# Difference between revisions of "Constructible number"

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− | We say that a | + | 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>. |

− | We say that a complex number <math>z = x+yi</math> is constructible if <math> | + | 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 is **constructible** if a segment of length can be constructed with a straight edge and compass starting with a segment of length .

We say that a complex number is constructible if and are both constructible (we also say that the point is constructible). It is easy to show that is constructible iff the point can be constructed with a straight edge and compass in the cartesian plane starting with the points and .