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### 26 Cards in this Set

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 Incommensurable --The side and Diagonal of a Square are non measureable --Pythagoreans fell apart because of this discovery. It proves that everything they discovered was wrong. Squaring the Circle Greek Pythagoras -went to Egypt to study -came back to Greece but left becuase it was being run by a tyrant -went to Italy -sfter his death there were colonied of pythagoreans ---liked music (chords) --harmony as an arithmatical phenomenon ---whole #'s are the underlying principle of the whole universe Greek Social Structure --High Class Aristocracy --Did math just to do it --Indepently wealthy mathemat. -Thales & Pythagoras-famous Thales & Pythagoras lived during the... Golden Era of Greece Positionsal Notation Babylonian Egyptian System for Numerals -non positional -symbols for 1, 10, etc.. --somewhat less efficient than Bab. --Treatment of fractions arose --there were symbols for the recipricals of whole numbers but not general ones --general fractions were writtne as sums of recipricals Descibe the Pythagorean Method of Geometrical Proof. Why was the discovery of incommensurabel magnitudes such a blow to this method? Given: 2 triangles with the same height and equal bases have the same area Prove: 2 triangles with the same height have areas proportional to their bases --dissect both triangles into triangles of the same h & b U --U divides both evenly --You couldn't always find U. Method of Mediation & Duplation . Interpolation Methods Babylonians Incommensurable Proves that square root of 2 is irratioansl Shook mathematics foundations Babylonian Social Structure --Figure Ruled --Scribes change and become less subscribed to preist began to show off --1st of their kind --used more algerbraic mathe --dissection Pythagorean Theorem Babylonians invented Geometric Algebra Greek Thales --1st person to have theore,s attributed to him --Congruence thms (ship rods) --Similarity thms-Tri. Shadows The Mathematics of Astronomy Babylonian Babylonians --organizers --efficiency-wanting to make things fit together --loved making tables -tables of pythagorean triples, square roots, powers, conversion, & astronomical The mathematics of Music Greek Eudoxus -ratio between two lengths as whole #'s even if they weren't -tried to save math -method of exhaustion -almost came up with concept of a limit Duplation and Mediation Egyptian Doubling the Cube Given a cube construct another cube whose volume is twice that of the original The method of False position Babylonian Surveying Egyptian Figurate Numbers Greek Egyptian social structure --Religious --Centralized State --Scribes --Utilitarian --Temples and Pyramids --Math dealt with Practical Matters --Started when they figured out hiw ti survey land due to the flooding of the Nile. Impact of Geograhy of Babylonia on the development of Math. X-Roads central to all civilazations of the time --Irrigation Canals (Geometry) --Plots of land irregular shape learned disection --Taxation and Commerce-1st --Interest calculations --Astronomy with Agri. Cycle --Clay influenced written form restrictions. --Number base 60