# Doing math in Elixir – calculating Great Circle Distance

In last two parts, I was setting up and consuming quick API to get additional airport data. One of this information was exact airport location on the Earth. In this part, I’ll use that information to calculate the distance of the travel and show how you can use standard math library in Erlang VM.

Calculating distance of air travel based on location is not super hard, but it needs to accommodate the fact that Earth is not flat. We’ll use something called “Great-circle distance“, as that’s how planes fly. So when you take most commonly used Mercator projection of the map, the shortest path between two points won’t be a straight line. It’s gonna have more parabolic-like shape. It’s best visible if you pick longer flights. Just go to flightradar24.com and check any plane overflying the Atlantic. They seem to be all flying towards north first and then turn south as the flight progresses. In fact, they fly a straight line, but because Eart is a sphere (in simplified model), meridians are not really parallel to each other.

After this geography primer, let’s get to math. The formula for calculating great-circle distance looks like that: Where and are latitude and longitude of two points on Earth. This formula takes in radians and outputs radians. The result is angle difference between two points. To get the distance in kilometres, we have to multiply it by the radius of the Earth, which in the metric system is around 6370kms. To the code! I changed my functions in view, so instead of returning separately latitude and longitude, they give back a pair of coordinates as a tuple.

https://gist.github.com/mlusiak/0c934302b100a8b0f8899010fdd8422b

Then I pass the tuples to newly created function distance, that calls newly created Flightlog.Math module. I put the module in /lib folder and it all worked by the first run!

https://gist.github.com/mlusiak/031d81a94c3302bb6be9068c8bc29345

:math is a reference to Erlang VMs math library. One thing that’s needs explanation is changing degrees into radians. Radian is a different mathematical representation of the angle. 1 radian means, that the length of the arc of the part of the circle, that this degree describes equals the length of the radius of that circle. So the full circle is slightly over 6 radians (2 * Pi), as a formula for the length of the circumference of the circle is 2 * Pi * radius.

That’s all for today. Next week we’ll try to test this new module. In the meantime, check previous episodesAnd if you’re interested in machine learning, look into my weekly link drop.