Difference between revisions of "Constructible number"
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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>. | 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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Revision as of 22:26, 20 August 2009
We say that a nonnegative 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 .