Practical geometry and land surveying

What it is

Calculation of field areas, granary volumes and canal gradients using arithmetic rules, knotted cords and set squares. The field plans of Lagash and the Rhind Papyrus show a geometry oriented towards taxation and public works.

The Rhind Papyrus (c. 1550 BCE) copies a Middle Kingdom original; the Plimpton 322 tablet (c. 1800 BCE) contains Pythagorean triples.

What it led to

• Cadastre and taxation proportional to cultivated area
• Redistribution of land after each Nile flood, the legendary origin of geometry according to Herodotus
• Pyramids and ziggurats aligned with precision to within arcminutes
• Pythagorean triples and the empirical basis of later Greek geometry

Built on

• Sexagesimal number systemc. 3000 BCE
• Square, plumb bob and A-frame level of Egyptian buildersc. 1300 BCE
• Sexagesimal system
• Measuring rope

Made possible

• Grid-planned cityc. 2600 BCE
• Great Pyramid: large-scale ashlar engineeringc. 2560 BCE
• Navigable canal and state irrigation networkc. 2400 BCE
• Topographic map and city planc. 2300 BCE
• Gudea of Lagash's graduated rulec. 2130 BCE
• Sundial / shadow clockc. 1500 BCE
• Euclidean axiomatic geometryc. 300 BCE
• Roman gromac. 150 BCE
• Great Pyramid of Giza
• Cadastral map
• Euclidean geometry

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