Center of a triangle

[+Always & Forever 5]

I'm working on a cache series that requires calculating the geographic center of a triangle to find the final. Yeah, right. Like I'm some big geometry/trig genius.

 

A Google search reveals a bunch of sites that require you to be just that, some big geometry/trig genius to figure it out.

 

Anyone out there have any help to offer? A "Calculate the geographic center of a triangle for Dummies" webpage, perhaps?

 

[+ArtieD]

Well, my dad used to have a method that worked pretty well when he was sighting in his guns...goes like this...

 

Find the middle point along one side of the triangle...from there, draw a straight line to the inside of the opposite corner. Repeat for the other two sides. All the intersecting lines should be close to dead center.

[+StarBrand]

Draw a line to connect the midpoint of each side to the angle opposite it. Where the 3 lines meet is the center.

 

I know that doesn't help to calculate coordinates but if you do that on a map it will give you a location to go to.

[+martinell]

It really depends upon which center you want. Triangles have 3 or 4 centers, depends upon what you are looking for.

 

The suggestion above is one of the middles (don't remember which one) -

 

draw a line center of AB to C

draw a line center of BC to A

draw a line center of AC to B

 

This only works if it is an equilateral triangle.

[+ArtieD]

Like this:

 

[Uberquandary]

If you use a map with UTMs you can find the coordinates (if the scale is small enough, of course)

[+Always & Forever 5]

Well, those ideas are what I've already thought of, but I didn't know if there was something more I was missing. ESPECIALLY after looking at some of the Google'd pages...

 

I'll try this and see if that works. Thanks for the help!

[+Always & Forever 5]

It really depends upon which center you want.

I'm not sure...what I need is the geographical center.

 

Whatever that is...

[+BBWolf+3Pigs]

Tons of different definitions for the center of a triangle. Which one is needed?

[+conradv]

As was stated above, the most common "center" is the Centroid, which is where the mass center is represented.

 

[+RocketMan]

It really depends upon which center you want.

I'm not sure...what I need is the geographical center.

 

Whatever that is...

Maybe you want to know how to calculate the orthocenter.

[Suscrofa]

If by "geographic" center you mean a point that is at equal distance from the three WP's that are the triangle summits (vertices), then you need the "circumcenter", the center of the circle passing by the said summits.

The URL stated above ( http://www.jimloy.com/geometry/centers.htm ) give you a graphic solution you can use on a map. It also gives you the way to compute the various elements provided trigonometric knowledge.

Edited May 15, 2007 by Suscrofa

[+OzGuff]

If by "geographic" center you mean a point that is at equal distance from the three WP's that are the triangle summits (vertices), then you need the "circumcenter", the center of the circle passing by the said summits.

The URL stated above ( http://www.jimloy.com/geometry/centers.htm ) give you a graphic solution you can use on a map. It also gives you the way to compute the various elements provided trigonometric knowledge.

You might want to check out these four caches placed by jratzlaf -- he calls them The Concurrence Theorems. They involve calculating the circumcenter, centroid, incenter, and orthocenter.

[+Always & Forever 5]

Thanks, everyone, for the help! I think I have it figured out now. I'm off tomorrow to see if I'm right or not!

[+Renegade Knight]

I'm working on a cache series that requires calculating the geographic center of a triangle to find the final. Yeah, right. Like I'm some big geometry/trig genius.

 

A Google search reveals a bunch of sites that require you to be just that, some big geometry/trig genius to figure it out.

 

Anyone out there have any help to offer? A "Calculate the geographic center of a triangle for Dummies" webpage, perhaps?

 

Draw it in Autocad. Then ID the point.

[+thedeadpirate]

You might want to check out these four caches placed by jratzlaf -- he calls them The Concurrence Theorems. They involve calculating the circumcenter, centroid, incenter, and orthocenter.

 

OzGuff, thanks so much for that link. I just spent the last few hours solving all four of the puzzles. Finally something I am actually good at. Unfortunately, they are too far for me to go find. But they were a lot of fun to solve. Geometry is fun.

[+Corp Of Discovery]

On one of the caches (centroid) above I just averaged the coords for all 3 points and checked them with the coord checker. It came back as correct.

[+trainlove]

It depends on the kind of center your talking about.

The geometric center of a triangle is found simply by taking the 3 points (in UTM coords) and averaging them. But you could do it the hard way and calculate the perpindicular lines from the midpoint between any 2 of the points, I.E. the slope is -1/m of the line between 2 points, do this for 2 of the sides and they intersect at the same point calculated simply above. Do this for the 3'rd set of 2 points for a sanity check but doing it this way is insane already.

 

The incenter, circumcenter, 9 point center or orthocenter are all much more difficult to do. But as you can see by my avatar image I have written a program that can do it all. But none of those other centers have any geocaching use excpet the incenter where all 3 points are at bearings that are 120 degrees apart.

 

The cool web site www.cut-the-knot.org/triangle/index.shtml has an applet that can show you all the different things that 3 points (i.e. a triangle) define.

Edited May 16, 2007 by trainlove

[+Kit Fox]

On one of the caches (centroid) above I just averaged the coords for all 3 points and checked them with the coord checker. It came back as correct.

 

That is how I solved a very hard puzzle cache called the Dragonfly Scroll.

[+trainlove]

I forgot that I posted a triangle image created with the same program that created my avatar image along with my log to a triangle based cache called Centroid. But just now checking the new My Friends feature along with the apparent new slideshow feature I saw it. Here is a link to it or go through my Gallery or profile or go directly to GCW370.

And no, neither traingle is actually the soultion to any of the few triangle puzzles I've visited, shame on any of you for hoping to cheat.

 

http://img.geocaching.com/cache/log/b75c75...fa8bf29ce0b.jpg

Edited May 18, 2007 by trainlove