Now that I know the location of one stronghold, can someone walk me through the calculation to find the other two? According to the wiki, the strongholds form at equilateral triangles from each other.

The stronghold I found is at x=-464, z= -650. The slope of the line from origin to the stronghold coordinates is 1.4, and the length of the line from origin to stronghold is 798. Now I've exhausted my memory of math. How do I figure out the 60 degree rotations for that line?

Nope, it doesn't work that way. The strongholds are at 120 degree angles from a point, but that point is not your spawn, and it's not the origin. Also, they're at different radii. It's rare, but possible to spawn right on top of one.

Nope, it doesn't work that way. The strongholds are at 120 degree angles from a point, but that point is not your spawn, and it's not the origin. Also, they're at different radii. It's rare, but possible to spawn right on top of one.

Much easier to just use AMIDST.

Wiki says it is from the origin. (Three points that don't share a line are always 120 degrees apart measured from some point. That wouldn't really be any help at all unless it was from somewhere specific.)

The slope m of a line is related to its angle φ (theta) by the tangent function:

m = tan θ
φ = arctan m

To find the angle of your line, we start with its slope of 1.4, and find the arctangent of that which is approx. 54.4 degrees. Then we add that to 120 and 240 to find the angles for the other lines we need: 174.4 and 294.4. Then we take the tangent of each of those angles to turn it back into a slope:

tan 174.4 = -0.09
tan 294.4 = -2.2

Those are the slopes of the two lines you'll need to follow. You ought to be able to figure out which way from origin based on the first stronghold's location. They should be found at a distance of between 640 and 1152 blocks from origin.

EDIT: no that's wrong. I don't know what I did there but something isn't right. I'll have to have a look at it sometime later.

Okay for starters, the positive direction for the z-coordinate is south, so if you want to convert it to an x/y system you need to flip the z-coordinate and call it y. So the slope of your line is actually -1.4,

So arctan -1.4 = about -54.5 degrees (measured anticlockwise from due east, so a negative angle would be clockwise, or towards the southeast.) But the coordinate is in the northwest, so we flip that around 180 degrees and end up with 125.5.

So the other two angles we're looking at are 5.5 and 245.5 degrees.

tan 5.5 = 0.0963
tan 245.5 = 2.1943

So yeah, basically what I said before, except inverted. I don't know why it didn't look right when I graphed it the first time.

That's about what it should look like. Remember when you're searching for them north is negative in the z-direction. So your first stronghold was northwest on the red line. The other two should be southwest on the green line and almost due east on the blue line.

Suppose I ought to have scaled it out before I took the screenshot. Just increase it by a factor of ten, the labels should be 1000 and 2000 instead of 100 and 200. Each mark on the grid is 200 blocks instead of 20.

If the strongholds truly do spawn in equal points around the origin (0,0). You should be able to apply a 120 degree rotation to the coordinates of the one you already found. Don't know the formula, but it looks like IronMagus more or less already did that.

At least thats what I'm thinking. Can't remember too much from Geometry.

I dont know what Im doing wrong, the first stronghold is at x=-830 y=60 z=-124 I've calculated it several times and i always get the same answer. But my coords are not right, there is no end portal or stronghold at my coords. Using the previously mentioned coords could someone tell me where my other two strongholds are?

Sorry to re-animate this thread, but I googled my way across it, and am currently facing the same issue. I've located one Stronghold, but need the other two.

The issue is: when a map spawns, does a random distance from Origin get selected, and then used to place all three strongholds? Or are the directions-from-Origin (vectors) selected, and then each stronghold gets a random distance that isn't shared.

That's what I can't work out.

If we assume that all strongholds on a map spawn with a shared distance from the (0,0) origin of the map [in other words, if you can draw a perfect circle through all 3 strongholds, and the center of the circle sits right on (0,0)], then the math is easy.

Let's call Xa and Za your first stronghold's coordinates.

To get stronghold #2, the math is:
Xb = (Xa * ( - 0.5)) - ( Za * (0.866)) <---- Remember the negative sign on the 0.5!
Zb = (Xa * ( 0.866)) + (Za * ( -0.5)) <---- Remember the negative sign on the 0.5!

To get stronghold #3, the math is:
Xc = (Xa * ( - 0.5)) - ( Za * ( - 0.866)) <---- Remember the negative sign on the 0.5 AND 0.866!
Zc = (Xa * ( - 0.866)) + (Za * ( -0.5)) <---- Remember the negative sign on the 0.5 AND 0.866!

So, for me:
Stronghold 1 is at Xa = 518, and Za = -165.

and my math, assuming equal distance, says:
Xb = -115, and Zb = -532
Xc = 402, and Zc = -366

But!!!
If they don't share a distance from center, I'm toast. That just gives me a direction to walk. Which means I have a line that it should have spawned on, so I'll have to go toss ender eyes, see where the flight intersects with my math-line, and find out.

I'll look for them this week. If I find them, I'll do the math and answer if Stronghold distances from center are equal or not.

They are not equidistant from origin. Only the angles between them (measured from origin) are equal, the distance is random, between 640 and 1152 blocks.

People have trouble with this because there's no official documentation, and the grammar used on the wiki is able to be parsed in two different ways. The degrees aren't my issue, the lack of clarity about vector length was.

IronMagnus: Thanks for the heads up. Like I said, it wasn't clear if it was random per Stronghold or per Map. Ok, well, at least this means I know what line to set myself perpendicular to for Eye-throwing, and a convenient starting estimate on distance.

