This small application has arisen from the spontaneous idea to find a place to meet for a small family gathering. The idea was to find a place that is equally far away for all participants. After a few discussions of how to tackle the problem mathematically correct, we actually got a simple solution for three participants.We declared the earth to be a flat disc and calculated the center of the circle on which all departure points lie. A point was therefore found very quickly!

The positive side effect: you will get to places that you would have probably never seen otherwise.

This website has been created based on this true story. It tries to solve the problem now a bit more comprehensive and mathematical though (the earth is not a flat disc anymore).

Over time (the family gathering has already taken place) new ideas have emerged how to dtermine a possible meeting place. In addition, there was a kind of objective to test how easy it is to integrate WebAPIs usefully in applications like this.Therefore essential functions of the application are implemented using WebAPIs:

- Representation of results on a map (Google Map)
- Input of coordinates by point & click on the map (Google Map)
- Searching for coordinates based on a given address (Google Geocoder)
- Searching for places of interest based on calculated coordinates (Google Reverse Geocoder)

As result these WebAPIs ensure that the application is simple to use and is providing useful results.

Other WebAPIs are used to improve the the attractiveness of the application:

- Calculation of routes (Google Map),
- Showing some picture around place of interrest (Google Panoramio),
- Using special fonts (Google WebFonts)

A quite simple model was used for all calculations:

The WSG-84 model, which assumes the earth as a ellipsoid is used to convert all coordinates of departure points into a two-dimensional, flat model.
This approach is relatively simple and of course not mathematically accurate but seems to be sufficient for the purpose.

The idea of green point is that a place should be found to which the sum of distances to all participants is minimized. So it is a king of most ecological point. This point is determined iteratively.

The blue point sometimes called fair point is the meeting point to which all participants have the same distance. Mathematically, lie all departure points on a circle and the center of this circle is the meeting point. Typically this point can be calculated only in the case of two (just the middle between) or three departure points.

Just from the practical point of in many cases it is the intention to meet at one of the departure points. Here is calculated which of the departure points is best suited as a meeting place - Best suited in the sense that the sum of distances to all participants is minimized.

If you want to make it really come to the lucky, you can take a meeting place by random. If the place doesn't fit you can just try it again.

A lot of fun to find a place in the area withn the departure points.

The Midpoint is in the mathematical sense the median point of the area determined by the departure points (e.g the median of a triangle). This median 'feels' like the middle and is quite easy to calculate.

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