3000-525 BC

Agricultural revolutionDevelopment of the fundamental math of

surveying,engineering and commerceMath started with arithmetic (algebra) and

measurement (geometry)

Chinese and Indians

Difficult to date discoveriesUsed perishable media like bark and

bambooBabylonians used baked clay tabletsEgyptians used stone and papyrus

Babylonians

Tablets were a few square inches to the size of a text

400 math tablets foundHigh level of computation200 tablets were math tables

Math Tables

Table of reciprocalsTable of squaresTable of cubesBusiness transactionsFarm activitiesHigh level of computational ability

Babylonian algebra

Solved quadratic equationsApproximated square root of 2

Babylonian Geometry

Chief feature its algebraic characterDivided circle into 360 equal partsRelated to measurementArea of a rectangleArea of a right triangleArea of an isosceles triangleVolume of a rectangular solid

Babylonian tablet

Plimpton 322

#322 in Plimpton collection at Columbia University

Piece broken off3 columns of figuresPythagorean tripleIntegral-sided right triangle

Summary

Babylonians were table makers, computers of high level,and stronger in Algebra than in Geometry

Egypt

Papyrus

Egypt

Remained secluded and naturally protected from foreign invasion

Math in Egypt never reached the level attained by Babylonians

Nile relatively peacefulEgypt not on caravan routesMore known due to preservation in tombs

Moscow Papyrus 1850BC

Moscow Papyrus 1850BC

18 feet long and 3 inches highMath text containing 25 problems

Rhind papyrus

http://www.thebritishmuseum.ac.uk/

Rhind papyrus 1650 BC

Math text in the form of a practical handbook

85 problems18 feet long and 13 inches highApplications of math to practical problems

Egyptian Arithmetic and Algebra

All 110 problems on Moscow and Rhind papyri are numerical

Method of multiplying and dividingRule of False position

Egyptian Geometry

26 problems were geometricMeasurement computing land area and

granary volumesArea of trianglesNo evidence that the Egyptians were

aware of the Pythagorean Theorem !