It's basic geometry. Nothing fancy. Very useful when flying some instrument approaches and easy to calculate on-the-run in your head. Also useful when using the tilt on the radar to figure out where the bottom of the beamwidth is at a certain distance from the aircraft.
At 60nm, radials are 1nm apart = 1 radial/nm
At 30nm, 2 radials/nm
At 15nm, 4 radials/nm
At 10nm, 6 radias/nm
As a practical application, say you were flying on a 15nm arc and wanted to know what you're lead radial should be to turn onto the course. Your speed is 180kts = approx 3nm/min. = approx 2nm turn radius.
Therefor, on a 15nm arc, 2nm turn radius = 8 radials (degrees) lead