'Skiplagging' to save money on plane tickets is only possible because airlines are breaking one of the basic laws of geometry

• Flyers have recently been fighting high airline prices by "skiplagging."
• They're booking cheaper tickets with a layover at the real destination and skipping the second leg.

One of the hottest money-saving travel hacks right now only works because of bad math on the airlines' part.

Skiplagging, also known as "hidden city" ticketing, involves booking a one-stop flight with the intention of "skipping" the second leg and getting off in the layover city. Simply, it's booking a flight from Airport A to Airport C and getting off at a layover at Airport B.

People can save hundreds of dollars doing this because a nonstop flight is more expensive than booking one with a layover in the intended-destination city.

However, airlines have been trying to cut down on this travel hack and haven't shied away from punishing passengers who get caught, including canceling the return flights of those who skiplagged on their outbound journeys.

And it's only possible because airfares don't follow one of the most intuitive rules in math.

One of the most basic laws of geometry is called the "triangle inequality." If you're trying to measure the distance between points, one of the basic rules is that the distance between two points has to be less than or equal to the distance from your first point to some other point and then back to your original second point.

The inequality gets its name from how triangles work in classic plane geometry. If you have a triangle, the sum of the length of any two sides of that triangle is bigger than the length of the third side.

We might expect airline fares to more or less follow this rule and act as a distance metric between cities. Between fuel, maintenance, and crew pay, it should cost more to fly a plane from New York to Amsterdam, followed by a leg from Amsterdam to London, than it would to fly the plane from New York to Amsterdam. That cost difference should be reflected in the price of tickets between the three cities.

But that's clearly not always the case, and that violation of the triangle inequality is what makes skiplagging possible. The fact that it's sometimes cheaper to book a flight from New York to London that has a stop in Amsterdam than to book a nonstop from New York to Amsterdam shows that the airlines are breaking the triangle inequality.

Skiplagging creates the possibility of two passengers being seated next to each other, one having paid less for two flights than the other had paid for one. This is pretty counterintuitive — the idea that taking a detour should be longer or more expensive than a straight shot is fundamentally baked into the human brain. That's why mathematicians use that idea as an axiom when measuring distance. But the world doesn't always match up with our intuitions, and factors other than distance go into the price of an airline ticket.

The math and science writer Brian Hayes came up with a possible explanation for this triangle-inequality-violating phenomenon in a 2013 blog post. He wrote that the discrepancy could come from the direct flight being in much higher demand than the layover flight, which he said could lead airlines to charge more for the nonstop. And the price of New York to Amsterdam to London is competing with the price of New York to London direct, not New York to Amsterdam.

Moreover, airlines' hub-and-spoke model means many travelers have to typically fly through a major hub to get to smaller regional cities. But, the rise of low-cost carriers offering point-to-point routes has made the market more competitive, prompting mainline carriers to lower the price for these connecting itineraries.