I was thinking the other day, and I came up with the craziest musical problem... It deals largely with math, so I decided to post it here instead of the Music Theory board...
Here's the problem: How many dots would one have to add to a quarter note to make it equal a half note? Seems like a simple question at first, but then you think about it... A dotted quarter note = a quarter note + an eighth note. A quarter note with two dots = a quarter note + an eighth note + a sixteenth note, and if you keep adding dots, the value added to the previous note continues to half, so, mathematically, the question is essentially this:
If we continue this pattern: 1+1/2+1/4+1/8, etc., How many additions are we going to have to make to the original 1 to make the answer equal to 2? I guess the question is really "WILL it ever equal 2?"
Math people help me out here! This one makes my head spin!