A Math Forum Web Unit
Transforming Magic Stars
Suzanne's Math Lessons ||
Magic Squares ||
First let's look at how to apply the transformation (or exchange) rule to yield stars with the number 1 not at the top, but at an inner corner.
Consider this star:
There are three exchange rules:
- A<-->L B<-->C D<-->E H<-->I J<-->K
- B<-->K H<-->F A<-->C L<-->J D<-->G
Rotate the star 60° to the right, use rule 1, and rotate 60° back
to the left.
- E<-->H A<-->D B<-->F G<-->K I<-->L
Rotate the star 60° to the left, use rule 1, and rotate 60° back
to the right.
Let's apply Exchange Rule 1:
Now let's rotate Derived Star 1 180°:
Derived Star 2 is not identical to the original but the number 1 is still on top!
Let's apply Exchange Rule 3 to the Original Star
and rotate Derived Star 3 60° to the right:
In the case of Derived Star 3, the number 1 is at an inner corner.
On to Combining exchange rules
Here Exchange Rule 3 is the same as (1) rotating 60° to the
left, (2) applying Exchange Rule 1, and (3) rotating
60° back to the right: after the
rotation, the number 1 is at B; with the
transformation the number 1 moves to the inner corner.
Back to Magic star sets
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12 October 1996
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