The Klein bottle is two projective planes connected-summed, equivalently two Möbius bands glued along their boundary.Suggest a slogan
The Klein bottle is a connected sum of two projective planes, \[ \KK \cong \RP^2 \# \RP^2 .\] Equivalently, \(\KK\) is the union of two Möbius bands glued along their boundary circles [@Hat02].