Triangler X factor

[+fishercz20]

Ok, off the bat I will tell you I am not good with numbers and figuring these things out. So now I need help finding the X factor. It was a multi cache, 4 points which I found and now to find out where X marks the spot. Where all 4 points intersect.

 

Cache site 1 coords are N26 16 177 W081 41 483

Cache site 2 coords are N26 16 330 w081 41 505

Cache site 3 coords are N26 16 096 W081 41 627

Cache site 4 coords are N26 16 159 W 081 41 692

 

The final cache [ ammo box] is where the the coords intersect. Can anyone help me?

 

THx Fishercz20

[+RiverCacher]

There are mathematical ways of doing this. I chose to use Delorme Topo USA 7.0, and I plotted all four of the points. Then, I ran lines between them, and established the coordinates of the intersection.

 

If I did not have Delorme Topo USA, and I didn't mind walking about 1500 feet (the distance between the two closest points that are opposite (ie East-West or North-South...in this case E/W), I would stand at, say, the east point, and enter the west point into my GPS. I would start walking towards the west point, knowing that the lines of the N-S points HAVE to intersect the line that I'm walking on at some point.

 

Scott

Edited November 20, 2007 by RiverCacher

[+fishercz20]

There are mathematical ways of doing this. I chose to use Delorme Topo USA 7.0, and I plotted all four of the points. Then, I ran lines between them, and established the coordinates of the intersection.

 

If I did not have Delorme Topo USA, and I didn't mind walking about 1500 feet (the distance between the two closest points that are opposite (ie East-West or North-South...in this case E/W), I would stand at, say, the east point, and enter the west point into my GPS. I would start walking towards the west point, knowing that the lines of the N-S points HAVE to intersect the line that I'm walking on at some point.

 

Scott

I did try walking from points 3 and 2 and then 1 and 4 and thought I found where the X factor was but found nothing. THought maybe there was an easier way.

 

Scott

[knowschad]

Ok, off the bat I will tell you I am not good with numbers and figuring these things out. So now I need help finding the X factor. It was a multi cache, 4 points which I found and now to find out where X marks the spot. Where all 4 points intersect.

 

Cache site 1 coords are N26 16 177 W081 41 483

Cache site 2 coords are N26 16 330 w081 41 505

Cache site 3 coords are N26 16 096 W081 41 627

Cache site 4 coords are N26 16 159 W 081 41 692

 

The final cache [ ammo box] is where the the coords intersect. Can anyone help me?

 

THx Fishercz20

 

Does this help? http://www.gps-practice-and-fun.com/gps-coordinates.html

[+the hermit crabs]

Ok, off the bat I will tell you I am not good with numbers and figuring these things out. So now I need help finding the X factor. It was a multi cache, 4 points which I found and now to find out where X marks the spot. Where all 4 points intersect.

 

Cache site 1 coords are N26 16 177 W081 41 483

Cache site 2 coords are N26 16 330 w081 41 505

Cache site 3 coords are N26 16 096 W081 41 627

Cache site 4 coords are N26 16 159 W 081 41 692

 

The final cache [ ammo box] is where the the coords intersect. Can anyone help me?

 

THx Fishercz20

Does your GPS have a Routing function? If so, you can have it generate a very close approximation of the intersection point for you (and learn a new feature of your GPS at the same time ). And no math is required on your part.

 

This is how it would work on some of the etrex models; your unit may have a different procedure:

 

If the four coords above are not in your GPS, add them.

Go to the Map screen and scroll/zoom enough so that you can see all four points.

You should them laid out roughly like this:

 

_____________________Site 2_____________________

_______________________________________________

_______________________________________________

_______________________________________________

_________________________________Site 1_________

____Site 4______________________________________

________________________________________________

____________Site 3______________________________

 

You want to create a route that goes through all four points, but in a way that the segments of the route intersect. So, you don't want the route to just follow the outline of a four-sided polygon -- you wouldn't want to the route to be something like "1 --> 2 --> 4 --> 3".

 

You want a route like ""1 --> 4 --> 3 -->2" or "2 --> 3 --> 1 --> 4". Any route that connects opposite diagonal corners will work, because they'll all end up with the same intersection.

 

To generate the route:

 

Select Main Menu -> Routes

Click "New"

Make up a name for this route.

Click "Select Next Point"

This brings up the "Find" page. Select "Waypoints" and then select Site 1.

This brings up the waypoint page for Site 1. Click "Use". This will be the first point in your route.

Click "Select Next Point" again, and this time add Site 4.

Repeat for Site 3 and then Site 2.

 

When all four points are in there, click "Map".

You should see the route, like this:

 

Scroll so that the cursor is right at the intersection point, and zoom in as close as you can. The resulting coordinates should be very close to the ones you're looking for.

[+klossner]

Time for math class.

 

All points have the same values for degrees and integer minutes, so ignore them and work with fractions of minutes. Multiply them all by 1000 to get integers and list them with longitude first, then latitude (and ignore the fact that X increases in the wrong direction since we're west of the prime meridian):

 

C1: 483, 177

C2: 505, 330

C3: 627, 96

C4: 692, 159

 

Treat these as (x,y) points, plot them on graph paper, and you see that C1 is to the east, C2 to the north, C3 to the south, and C4 to the west. So we want to know where the line from C1 to C4 intersects the line from C3 to C2.

