Roots of Unity Application
Show that $ \sin\left(\dfrac{\pi}{n}\right) \cdot \sin\left(\dfrac{2\pi}{n}\right) … \sin\left(\dfrac{(n-1)\pi}{n}\right) = \dfrac{n}{2^{n-1}} $...
roots of unity
Regular Heptagon puzzle walk through
There are too many wildly different an interesting ways to attack this problem to not document.
Roots of Unity: Pursuing Extra Roots
Background: This piece all started with my last post thinking about equalities of the form $ \cos (nx) = \cos(mx) $
Trigonometry Walk Through Three Ways
I saw the following trigonometry problem the other day and decided it would make another good walk through since it hits several themes I’ve been exploring.
Roots of Unity and Cyclotomic Polynomials
Most of the treatments of this topic are fairly grounded in Abstract Algebra and for this post I wanted to record my hopefully simpler conceptual framework.