Shape

117 A Second Look at Calculating
and their transformations when triangles like mine
are translated along different axes. And there are still other shapes
that can be transformed when triangles are changed in a more complicated way. Even
so, these possibilities are merely a trivial beginning.
The five-pointed star
initiates twin series of stars and superstars that have the kind of ambiguity that I’ve
been playing with. The stars in this series
have an odd number of points. And I can trace polygons in each one
that work just like triangles and chevrons in the five-pointed star. There are 2n 1
pairs of polygons—one with n sides and the other with n þ 1 sides—in a star with
2n 1 points. Each of these pairs provides its own description of the star that’s incompatible
with the others when I calculate with two rules—and each description leads to
different results. One rule is defined for the polygon with n sides according to the
schema
x fi tðxÞ