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The math behind radius searches is somewhat complex, and there are several possible approaches.
One might think that the easiest approach would be to simply search for a latitude between x and y, and a longitude between x and y. This is very simple, but leads to a lot of inaccuracy. Such a range produces something close to a square rather than a circle. (In fact, because of the nature of longitudinal lines, it produces a near-trapezoid shape.) The area of a circle is about 78% of the area of a radius, so this would lead to a lot of additional rows that are not intended. Moreover, the corner of the square is about 141% of the radius of the circle, and that would be generally unacceptable.
Remember “a2 + b2 = c2”? This Pythagorean algorithm calculates the third side of a right triangle, called a hypotenuse. If the Earth was completely flat, and map coordinates were completely squares, this would be an easy way to calculate distances. But alas, the Earth is a sphere, or an egg-shaped, slightly wobbly approximation of a sphere, so Euclidean geometry will not give us the desired result.