# How to find the center of three sets of coordinates

Followers 2

## Recommended Posts

A local puzzle cache requires me to find the middle of three sets of coordinates.

How would I do this?

I'd call this a center of a triangle problem. There are a number of different definitions for center of a triangle (ignoring earth curvature, which does come into play when the triangle is defined by coords).

Here's an article on it

http://www.jimloy.com/geometry/centers.htm

fascinating stuff

thank you very much for the link

- - - -

to the original poster -

sounds like you'd better hope that the points make an equilateral triangle

one way to work with this type of problem is to use UTM

convert the points to this datum, and plot them on graph paper

once you have worked out a solution point, convert it from UTM back to DDD MM.MMM

(or just put your GPSr in UTM mode, and enter them directly)

I have used this site in the past, to good effect. It calculates a geographical centroid for two or more points. I own a puzzle that requires finding the centroid of 19 caches, and I've sent this link to folks who don't have GSAK:

http://www.geomidpoint.com/

Here's an article on it

http://www.jimloy.com/geometry/centers.htm

Interesting stuff. For the 3 puzzles I've solved that looked for the center of the circle, I just averaged the 3 coordinates. I think that would give the "centroid" as defined on the linked page.

And yes, this method would assume a flat Earth, but for sufficiently close coordinates, it works well enough. I found all 3 caches

Have you asked the cache owner for help?

Yes and got a few irrelevant links

Try Fizzycalc

The problem here is that there are a lot of different "centers" for three points; there is the circumcenter, which is the point equidistant from all three points; there is the centroid, which is the point you get by averaging the three points together, and there is the incenter, which is the point that is equidistant from the edges of the triangle made from the points.

Without knowing which center you want, it is impossible to give you an answer. Of course, the cache hider might not even know the difference between the 3 centers and just call whichever they chose as the "center," in which case that is a problem with the cache puzzle.

The problem here is that there are a lot of different "centers" for three points; there is the circumcenter, which is the point equidistant from all three points; there is the centroid, which is the point you get by averaging the three points together, and there is the incenter, which is the point that is equidistant from the edges of the triangle made from the points.

Without knowing which center you want, it is impossible to give you an answer. Of course, the cache hider might not even know the difference between the 3 centers and just call whichever they chose as the "center," in which case that is a problem with the cache puzzle.

Thanks for pointing this out. From the cache page:

The cache is NOT at the co-ordinates given. Those co-ordinates are part of the data that you will need to calculate it's position. I have raised the difficulty to 3 based on seeker feedback. The cache only contains the log. Please bring your own writing implement.

Somewhere along the way in high school you may remember learning that a circle can be described by any three points and your long suffering mathematics teacher would have shown you a method of locating the centre of that circle. This cache was inspired by a conversation I overheard amongst my mathematics colleagues in the corner of the staffroom I share with them.

If I am right that is a circumcentre. Now any ideas?

If I am right that is a circumcentre. Now any ideas?

The article mentioned above has a diagram (upper-right) that illustrates this perfectly.

## Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.
Note: Your post will require moderator approval before it will be visible.

×   Pasted as rich text.   Paste as plain text instead

Only 75 emoji are allowed.

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.

×
Followers 2
×
×
• Create New...