Triangulation

[+M-T-P]

Does anyone know an easy, more precise method for triangulating coordinates from three other coordinates? A new local cache "Uh Oh! Not Again!" gives me three points and tells me that the cache is 1 mile from one of the points, 2 miles from another, and 3 miles from another. I've printed out a map and pulled out my trusty compass, but surely there has to be a better way that drawing circles to identify the 6 possible waypoints.

 

Thoughts?

[+Kewaneh & Shark]

Drawing three circles on a map would probably be the easiest way for you to do it. That's how a surveyor would probably do it. They may not use a map, but a computer program, but the results would be the same - six possible combinations with the information given. That kind of turns this cache into a multi, of sorts. Especially if there's not much of a clue given.

Keep on Caching! - Kewaneh

[+SeventhSon]

I'm gonna guess only one point fits the puzzle, and since I like puzzles, I gotta figure it out

[+SeventhSon]

OK I know where it's at . Very kewl puzzle.

[+dkwolf]

My thoughts? It's generally not good practice to discuss puzzle caches in the forums.

 

But since you've mentioned it, what you're doing is probably the easiest. I can think of several ways I would do it at work, but I doubt you want to drop $10k on software to solve this.

[tossedsalad]

Does anyone know an easy, more precise method for triangulating coordinates from three other coordinates?  A new local cache "Uh Oh!  Not Again!" gives me three points and tells me that the cache is 1 mile from one of the points, 2 miles from another, and 3 miles from another.  I've printed out a map and pulled out my trusty compass, but surely there has to be a better way that drawing circles to identify the 6 possible waypoints.

 

Thoughts?

Without knowing how far apart the starting points are I can't say if you have one or two or no solutions, but in general you need three points and three distances to define another point on a surface.

 

Two circles with different diameters can intersect at 2, 1 or no points. A third circle with yet another diameter will intersect one of those points. So unless it is a degenerate case where you don't have all three circles intersecting at two points, or the third circle intersects at the same two points as the first two (all three centers on a line), you will be left with just one point where all three circles intersect. So you should not have 6 possible points, just one.

[Utsman]

Two circles with different diameters can intersect at 2, 1 or no points. A third circle with yet another diameter will intersect one of those points. So unless it is a degenerate case where you don't have all three circles intersecting at two points, or the third circle intersects at the same two points as the first two (all three centers on a line), you will be left with just one point where all three circles intersect. So you should not have 6 possible points, just one.

Well said.

[+fizzymagic]

There's a well-known solution to this problem that you can do on a pocket calculator using UTM coordinates. It's pretty straightforward. I have one of these caches, and so I have an explanation here.

[+M-T-P]

There's a well-known solution to this problem that you can do on a pocket calculator using UTM coordinates. It's pretty straightforward. I have one of these caches, and so I have an explanation here.

There we go. This is the answer I'm looking for! A mathematical way to solve it.

[+unicyclist]

where do you find a city map to do triangleation?

[+Wacka]

There's a well-known solution to this problem that you can do on a pocket calculator using UTM coordinates.  It's pretty straightforward.  I have one of these caches, and so I have an explanation here.

There we go. This is the answer I'm looking for! A mathematical way to solve it.

I did that cache of Fizzy's. I got the distances and used a compass (drawing tool) and a AAA map to get the park correct. I went there and walked around until the #s to each of the 3 points were correct. I marked that point and looked around. Couldn't find it.

Several months later, I got that formula from him and did the math. Well I did it wrong, because it put me 200 ft away in a creek.

I went looking around at the coords I had walked around to determine. The cache was about 20 ft away! It was very well hidden.

 

So. Fizzy's equations= 200 ft off. My walking around =20 ft off.

That was due to my math mistakes. It can be done another way if you are not mathematically inclined.

Edited October 18, 2005 by Wacka

[+webscouter.]

If you have a gps that will let you set proximity alerts you can set up the three waypoints with a proximity and the circles will overlap at the intersection.

[+Kit Fox]

My question is how does one create a cache like this? Which program was used to come up with the 1,2, and 3 miles distances?

 

I have a similar concept in one of my caches, but it doesn't require the use of circles Crosshairs

[+AtoZ]

write a computer program that will calculate the point. Also use UTM as it is much easier then degrees.

cheers

[+EScout]

My question is how does one create a cache like this? Which program was used to come up with the 1,2, and 3 miles distances?

 

Enter the Cachepoint in your GPSr, and then use the projection-of-waypoint function to set your waypoints at a certain distance and direction.. You will then have the coords of these waypoints.

[+Kit Fox]

My question is how does one create a cache like this? Which program was used to come up with the 1,2, and 3 miles distances?

 

Enter the Cachepoint in your GPSr, and then use the projection-of-waypoint function to set your waypoints at a certain distance and direction.. You will then have the coords of these waypoints.

Great Idea!

[+M-T-P]

My question is how does one create a cache like this? Which program was used to come up with the 1,2, and 3 miles distances?

 

Enter the Cachepoint in your GPSr, and then use the projection-of-waypoint function to set your waypoints at a certain distance and direction.. You will then have the coords of these waypoints.

The problem with this idea is that the direction is not known. We know the distance, but not the direction.

[+Kit Fox]

The problem with this idea is that the direction is not known. We know the distance, but not the direction.

Wouldn't the Bearing be known, if the "projector" picked three different directions example 0 degrees at 1 mile, 70 degrees at 2 miles, 180 degrees at 1.5 miles?

[+fizzymagic]

Wouldn't the Bearing be known, if the "projector" picked three different directions example 0 degrees at 1 mile, 70 degrees at 2 miles, 180 degrees at 1.5 miles?

In that case, the cache location could be determined from any one of the three (bearing, distance) pairs, and it wouldn't be much of a puzzle, would it?

 

The puzzle type OP referred to is one in which you are given three points and three distances. No bearings are included.

[+Kit Fox]

Wouldn't the Bearing be known, if the "projector" picked three different directions example 0 degrees at 1 mile, 70 degrees at 2 miles, 180 degrees at 1.5 miles?

In that case, the cache location could be determined from any one of the three (bearing, distance) pairs, and it wouldn't be much of a puzzle, would it?

 

The puzzle type OP referred to is one in which you are given three points and three distances. No bearings are included.

If I was to place a cache like this, I wouldn't post the bearings.

 

I may have misunderstood MTPs remark.