Definition:Dipper Operation/Illustration

Illustration of Dipper Operation

When the stars of the 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 clockwise round the pan.

Then count $b$ stars more from there.

$a +_{m, n} b$ is the number of the star you land on.

Sources

• 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text I$: Algebraic Structures: $\S 2$: Compositions: Exercise $2.8 \ \text{(a)}$