3000-525 bc zagricultural revolution zdevelopment of the fundamental math of surveying,engineering...
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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 !