Difference between revisions of "Comparison between the three geometries Exploration"

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{| border="1"
 
{| border="1"
 
|+ Comparing and Contrasting the 3 geometries
 
|+ Comparing and Contrasting the 3 geometries
! Question !! Euclidean Geometry !! Sperical Geometry !! Hyperbolic Geometry
+
! Question !!     Euclidean Geometry     !!     Sperical Geometry     !!     Hyperbolic Geometry  
 
|-
 
|-
 
! Geodesics
 
! Geodesics
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! Parallel Lines
 
! Parallel Lines
 
(How many, if any?)
 
(How many, if any?)
 +
 
|
 
|
 
|
 
|
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! Polygons (Do we get new ones?  
 
! Polygons (Do we get new ones?  
 
Which ones don’t exist?)
 
Which ones don’t exist?)
 +
 
|
 
|
 
|
 
|
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|-
 
|-
 
! Sum of the angles in a triangle.
 
! Sum of the angles in a triangle.
 +
 
|
 
|
 
|
 
|
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! Regular tessellations
 
! Regular tessellations
 
(How many different ones are there?)
 
(How many different ones are there?)
 +
 
|
 
|
 
|
 
|
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! Semi-regular tessellations.
 
! Semi-regular tessellations.
 
(How many different ones are there?)
 
(How many different ones are there?)
 +
  
 
|
 
|
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! Isometries
 
! Isometries
 
(Which ones have we encountered?)
 
(Which ones have we encountered?)
 +
 
|
 
|
 
|
 
|
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! Area of a triangle.
 
! Area of a triangle.
 
(What is the formula?)
 
(What is the formula?)
 +
 
|
 
|
 
|
 
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! Escher’s work based on each geometry.
 
! Escher’s work based on each geometry.
 
(How extensively did he work on each of the geometries?)
 
(How extensively did he work on each of the geometries?)
 +
 
|
 
|
 
|
 
|

Revision as of 11:22, 24 July 2007


Time-35.svg

Objective: Compare and contrast Eclidean, spherical and hyperbolic geometry


Fill in the following table with as much detail as you can.


Comparing and Contrasting the 3 geometries
Question Euclidean Geometry Sperical Geometry Hyperbolic Geometry
Geodesics

(What do they look like?)

Parallel Lines

(How many, if any?)

Polygons (Do we get new ones?

Which ones don’t exist?)

Sum of the angles in a triangle.
Regular tessellations

(How many different ones are there?)

Semi-regular tessellations.

(How many different ones are there?)


Isometries

(Which ones have we encountered?)

Area of a triangle.

(What is the formula?)

Escher’s work based on each geometry.

(How extensively did he work on each of the geometries?)