Circle of Fifths
The circle of fifths is a special device used in music theory to remember key signatures and other similar techniques. To create the circle, one may begin with any note. Then, going clockwise, each ascending note will be a perfect fifth above the previous note. You could also go counter-clockwise using fourths instead, since fourths are the inversion of fifths. Notice that the completed circle has all twelve notes of the chromatic scale.
As you may have noticed, if you read clockwise beginning with C and ending with C# you have a list of consecutive major sharp key signatures. C major has no sharps, G major has one sharp, D major has two sharps, and so on until C# major, which has seven sharps.
If you read in a descending order beginning with C and ending with Cb, you have a list of consecutive major flat key signatures. C major has no flats, F major has one flat, Bb major has two flats, and so on until Cb major, which has seven flats.
If you read in an ascending order beginning with A (whose minor key is the relative minor key of C major) and ending with A#, you have a list of consecutive minor sharp key signatures.
If you read in a descending order beginning with A and ending with Ab, you have a list of consecutive minor flat key signatures.