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26 Cards in this Set
 Front
 Back
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 & Pythagorasfamous 

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 thmsTri. Shadows 

The Mathematics of Astronomy

Babylonian


Babylonians

organizers
efficiencywanting 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.

XRoads central to all civilazations of the time
Irrigation Canals (Geometry) Plots of land irregular shape learned disection Taxation and Commerce1st Interest calculations Astronomy with Agri. Cycle Clay influenced written form restrictions. Number base 60 