Augmented Chords
----------------
The formula for augmented chords is 1, 3, and #5.  Augmented chords are
symmetrical chords.  That is, the distance from each tone to the next is
the same in half steps, or frets.  Since each note in an augmented chord
is equidistance in tone from each other, the augmented chord can be 
identified by any note in the chord.  For example the C aug chord contains
the notes C, E and G#.  Therefore it can be called a C aug, E aug, G# aug,
or Ab (same as G#) aug.  

Caug, C form    Caug, A form    Caug, G form    Caug, E form    Caug, D form
===========     +-+-+-+-+-+     +-+-+-+-+-+     +-+-+-+-+-+     +-+-+-+-+-+
| | | 1 1 | -1  | | | | | 1 -4  | | | 1 1 | -5  | | | | | 1 -8  | | | | | 1 -12
+-+-+-+-+-+     +-+-+-+-+-+     +-+-+-+-+-+     +-+-+-+-+-+     +-+-+-+-+-+
| | 2 | | |     | | | 2 3 |     | | 2 | | |     | | | 2 3 |     | | | 2 3 |
+-+-+-+-+-+     +-+-+-+-+-+     +-+-+-+-+-+     +-+-+-+-+-+     +-+-+-+-+-+
| 3 | | | |     | | 4 | | |     | 3 | | | |     | | 4 | | |     | | 4 | | |
+-+-+-+-+-+     +-+-+-+-+-+     +-+-+-+-+-+     +-+-+-+-+-+     +-+-+-+-+-+
4 | | | | |     | | | | | |     4 | | | | |     | | | | | |     | | | | | |
+-+-+-+-+-+     +-+-+-+-+-+     +-+-+-+-+-+     +-+-+-+-+-+     +-+-+-+-+-+
===========     ===========     ===========     ===========     ===========         
5#  3   1       x   5#  3       1   5#  3       x   1   5#      x   3   1 
  1   5#  x       x   1   5#      3   1   x       x   3   1       x   5#  3

Notice the same shapes in different fretboard positions producing the same 
chord.  Also notice that the two shapes shown above really overlap:

+-+-+-+-+-+
| | | | | O
+-+-+-+-+-+  
| | | O O |
+-+-+-+-+-+  
| | O | | |     
+-+-+-+-+-+    
| O | | | |  
+-+-+-+-+-+    
O | | | | |   
+-+-+-+-+-+