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  2. Pushforward (differential) - Wikipedia

    en.wikipedia.org/wiki/Pushforward_(differential)

    If a map, φ, carries every point on manifold M to manifold N then the pushforward of φ carries vectors in the tangent space at every point in M to a tangent space at every point in N. In differential geometry , pushforward is a linear approximation of smooth maps (formulating manifold) on tangent spaces.

  3. Convex curve - Wikipedia

    en.wikipedia.org/wiki/Convex_curve

    Supporting lines and tangent lines are not the same thing, [11] but for convex curves, every tangent line is a supporting line. [8] At a point of a curve where a tangent line exists, there can only be one supporting line, the tangent line. [12] Therefore, a smooth curve is convex if it lies on one side of each of its tangent lines.

  4. Map projection - Wikipedia

    en.wikipedia.org/wiki/Map_projection

    Distance from the tangent point on the map is proportional to straight-line distance through the Earth: r(d) = c sin ⁠ d / 2R ⁠ [38] Logarithmic azimuthal is constructed so that each point's distance from the center of the map is the logarithm of its distance from the tangent point on the Earth.

  5. Transversality (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Transversality_(mathematics)

    An extremely special case of this is the following: if a differentiable function from reals to the reals has nonzero derivative at a zero of the function, then the zero is simple, i.e. it the graph is transverse to the x-axis at that zero; a zero derivative would mean a horizontal tangent to the curve, which would agree with the tangent space ...

  6. Exponential map (Riemannian geometry) - Wikipedia

    en.wikipedia.org/wiki/Exponential_map...

    Then there is a unique geodesic γ v:[0,1] → M satisfying γ v (0) = p with initial tangent vector γ′ v (0) = v. The corresponding exponential map is defined by exp p (v) = γ v (1). In general, the exponential map is only locally defined, that is, it only takes a small neighborhood of the origin at T p M, to a neighborhood of p in the ...

  7. Mercator projection - Wikipedia

    en.wikipedia.org/wiki/Mercator_projection

    For example, a Mercator map printed in a book might have an equatorial width of 13.4 cm corresponding to a globe radius of 2.13 cm and an RF of approximately ⁠ 1 / 300M ⁠ (M is used as an abbreviation for 1,000,000 in writing an RF) whereas Mercator's original 1569 map has a width of 198 cm corresponding to a globe radius of 31.5 cm and an ...

  8. Ford circle - Wikipedia

    en.wikipedia.org/wiki/Ford_circle

    In mathematics, a Ford circle is a circle in the Euclidean plane, in a family of circles that are all tangent to the -axis at rational points. For each rational number p / q {\displaystyle p/q} , expressed in lowest terms, there is a Ford circle whose center is at the point ( p / q , 1 / ( 2 q 2 ) ) {\displaystyle (p/q,1/(2q^{2}))} and whose ...

  9. Tangent space - Wikipedia

    en.wikipedia.org/wiki/Tangent_space

    [1] [2] More strictly, this defines an affine tangent space, which is distinct from the space of tangent vectors described by modern terminology. In algebraic geometry , in contrast, there is an intrinsic definition of the tangent space at a point of an algebraic variety V {\displaystyle V} that gives a vector space with dimension at least that ...

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