It don’t remember how the story begins, but I think it’s a cool problem easy to understand. I shared it with friends and colleagues working in geometry and geography so they could give it a go.
I was wondering what is the place on Earth (land or sea) for which the closest airport is at the largest distance. Put it in other words: from that place, you don’t find any airport in a radius of X kilometers. We need to find the place for which X is the maximum.
I quickly found out a list of airports at OpenFlights, from which we can begin the analysis. First of all I was curious to see a heatmap, it’s the first image of this post.
What comes out of that map is that you almost don’t need coastlines, they appear clearly because of the airport locations. Seeing the U.S. and Europe like this is not a surprise, what I especially like is how the Caribbean Islands are highlighted.
Concerning the point we are looking for, one might say it should be in the southern ocean, but don’t forget that we are working on a sphere (more or less) and that the projection of our map can deform the reality.
When I submit the problem to the mathematician colleague, he started with 2 questions:
Let’s imagine there are only 2 airports on earth surface: Liège and Denver. If we consider the great circle containing these two points:
This jsfiddle was useful for the halfway point.
The code to find out these 2 airports is not very clever: a loop over all the pairs
to compute the distance using the Haversine formula. I used Julia for that part, first to
have something fast, second to force me to use this language.
We learn that the maximal distance, 20015 km, is between Sultan Mahmud Badaruddin II Airport (🇮🇩 Indonesia) and Benito Salas Airport (🇨🇴 Colombia).
My idea was to find the pair of airports separated by the largest distance, and then the point between them would be the location we’re looking for. That’s obviously not correct.
The next tries will be presented in another post.