Talk:Constructible number

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Mathematics rating:	Start Class	Mid Priority	Field: Number theory
Please update this rating as the article progresses, or if the rating is inaccurate. Click to show/hide comments. Please add to or update the comments to suggest improvements to the article. Needs references. Geometry guy 22:42, 16 June 2007 (UTC)

In the table at the end, in the row about trisecting an angle, the"counterexample" does not match the "associated set of numbers", i.e. it is not obviously a counterexample. Could one of the authors correct this?

e^(2πi) / 7 is not constructible, because 7 is not a Fermat prime

This can lead to confusion, because its not a necesarely condition that n should be a fermat prime in order to a regular n-gon to be constructible.

A regular 15-gon is constructible, cause cos(2pi/15) is constructible, but 15 is not a fermat prime

[edit] Unclear definition

What is a "fixed" coordinate system? Our article on coordinate systems lists many systems. Could we fix the system to bipolar coordinates? Even if we have the standard Cartesian system, how does that impact the rules for what is allowed in construction with Straightjacket & Compassion? And next, what does it mean for a point to be constructible from the axes? It is all very unclear.

Why not simply define a constructible point as a point that can be constructed with S&C, starting from two given distinct points. Then we can define constructible complex numbers as those whose points in the complex plane are constructible when the given starter points are (0,0) and (1,0).

Comments?  --Lambiam 13:03, 31 January 2008 (UTC)