Prove that Euclidean area is in square units

  • Thread starter kotreny
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  • #1
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Main Question or Discussion Point

Where is it proven that the unit of area in Euclidean geometry must be a square with side=1? Or is it an axiom? Why not triangles or circles to represent area?
 

Answers and Replies

  • #2
907
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That's the way it is defined. We use a square because it's most convenient.
 
  • #3
HallsofIvy
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Just seconding hamster143- the unit of area is defined as the area of a square one unit length on a side. Then we prove the formulas for areas of other figures in terms of that.
 

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