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 
.
