Okay. I wanna find strongholds so bad but I only got two eyes of ender. How do?
Like this.
Imagine from birds-eye-view that the Minecraft world is a big graph of X and Y. Oh wait, it is. So for all subsequent coordinate geometry, use the X and Z values given to you within Minecraft. I will refer to Z as Y.
Let A be the point at which an Eye of Ender is thrown, and let B be the point at which it lands. Do this two times, on level ground. Let D be the distance between A1 and A2
Let S mark the spot where your stronghold is.
Let vectors
V1=B1-A1
V2=B2-A2
and
D=A2-A1
We seek S, where the relationship can be defined as
S=A1+k1V1 where k1 is unknown.
We can substitute to give us
A1+k1V1=A2+k2V2
Therefore D=[V1V2][k1,k2]
Now it gets tricky.
[V1xV2x,V1yV2y]x[k1,k2]=[A2x-A1x,A2y-A1y]
so we can find k1
k1=(A2x-A1x)V2y-(A2y-A1y)V2x / V1xV2y-V1yV2x
now we can dump that into our original X equation to get our solution!
S=A1+{(DxV2y-DyV2x) / (V1xV2y-V1yV2x)}V1
It's late, so I won't be going through the trigonometry required to locate the other two strongholds quite yet, so stay tuned!
(The moral of the story, I really needed a bloody subscript button on the Rich Text editor)