\begin{definition}[Definition:Big Dipper Operation/Illustration]
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When the stars of the {{WP|Big_Dipper|Big Dipper}} 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 lockwise round the pan. Then count $b$ stars more from there. $a +_{m, n} b$ is the number of the star you land on.''
\end{definition}