Math 300 Test 1
Terms
undefined, object
copy deck
- Incommensurable
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Proves that square root of 2 is irratioansl
Shook mathematics foundations
- Squaring the Circle
- Greek
- Pythagoras
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-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
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-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
- 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
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-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
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--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.
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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