Welcome back to free online math tutoring,
We did have a good discussion again today with a few insights. I saw
that the definition you provided - counting sides - is really
topological, more examples on math helper; but it is also very pleasing because it can be
generalized to points and angles. So a side (or point, or angle) is
opposite another side (or point, or angle) if there is an equal
number of sides between the two counting in both directions. So we
preserve the idea that in a pentagon there is a vertex or an angle
opposite each side, but not a side opposite.
One approach that a colleague suggested to try to preserve the common-
sense feeling of opposite was to draw an axis through the "middle" of
the polygon and define two sets of opposition - X-opposite and
Y-opposite. Of course, rotating the figure destroys the relationships,
so I think we set that notion aside. more examples on math tutoring.
We did have a good discussion again today with a few insights. I saw
that the definition you provided - counting sides - is really
topological, more examples on math helper; but it is also very pleasing because it can be
generalized to points and angles. So a side (or point, or angle) is
opposite another side (or point, or angle) if there is an equal
number of sides between the two counting in both directions. So we
preserve the idea that in a pentagon there is a vertex or an angle
opposite each side, but not a side opposite.
One approach that a colleague suggested to try to preserve the common-
sense feeling of opposite was to draw an axis through the "middle" of
the polygon and define two sets of opposition - X-opposite and
Y-opposite. Of course, rotating the figure destroys the relationships,
so I think we set that notion aside. more examples on math tutoring.
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