Yesterday I've noticed some relationships with cosine and square root. Anything interesting about it?
I was trying to find the smallest width on an hexagon with radius $1.0$ and I noticed that I could get it both by $\sqrt 3$ and the or two times the cosine of $30^\circ$.
I wondered if there would be more matches and so I notice these even though might look silly...
$2 \times \cos 90^\circ = \sqrt 0$
$2 \times \cos 60^\circ = \sqrt 1$
$2 \times \cos 45^\circ = \sqrt 2$
$2 \times \cos 30^\circ = \sqrt 3$
$2 \times \cos 0^\circ = \sqrt 4$
Is there anything interesting to know about these?