Computing element of fundamental group of Möbius strip How does one go about computing the element of the fundamental group of a Möbius strip represented by the loop $(\cos 10\pi t, \sin 10\pi t)$.

HINT: You know that $\pi_1(M)\cong \mathbb{Z}$ via the isomorphism which takes $1\in\mathbb{Z}$ to the loop which goes around the Möbius strip once. Find how to express your loop as a product of the once-around loop and just pull back.
