What rock group has four men who don't sing?

A stone of green, both smooth and bright, more prized than gold in ancient sight. From China’s courts to the Maya’s lands, I passed through many a ruler’s hands.

I am an exercise, I am a means of execution, I am a temporary access. What am I?

I won the battle, of course I had to use my wit, Since I had nothing else, but now the war is over and I'm spent, I lost a lot of friends along the way, I'm sad that they're gone, But now I have to accept the reward, make it worthwhile, and live on.

Fibonacci saw my beauty as a point on a spiral of constant angle. Newton knew that the bible loved my two digits like wings on an angel.