The unit circle
Feb. 15th, 2012 04:44 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
chickenfeetOccasionally I have this urge to play around with mathematics again. Usually it's nothing too hard as it's over 35 years since I did mathematics seriously. One thing I've been fooling around with is the representation of the roots of x^n-1=0 on the unit circle in the complex plane. This is is one of those lovely bits of mathematics which is both simple and very profound.
For example, consider the relationship between the solutions of x^12-1=0 and x^3-1=0.
If one takes the representations of the latter on the complex plane, one can get to the former by either of two methods
(a) Make three rotations of π/6 in either direction
(b) Make a reflection in x=0 and then make a single rotation by π/6
Pretty cool really.
For example, consider the relationship between the solutions of x^12-1=0 and x^3-1=0.
If one takes the representations of the latter on the complex plane, one can get to the former by either of two methods
(a) Make three rotations of π/6 in either direction
(b) Make a reflection in x=0 and then make a single rotation by π/6
Pretty cool really.
no subject
Date: 2012-02-15 10:07 pm (UTC)