 

The slope of the south-north line (connecting C3 to C2) is:

 

(330 - 96) / (505 - 627) = -1.91803

 

The slope of the east-west line (connecting C1 to C4) is:

 

(159 - 177) / (692 - 483) = -0.086124

 

Equations for the two lines, then, are:

 

y = -1.91803 * (x - 505) + 330

y = -0.086124 * (x - 483) + 177

 

Solve:

 

x = 589.554, round to 590

y = 167.823, round to 169

 

The intersection point is N 26 16.169 W 081 41.590.

Edited November 21, 2007 by klossner

[+fishercz20]

Thank you all for your Help. You are guys are the Best!!!!!

 

Scott

[+The Leprechauns]

I wonder what the owner of that multicache would think about the solution for their cache being given away in the forums. It's now a traditional cache.

[sophie&kristof]

I remember using the following excell-sheet for a similar geocache. Although the solution has already been found, it might be something to put in your "geocaching"-folder

 

http://tex.geocacher.nl/XMarksTheSpot2.xls

[+Rattlebars]

Ok, what did I do wrong to get a different answer in Google Earth....??? Unless it's just the inherent inaccuracies of GE.

 

N 26º 16.250' W 81º 41.592'

 

[+trainlove]

The intersection f 2 lines is just about the easiest geometric puzzle. I did one where the hider actually used 4 points that form a rectangle so it's even easier then the generic case. One of my pizzles us a point 1/3 of the way along a linie which is also just a piece of cake.

 

Now triangular geometric puzzles are fun and more challenging. Does he mean the centroid, the inscribed circle, the circumcribed circle, the 9-point circle... Way cool, which is the reason for my forum avatar iimage.

[+Dread_Pirate_Bruce]

Time for math class.

 

All points have the same values for degrees and integer minutes, so ignore them and work with fractions of minutes. Multiply them all by 1000 to get integers and list them with longitude first, then latitude (and ignore the fact that X increases in the wrong direction since we're west of the prime meridian):

 

C1: 483, 177

C2: 505, 330

C3: 627, 96

C4: 692, 159

 

Treat these as (x,y) points, plot them on graph paper, and you see that C1 is to the east, C2 to the north, C3 to the south, and C4 to the west. So we want to know where the line from C1 to C4 intersects the line from C3 to C2.

 

The slope of the south-north line (connecting C3 to C2) is:

 

(330 - 96) / (505 - 627) = -1.91803

 

The slope of the east-west line (connecting C1 to C4) is:

 

(159 - 177) / (692 - 483) = -0.086124

 

Equations for the two lines, then, are:

 

y = -1.91803 * (x - 505) + 330

y = -0.086124 * (x - 483) + 177

 

Solve:

 

x = 589.554, round to 590

y = 167.823, round to 169

 

The intersection point is N 26 16.169 W 081 41.590.

 

Are you sure this works? I tried something similar once and was way off. As I see it, this method does not work as a minute of latitude is not the same length as a minute of longitude.

[+Scare Force One]

Time for math class.

 

All points have the same values for degrees and integer minutes, so ignore them and work with fractions of minutes. Multiply them all by 1000 to get integers and list them with longitude first, then latitude (and ignore the fact that X increases in the wrong direction since we're west of the prime meridian):

 

C1: 483, 177

C2: 505, 330

C3: 627, 96

C4: 692, 159

 

Treat these as (x,y) points, plot them on graph paper, and you see that C1 is to the east, C2 to the north, C3 to the south, and C4 to the west. So we want to know where the line from C1 to C4 intersects the line from C3 to C2.

 

The slope of the south-north line (connecting C3 to C2) is:

 

(330 - 96) / (505 - 627) = -1.91803

 

The slope of the east-west line (connecting C1 to C4) is:

 

(159 - 177) / (692 - 483) = -0.086124

 

Equations for the two lines, then, are:

 

y = -1.91803 * (x - 505) + 330

y = -0.086124 * (x - 483) + 177

 

Solve:

 

x = 589.554, round to 590

y = 167.823, round to 169

 

The intersection point is N 26 16.169 W 081 41.590.

I lost you after math class. Im sure that you know what your doing but I have to ask, What?

~.~Scare Force One

[+trainlove]

Time for math class.

 

All points have the same values for degrees and integer minutes, so ignore them and work with fractions of minutes. Multiply them all by 1000 to get integers and list them with longitude first, then latitude (and ignore the fact that X increases in the wrong direction since we're west of the prime meridian):

 

C1: 483, 177

C2: 505, 330

C3: 627, 96

C4: 692, 159

 

Treat these as (x,y) points, plot them on graph paper, and you see that C1 is to the east, C2 to the north, C3 to the south, and C4 to the west. So we want to know where the line from C1 to C4 intersects the line from C3 to C2.

 

The slope of the south-north line (connecting C3 to C2) is:

 

(330 - 96) / (505 - 627) = -1.91803

 

The slope of the east-west line (connecting C1 to C4) is:

 

(159 - 177) / (692 - 483) = -0.086124

 

Equations for the two lines, then, are:

 

y = -1.91803 * (x - 505) + 330

y = -0.086124 * (x - 483) + 177

 

Solve:

 

x = 589.554, round to 590

y = 167.823, round to 169

 

The intersection point is N 26 16.169 W 081 41.590.

 

Are you sure this works? I tried something similar once and was way off. As I see it, this method does not work as a minute of latitude is not the same length as a minute of longitude.

 

That should work but since Latitude and Longitude are not orthogonal it will be increasingly erronious the bigger the area. It would be better to use UTM. A 6 mile area once gave me a half a mile difference in a similar problem, but in my 6 mile puzzle Lat/Lon vs UTM give you only a 6 foot error, so your might work depending on the orientation of the problem.