When I came to America, it was on the understanding that I would only be here for 6 months. My contracts said as much; there was even an insistence that I book a return flight. Fortunately for me, that means I have a free trip home coming up, and can grab an armful of guitars and teabags with which to populate my new New York, New York home.

I’m a little worried about returning to the UK. It’ll be strange being surrounded by British accents again, and having to remember to actually give a response to ‘How are you?‘ but I’m sure I’ll be able to work around that. The thing I’m really worried about though, is the fact that I’ll be 5,113km from the nearest Chipotle in South Portland, Maine.

You might (but probably won’t) ask, how can I be sure that’s the closest Chipotle? You could (but almost certainly aren’t going to) further inquire, can I give a brief overview of geodesy and cartographic principles whilst I explain? Read on.

The shortest distance between any two points on a sphere is to travel across the minor arc (yellow) of the Riemann Sphere (red) that intersects them. The earth is actually not a sphere, but an oblate spheroid – which, as you may remember, is the shape of an M&M – but whilst the distinction was important when calculating the cost of filling a room, it isn’t particularly important to understand the following.

On a ‘standard’ map that one might come across in any book or atlas, the shortest path between two points will not appear as a straight line, but rather as a curved arc. You may have noticed the phenomenon when staring blankly at the low-fidelity map that shows your flight path on your way to a country where they lack toilet paper.

The reason for this is that various projections are used to represent the earth on a two-dimensional plane, each a trade-off between properly representing area, distance and angles. The common Robinson and Winkel Tripel projections both significantly distort angles.

Possibly you’re more familiar with Google Maps which not only perverts the angles we’re interested in but also grossly distorts dimensions as distance from the equator increases. Consider for example, Greenland, which is actually more than 14 times smaller than Africa, but occupies roughly the same area on a Mercator projection (below) that Google uses. This is a terrible, but unfortunately common choice of projection; it’s a 16^th century representation best suited for nautical navigation that is inexplicably still popular.

For the record my favourite projection is the Goode homolosine.

The upshot of all this, is that the shortest distance between two points – in our case, between London Heathrow and any given Chipotle – cannot be calculated by sight on any non-Gnomonic projection, but must instead use the haversine formula. This proffers the Chipotle in South Portland, Maine, as the closest option.

Of course, the entire premise of this post is moot when I point out that this particular Maine branch fell into second place when Chipotle opened its first non-US restaurant a little less than a year ago. On Charing Cross Road.

You’ve just learned all that for nothing.

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