Primes, Gaps and Gaps of Gaps
The prime number sequence fascinates me. I am not sure why but exposing properties in it is exciting. Even if they are mundane and "obvious to everyone else", the fact that I can answer questions visually, sometimes thrills me.
tl;dr: gaps-of-gaps
One day I became curious about musical triads (three note chords) as geometric triangles. I speculated about the actual sizes of the sides, given the intervals between the notes at the corners. Then, in no time, I was off day-dreaming about wobbling, vibrating triangles and string theory...