TITLE: Why is the thing dual to a "meridian" called a "longitude"?
QUESTION [15 upvotes]: A pair of distinguished generators of the fundamental group $\pi_1(\partial(S^3 \setminus K))$ of the boundary torus of a knot complement are usually called the "meridian" and "longitude". However, this terminology has always seemed a bit odd to me: in geography a meridian is a line of longitude, so shouldn't the curve it intersects be a "latitude"? Does anyone know the origin of this language?

REPLY [13 votes]: There is a fundamental asymmetry between latitude and longitude on a sphere, whereas on a torus, there is a symmetry between the two generators.  This symmetry could motivate the use of nearly synonymous words.
The terminology may originate with the paper On the homology invariants of knots by H. Seifert (Quart. J. Math. Oxford (2) 1 (1950), 23–32).  The torus $T$ of interest to Seifert is the boundary of a closed tubular neighborhood $V$ of a knot in $\mathbb{R}^3$.  Seifert says that a Jordan curve on $T$ that bounds on $V$ (respectively, on $\mathbb{R}^3 - V + T$) but not on $T$ is called a meridian (respectively, a longitudinal circuit). Seifert phrases these definitions in a way that highlights the symmetry, which makes the use of near synonyms seem natural.