When are a coffee cup and a doughnut equivalent to
each other?
Answer:
To the casual observer, this question may seem silly, and
a fun response might be "when they are in my belly." Really, at a
quick glance, these items seem to have nothing in common.
Yet, what if the cup was made of clay. One could mold
that cup into the shape of a doughnut with a little twisting, bending,
and shaping. Also consider that with each item there exists only
one hole to account for.
A topologist would say that these two items are of genus
1. (since there is only one hole in each.)
This genus idea opens doors to equivalencies
that to the untrained eye might never be discerned.
