dschmidt

I did some calculations on triangles of different sizes to find the midpoint (center of mass/centroid) method and compared the results with a plain flat map calculated by hand and the Geographic Midpoint Calculator. For a triangle roughly 100 miles per side at mid US latitudes the flat map and the calculator were 190 feet apart at their calculated centers. For a triangle with 50 mile sides the 2 centers were 53 feet apart. For a triangle with 10 mile sides the 2 centers were 24 feet apart. I'm the software developer for the site, I'm giving some thought to creating another calculator page that would look pretty much the same as the current page, but would do the centroid/center of mass calculations based on a flat map instead of a spherical earth model. It wouldn't actually take a lot of work. dschmidt

I've been studying this more today. It turns out that the only triangle on a sphere where the points are equal distance from a center point is a triangle where all 3 sides are the same length, and the calculator handles this ok. The calculated midpoint doesn't give you an overall combined minimum distance from all points, however it gives a reasonable approximation to the location of minimum distance. The center of mass method that it uses for a problem using 3 points would be like putting a weight at each point on a massless triangle, and the calculated midpoint would be the exact point on the triangle where the triangle balances on a pin. dschmidt

You've got a good point. The method uses the center of mass (or center of gravity). For 2 points it works perfectly. It doesn't necessarily find the equidistant point for 3 points; it seems it may be possible to calculate that but I don't know the mathematical procedure. For 4 or more points the center of mass method is by far the best, for example if you made a 3 point triangle then put the 4th point near the center. It would be impossible to find a point with equal distance from all four points. I suppose that if folks understand that this site finds the midpoint based on center of gravity/mass and accept that as their definition of geographic midpoint when setting up and solving their multipoint problems, they should get consistent results when using the calculator. If they want to find a point that is equal distance from other points they should use another method. dschmidt

The midpoint calculation is based on the model of a spherical earth. For more than 2 points each point is converted into cartesian coordinates (x,y,z). The average x, y and z coordinate is calculated, then that average coordinate is converted back into latitude and longitude. dschmidt

The Geographic Midpoint Calculator, a free online tool has recently been updated with new features: http://www.geomidpoint.com It is used to calculate the midpoint (or central location) for two or more places. You select your places and the latitude and longitude of the midpoint are calculated. You can view a map with a marker pointing at the exact midpoint for those places. It has been used for setting up and solving puzzle caches and for caching at midpoints. New features--it now has a built-in geocoder so that you have millions of world cities, towns and street addresses at your fingertips. You can now import multiple latitude/longitude data from another source such as Excel or your word processor. It's fast, accurate and fun to use. dschmidt

No problem. I've just been having some fun playing around with this thing.

Check out the new free online tool available at: http://www.geomidpoint.com that could come in handy for the sport of geocaching. You can quickly find the true midpoint coordinates (based on a spherical earth) for two or more cities, such as Chicago, Los Angeles and London, or you can enter your own latitude/longitude points and get the exact midpoint coordinates. You can see your points and the midpoint on a map (Google maps).

The cool thing is that that is one of my caches! That is cool, it's a small world sometimes. Reading this story makes me think about how fast things are changing nowadays in our world. How many people were thinking about geocaching 10 years ago, , and what about the internet, 15 years ago it didn't really exist and now it plays a huge role in our lives.

I agree, 26 miles in kayak or canoe is too much unless you are experienced. The only real solution is to use a boat.