Definition:Dipper Operation/Illustration

Illustration of Dipper Operation

 * BigDipper.png

When the stars of the are numbered as shown, the sequence:
 * $1, 1 +_{3, 4} 1, 1 +_{3, 4} 1 +_{3, 4} 1, \ldots$

traces out those stars in the order:
 * first the handle: $\text{Alkaid}, \text{Mizar}, \text{Alioth}$

then:
 * round the pan indefinitely: $\text{Megrez}, \text{Dubhe}, \text{Merak}, \text{Phecda}, \text{Megrez}, \ldots$

Hence $a +_{m, n} b$ can be interpreted as:
 * Start at $\text{Alkaid}$ and count $a$ stars along the handle and then clockwise round the pan.
 * Then count $b$ stars more from there.
 * $a +_{m, n} b$ is the number of the star you land on.