"Giant Steps" derived from the bridge of "Have You Met Miss Jones". It's very Wagnerian
in that the tonal center changes continuously. It really has little utility for folk music.
Coltrane is a musical genius who has innovated a new kind of contemporary jazz.

The circle of fifths should be thought of as the circle of fourths, rewritten so instead of progressing by fifths, it should progress clockwise by fourths: ex. C, F, Bb, Eb, Ab, etc.

This is more useful in its application to harmonies in jazz. For example: "Sweet Georgia Brown" in the key of F starts with a D7, then progresses a fourth away to G7, another fourth to C7, then to the tonic chord of F which moves to an A7, and proceeds a fourth to D7,
G7, C7 etc.

In jazz this is called back-cycling.