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Difference between revisions of "Constructible number"

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We say that a nonnegative [[real number]] <math>x</math> is '''constructible''' if a segment of length <math>x</math> can be constructed with a [[straight edge]] and [[compass]] starting with a segment of length <math>1</math>.
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We say that a [[real number]] <math>x</math> is '''constructible''' if a segment of length <math>|x|</math> can be constructed with a [[straight edge]] and [[compass]] starting with a segment of length <math>1</math>.
  
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We say that a complex number <math>z = x+yi</math> is constructible if <math>|x|</math> and <math>|y|</math> are both constructible (we also say that the point <math>(x,y)</math> is constructible). It is easy to show that <math>x+yi</math> is constructible iff the point <math>(x,y)</math> can be constructed with a [[straight edge]] and [[compass]] in the [[cartesian plane]] starting with the points <math>(0,0)</math> and <math>(1,0)</math>.
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We say that a complex number <math>z = x+yi</math> is constructible if <math>x</math> and <math>y</math> are both constructible (we also say that the point <math>(x,y)</math> is constructible). It is easy to show that <math>x+yi</math> is constructible iff the point <math>(x,y)</math> can be constructed with a [[straight edge]] and [[compass]] in the [[cartesian plane]] starting with the points <math>(0,0)</math> and <math>(1,0)</math>.
  
 
[[Category:Geometry]]
 
[[Category:Geometry]]
 
[[Category:Field theory]]
 
[[Category:Field theory]]

Revision as of 21:44, 20 August 2009

We say that a real number $x$ is constructible if a segment of length $|x|$ can be constructed with a straight edge and compass starting with a segment of length $1$.

We say that a complex number $z = x+yi$ is constructible if $x$ and $y$ are both constructible (we also say that the point $(x,y)$ is constructible). It is easy to show that $x+yi$ is constructible iff the point $(x,y)$ can be constructed with a straight edge and compass in the cartesian plane starting with the points $(0,0)$ and $(1,0)$.

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