# Erica Minuz

”Twice upon a time there was a king…” The narrator tells a distorted
fairy tale that seems absurd, but that is actually built on a
mathematical structure. The king realizes that he has a double and
his power falls apart, like a playing card castle. He then asks help
from a magician (or a mathematician?). In order to solve the
situation, the magician puts a spell on the kingdom (takes the
quotient space) identifying every point with its reflection in the
mirror. Now the king is one, but the kingdom has no more
orientation: there’s no left nor right. ”What kind of kingdom is
that?” the people ask themselves. The narrator will then show some
examples of spaces where right and left do not make sense: Moebius
Bands, Klein Bottles and Projective Spaces. These are examples of
non-orientable spaces. What will happen to the king? What does it
mean to be twice? And if the king was once two, why not three, four,
five, or infinite?