nLab meridian

Idea

Given an n-sphere $S^n$ for $n \,\geq 1\,$, regarded under its standard unit sphere embedding into Cartesian space

$$S^n \;\subset\; \mathbb{R}^{n+1} \,\simeq\, \mathbb{R} \times \mathbb{R}^n \,,$$

then a meridian is any geodesic (great half-circle) from the “north pole” $\big(1,\vec 0\big)$ to the “south pole” $\big(-1,\vec 0\big)$ (or more generally between any pair of antipodes).

Hence the $n$-sphere may be regarded as the union of

1. its north pole

2. its south pole

3. all meridians.

This decomposition exhibits the $n$-sphere as the (un-reduced) suspension of the $(n-1)$-sphere which is its equator.

Related concepts

• suspension, suspension type

• equator

• hemisphere, antipode

• stereographic projection

• clutching construction

References

See also:

• Wikipedia, Meridian_(geography)