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Sources & notes

1. This game's own engine, which is pure and deterministic and never touches the page. Warmer Globe is a guessing game: a country is hidden, and the player names countries to home in on it. Each guess is scored by how close it sits to the hidden country, and the closer it is the hotter it glows, a guess exactly on the target reads as boiling, and the heat falls off smoothly with distance, cooling toward the far side of the world without quite levelling out, so even two distant guesses can be told apart. That closeness is a great-circle distance: the engine holds each country's latitude and longitude and measures the distance between two points with the haversine formula, taking the Earth's radius as about six thousand three hundred seventy-one kilometres and the greatest possible separation, at the antipode, as about twenty thousand kilometres. It also computes the initial bearing from a guess toward the target, a compass direction to point the way. A round is a five-stop expedition, and the hidden country and the order are drawn from a seed, so the daily game is the same for everyone.
2. "Great-circle distance," Wikipedia, the great-circle distance is the shortest distance between two points on the surface of a sphere, measured along the surface rather than through its interior. It lies along a great circle, whose centre is the sphere's centre, and equals the central angle between the points, in radians, times the sphere's radius. For points on the Earth, given by latitude and longitude and treating the Earth as a sphere of mean radius about six thousand three hundred seventy-one kilometres, the distance is usually computed with the haversine formula, which stays accurate even for small distances where simpler methods lose precision; treating the Earth as a sphere keeps the result within about half a percent, so the method is widely used in navigation. en.wikipedia.org/wiki/Great-circle_distance.
3. "Geographic coordinate system," Wikipedia, a geographic coordinate system specifies locations on the Earth using coordinates, most commonly latitude and longitude. Latitude is the angle north or south of the equator, from zero degrees there to ninety at the poles, its lines called parallels; longitude is the angle east or west of the prime meridian through Greenwich, from zero to one hundred and eighty degrees, its lines called meridians; together they form a grid called the graticule. The system was invented by Eratosthenes in the third century before the common era, improved by Hipparchus, and refined by Ptolemy in the second century, and in 1884 an international conference fixed Greenwich as the reference for the prime meridian. Near the equator one degree of latitude spans about one hundred and eleven kilometres. en.wikipedia.org/wiki/Geographic_coordinate_system.
4. Further reading on Great-circle distance, Great Circle -- from Wolfram MathWorld. mathworld.wolfram.com.