For some I'm an arm, A wooden limb; a chair for a pigeon; For others I'm a military force, A strategic subdivision; I am also choices, Decisions stretching to the unknown; Or a section of a business, That has expanded and grown.

My first two is the name for a circle's fundamental ratio, my last two are the symbol for an element, used to make signs stand out at night. Together, I'm a synonym for yearn.

One part of my name is sour, the other has bite, I’m more social than ready to fight.

A smoke, a hair so sparse you can see right through me. A ghost, a flare in foresty swamps leading you astray.

I come from an egg, yet the egg came before me.