Since the differential equation is first order, it only puts a condition on the tangent plane to the graph, so that any function everywhere tangent to a solution must also be a solution.
42.
Like the first fundamental form, the second fundamental form may be viewed as a family of symmetric bilinear forms on the tangent plane at each point of the surface depending smoothly on the point.
43.
1 ) The nucleus of a hydrogen-1 atom exists such that a tangent plane to it would be the same plane as a tangent plane to the event horizon of a black hole.
44.
1 ) The nucleus of a hydrogen-1 atom exists such that a tangent plane to it would be the same plane as a tangent plane to the event horizon of a black hole.
45.
This provides a way to identify the tangent planes at different points along the curve by affine ( in fact Euclidean ) transformations, and is an example of a Cartan connection called an affine connection.
46.
This is achieved by casting surface points of the sphere onto a tangent plane, each landing where a ray from the center of the sphere passes through the point on the surface and then on to the plane.
47.
This is achieved by casting surface points of the sphere onto a tangent plane, each landing where a ray from the center of the earth passes through the point on the surface and then on to the plane.
48.
The "'normal line "', or simply "'normal "'at a point of a surface is the unique line passing through the point and perpendicular to the tangent plane.
49.
As stated in the observations, the tangent plane T _ p ( S ) is endowed with the metric induced by the exponential map \ exp _ p : T _ p ( S ) \ longrightarrow S.
50.
The stress represented by a radius-vector of the stress ellipsoid acts on a plane oriented parallel to the tangent plane to the stress-director surface at the point of its intersection with the radius-vector.
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