Used in math but not a number. I can be golden, inverse, or direct. I remain constant when my parts change size.

Present when you speak but never when you're silent. Broken without being touched, and kept without being held. Given freely but once broken, nearly impossible to repair. Kings and beggars possess me equally, yet it's measured differently for each.

I ate the one after the next - who was three by three, The count of the rainbow's arcs, The steps on music's marks.

I am a thousand threads of what is possible. When it is threaded into string, my many becomes one, undeniable possibility and the rest impossible. I am always ahead, but my opposite is always behind. What am I?

A face, aloof, upon my head, And feathers on my tail. My name: the fraction I am worth. Used oft to label hail.