Re: How is amethyst formed?

Hmmm....a research project will require references, so let me start with 
a couple of books you should go to.  First, amethyst is a particular color
phase of quartz, and why it is that color you will find explained in
"The Physics and Chemistry of Color" by Kurt Nassau, pg. 192. As to the
formation of quartz in general and amethyst in particular, a good intro-
ductory book is George Robinson's "Minerals". 

Basically, amethyst forms fairly deep in the earth's crust from what are
called hydrothermal solutions that arise from cooling magma. The word 
"hydrothermal" means that the fluid contains considerable water and is hot, 
but by no means does this mean it is anything like the what you know as 
water, because it is at extremely high pressure and generally loaded with 
dissolved sulfides, silica, and so forth. You will find more about this
in Robinson's book.

Amethyst is purple because the quartz contains an amount of iron in it
as an impurity. This creates a defect that, upon exposure to certain kinds
of radiation, gives the purple color. The source of the irradiation is
radioactive atoms, chiefly uranium, that are also dissolved into the hydro-
thermal solution (here's a good question for you to answer in your project:
why is uranium concentrated into the hydrothermal solution?). There is more
detail in Nassau's book.