We blundered across the first Stronghold on my server, because the arbitrary spot we found that was big enough and flat enough for our shared village turned out to be 160 blocks due south of the End Portal. Completely random luck.

The stronghold I found is at x=-464, z= -650. The slope of the line from origin to the stronghold coordinates is 1.4, and the length of the line from origin to stronghold is 798. Now I've exhausted my memory of math. How do I figure out the 60 degree rotations for that line?

I am ninja'd far too often.

Much easier to just use AMIDST.

Wiki says it is from the origin. (Three points that don't share a line are

always120 degrees apart measured fromsomepoint. That wouldn't really be any help at all unless it was from somewhere specific.)The slope m of a line is related to its angle φ (theta) by the tangent function:

m = tan θ

φ = arctan m

To find the angle of your line, we start with its slope of 1.4, and find the arctangent of that which is approx. 54.4 degrees. Then we add that to 120 and 240 to find the angles for the other lines we need: 174.4 and 294.4. Then we take the tangent of each of those angles to turn it back into a slope:

tan 174.4 = -0.09

tan 294.4 = -2.2

Those are the slopes of the two lines you'll need to follow. You ought to be able to figure out which way from origin based on the first stronghold's location. They should be found at a distance of between 640 and 1152 blocks from origin.

EDIT: no that's wrong. I don't know what I did there but something isn't right. I'll have to have a look at it sometime later.

Okay for starters, the positive direction for the z-coordinate is south, so if you want to convert it to an x/y system you need to flip the z-coordinate and call it y. So the slope of your line is actually -1.4,

So arctan -1.4 = about -54.5 degrees (measured anticlockwise from due east, so a negative angle would be clockwise, or towards the southeast.) But the coordinate is in the northwest, so we flip that around 180 degrees and end up with 125.5.

So the other two angles we're looking at are 5.5 and 245.5 degrees.

tan 5.5 = 0.0963

tan 245.5 = 2.1943

So yeah, basically what I said before, except inverted. I don't know why it didn't look right when I graphed it the first time.

That's about what it should look like. Remember when you're searching for them north is negative in the z-direction. So your first stronghold was northwest on the red line. The other two should be southwest on the green line and almost due east on the blue line.

Suppose I ought to have scaled it out before I took the screenshot. Just increase it by a factor of ten, the labels should be 1000 and 2000 instead of 100 and 200. Each mark on the grid is 200 blocks instead of 20.

Village Mechanics: A not-so-brief guide - Update 2017! Now with 1.8 breeding mechanics! Long-overdue trading info, coming soon!

You think magic isn't real? Consider this: for every person, there is a sentence -- a series of words -- which has the power to destroy them.

Message me creative ideas to add to my underground base!

Done. I edited it into my other post.

Village Mechanics: A not-so-brief guide - Update 2017! Now with 1.8 breeding mechanics! Long-overdue trading info, coming soon!

You think magic isn't real? Consider this: for every person, there is a sentence -- a series of words -- which has the power to destroy them.

Lol how would someone be offended.

Also lots of cursing. 12 confirmed

At least thats what I'm thinking. Can't remember too much from Geometry.

"Look at me still talking when there's science to do. When I look out there it makes me glad I'm not you."

Nope, still just the three. At least according to the wiki. Where'd you hear otherwise?

Village Mechanics: A not-so-brief guide - Update 2017! Now with 1.8 breeding mechanics! Long-overdue trading info, coming soon!

You think magic isn't real? Consider this: for every person, there is a sentence -- a series of words -- which has the power to destroy them.

The issue is:when a map spawns, does a random distance from Origin get selected, and then used to place all three strongholds? Or are the directions-from-Origin (vectors) selected, and then each stronghold gets a random distance that isn't shared.That's what I can't work out.

If we assume that all strongholds on a map spawn with a shared distancefrom the (0,0) origin of the map [in other words, if you can draw a perfect circle through all 3 strongholds, and the center of the circle sits right on (0,0)], then the math is easy.Let's call Xa and Za your first stronghold's coordinates.

To get stronghold #2, the math is:

Xb = (Xa * ( - 0.5)) - ( Za * (0.866)) <---- Remember the negative sign on the 0.5!

Zb = (Xa * ( 0.866)) + (Za * ( -0.5)) <---- Remember the negative sign on the 0.5!

To get stronghold #3, the math is:

Xc = (Xa * ( - 0.5)) - ( Za * ( - 0.866)) <---- Remember the negative sign on the 0.5 AND 0.866!

Zc = (Xa * ( - 0.866)) + (Za * ( -0.5)) <---- Remember the negative sign on the 0.5 AND 0.866!

So, for me:

Stronghold 1 is at Xa = 518, and Za = -165.

and my math, assuming equal distance, says:

Xb = -115, and Zb = -532

Xc = 402, and Zc = -366

But!!!If they don't share a distance from center, I'm toast. That just gives me a direction to walk. Which means I have a line that it should have spawned on, so I'll have to go toss ender eyes, see where the flight intersects with my math-line, and find out.

I'll look for them this week. If I find them, I'll do the math and answer if Stronghold distances from center are equal or not.

(I don't think they are. )

IronMagnus: Thanks for the heads up. Like I said, it wasn't clear if it was random per Stronghold or per Map. Ok, well, at least this means I know what line to set myself perpendicular to for Eye-throwing, and a convenient starting estimate on distance.

We blundered across the first Stronghold on my server, because the arbitrary spot we found that was big enough and flat enough for our shared village turned out to be 160 blocks due south of the End Portal. Completely random luck.

It's Magus. No "n".