Tangent in a sentence

Intersection of a tangent and perpendicular from focus Perpendicular from focus to tangent Since triangles FBE and CBE are congruent, FB is perpendicular to the tangent BE.

More specifically, two curves are said to be tangent at a point if they have the same tangent at a point, and orthogonal if their tangent lines are orthogonal.

The introduction of a Riemannian metric or a symplectic form gives rise to a natural isomorphism between the tangent space and the cotangent space at a point, associating to any tangent covector a canonical tangent vector.

Above internally and below externally tangent Two circles of non-equal radius, both in the same plane, are said to be tangent to each other if they meet at only one point.

All the tangent spaces can be "glued together" to form a new differentiable manifold of twice the dimension of the original manifold, called the tangent bundle of the manifold.

Alternative proofs Parabola and tangent The above proofs of the reflective and tangent bisection properties use a line of calculus.

As it passes through the point where the tangent line and the curve meet, called the point of tangency, the tangent line is "going in the same direction" as the curve, and is thus the best straight-line approximation to the curve at that point.

Because V2 is tangent to the arc of cycloid in P2, it follows that also P1P2 is tangent.

Dirac, 1975, General Theory of Relativity, Princeton University Press More strictly this defines an affine tangent space, distinct from the space of tangent vectors described by modern terminology.

For example, the tangent bundle consists of the collection of tangent spaces parametrized by the points of a differentiable manifold.

However, it is more convenient to define the notion of tangent space based on the manifold itself. citation There are various equivalent ways of defining the tangent spaces of a manifold.

If one forms a rectangle with vertices on the asymptotes and two sides that are tangent to the hyperbola, the sides tangent to the hyperbola are 2b in length while the sides that run parallel to the line between the foci (the major axis) are 2a in length.

Instead, the total derivative gives a function from the tangent bundle of the source to the tangent bundle of the target.

It cannot be a function on the tangent bundle because the tangent bundle only has room for the base space and the directional derivatives.

It gets its name from its operating principle, the tangent law of magnetism, which states that the tangent of the angle a compass needle makes is proportional to the ratio of the strengths of the two perpendicular magnetic fields.

Tangent galvanometer Tangent galvanometer made by J. H. Bunnell Co. around 1890.

Tangent property The angle containing part of the ellipse, formed at a point on the major axis by a tangent line to the ellipse and the major axis, has measure less than 45°.

The derivative (or differential) of a (differentiable) map f: M → N between manifolds, at a point x in M, is then a linear map from the tangent space of M at x to the tangent space of N at f(x).

The local ENU coordinates are formed from a plane tangent to the Earth's surface fixed to a specific location and hence it is sometimes known as a "Local Tangent" or "local geodetic" plane.

The mapping of radial lines can be visualized by imagining a plane tangent to the Earth, with the central point as tangent point.