Talk:Constructible number

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Mathematics rating:
Start Class
Mid Importance
 Field: Number theory

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

You are correct. But 15 is the product of the two Fermat primes 3 and 5. 7 is neither a Fermat prime nor the product of 2^n and one or more Fermat primes (the only known ones being 3, 5, 17, 257 and 65,537). I've edited the main article accordingly. --Glenn L (talk) 05:50, 13 April 2010 (UTC)

Unclear definition[edit]

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)

Fourth Root of 2[edit]

It's possible that you can construct line ABC which AC=2^(1/4)*AB. 220.255.2.63 (talk) 03:48, 30 October 2011 (UTC)