; their surveyors did use knotted cords for measurement;

Plutarch Plutarch (; grc-gre, Πλούταρχος, ''Ploútarchos''; ; – after AD 119) was a Greek Middle Platonist philosopher, historian, biographer, essayist, and priest at the Temple of Apollo in Delphi. He is known primarily for his ''P ...

recorded in '' Isis and Osiris'' (around 100 AD) that the Egyptians admired the 3-4-5 triangle; and the

Berlin Papyrus 6619 The Berlin Papyrus 6619, simply called the Berlin Papyrus when the context makes it clear, is one of the primary sources of ancient Egyptian mathematics. One of the two mathematics problems on the Papyrus may suggest that the ancient Egyptians kn ...

from the Middle Kingdom (before 1700 BC) made statements that suggest knowledge of Pythagoras' theorem. The 3-4-5 triangle was used because it is the smallest right-angled triangle with whole-numbered side lengths. However, no Egyptian text before 300 BC actually mentions the use of the theorem to find the length of a triangle's sides. Therefore, the historian of mathematics Roger Cooke published that the Ancient Egyptians probably did know the Pythagorean theorem, but concludes that "there is no evidence that they used it to construct right angles".

References

{{reflist Surveying

Ancient Egypt

See also

References