About this route:
A direct, nonstop flight between Kikai Airport (KKX), Kikaiga Shima, Kikai-Shima Island, Japan and Carlos Alberto da Costa Neves Airport (CFC), Caçador, Santa Catarina, Brazil would travel a Great Circle distance of 12,318 miles (or 19,824 kilometers).
A Great Circle is the shortest distance between 2 points on a sphere. Because most world maps are flat (but the Earth is round), the route of the shortest distance between 2 points on the Earth will often appear curved when viewed on a flat map, especially for long distances. If you were to simply draw a straight line on a flat map and measure a very long distance, it would likely be much further than if you were to lay a string between those two points on a globe. Because of the large distance between Kikai Airport and Carlos Alberto da Costa Neves Airport, the route shown on this map most likely appears curved because of this reason.
Try it at home! Get a globe and tightly lay a string between Kikai Airport and Carlos Alberto da Costa Neves Airport. You'll see that it will travel the same route of the red line on this map!
The distance between KKX and CFC makes them almost exactly antipodal (the exact opposite side of the world) to each other. Nonstop flights between Kikai Airport and Carlos Alberto da Costa Neves Airport would be very impractical for the airlines, because only a lightly loaded Boeing 777-200LR would be able to make the trip. Since airlines need to be able to take as many people and cargo as possible in order to make a profit, the odds of ever seeing a nonstop flight between KKX and CFC are slim to none. However, you'll still be able to get from Kikaiga Shima, Kikai-Shima Island, Japan and Caçador, Santa Catarina, Brazil by taking some connecting flights!
Did you know that one full circling of the Earth (measuring from the equator) is about 24,901.5 miles (or 40,075 kilometers), which means if you were 12,450 miles from any given point on the planet, the distance back to your starting point would be about the same -- in any direction! The same can be said for a nonstop flight between KKX and CFC!