* specific way, rather than to have unit norm. See the documentation of
* Manifold::get_tangent_vector(), as well as below, for more information.
*
- * In the simplest case (namely, the FlatManifold class), these direction
+ * In the simplest case (namely, the FlatManifold class), these tangent
* vectors are just the difference vector between the two given points.
* However, in more complicated (and more interesting) cases, the direction may
* be different. For example, for the SphericalManifold case, if the two given
- * points lie on a common grand circle around the origin, then the direction
+ * points lie on a common grand circle around the origin, then the tangent
* vector will be tangential to the grand circle, rather than pointing straight
* from one point to the other.
*
* via a metric specific to a particular implementation of this class in a
* derived class. For example, in the case of a FlatManifold, the shortest
* line between two points is just the straight line, and in this case the
- * direction vector is just the difference $\mathbf d=\mathbf x_2-\mathbf x_1$.
+ * tangent vector is just the difference $\mathbf d=\mathbf x_2-\mathbf x_1$.
* On the other hand, for a manifold that describes a surface embedded in
* a higher dimensional space (e.g., the surface of a sphere), then the
- * direction vector is tangential to the surface, and consequently may point in
+ * tangent vector is tangential to the surface, and consequently may point in
* a different direction than the straight line that connects the two points.
*
* While tangent vectors are often normalized to unit length, the vectors