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  2. Simpson's rules (ship stability) - Wikipedia

    en.wikipedia.org/wiki/Simpson's_rules_(ship...

    Simpson's rules are used to calculate the volume of lifeboats, [6] and by surveyors to calculate the volume of sludge in a ship's oil tanks. For instance, in the latter, Simpson's 3rd rule is used to find the volume between two co-ordinates. To calculate the entire area / volume, Simpson's first rule is used. [7]

  3. Limaçon - Wikipedia

    en.wikipedia.org/wiki/Limaçon

    Construction of the limaçon r = 2 + cos(π – θ) with polar coordinates' origin at (x, y) = (⁠ 1 / 2 ⁠, 0). In geometry, a limaçon or limacon / ˈ l ɪ m ə s ɒ n /, also known as a limaçon of Pascal or Pascal's Snail, is defined as a roulette curve formed by the path of a point fixed to a circle when that circle rolls around the outside of a circle of equal radius.

  4. Polar coordinate system - Wikipedia

    en.wikipedia.org/wiki/Polar_coordinate_system

    A mechanical device that computes area integrals is the planimeter, which measures the area of plane figures by tracing them out: this replicates integration in polar coordinates by adding a joint so that the 2-element linkage effects Green's theorem, converting the quadratic polar integral to a linear integral.

  5. Solving the geodesic equations - Wikipedia

    en.wikipedia.org/wiki/Solving_the_geodesic_equations

    On an n-dimensional Riemannian manifold, the geodesic equation written in a coordinate chart with coordinates is: + = where the coordinates x a (s) are regarded as the coordinates of a curve γ(s) in and are the Christoffel symbols.

  6. Radius of curvature - Wikipedia

    en.wikipedia.org/wiki/Radius_of_curvature

    We want to find the radius ρ of a parametrized circle which matches γ in its zeroth, first, and second derivatives at t. Clearly the radius will not depend on the position γ(t), only on the velocity γ′(t) and acceleration γ″(t). There are only three independent scalars that can be obtained from two vectors v and w, namely v · v, v ...

  7. Polar curve - Wikipedia

    en.wikipedia.org/wiki/Polar_curve

    If the polar line of C with respect to a point Q is a line L, then Q is said to be a pole of L. A given line has (n−1) 2 poles (counting multiplicities etc.) where n is the degree of C. To see this, pick two points P and Q on L. The locus of points whose polar lines pass through P is the first polar of P and this is a curve of degree n−1.

  8. Linear interpolation - Wikipedia

    en.wikipedia.org/wiki/Linear_interpolation

    Given the two red points, the blue line is the linear interpolant between the points, and the value y at x may be found by linear interpolation.. In mathematics, linear interpolation is a method of curve fitting using linear polynomials to construct new data points within the range of a discrete set of known data points.

  9. Signed area - Wikipedia

    en.wikipedia.org/wiki/Signed_area

    The blue area above the x-axis may be specified as positive area, while the yellow area below the x-axis is the negative area. The integral of a real function can be imagined as the signed area between the x {\displaystyle x} -axis and the curve y = f ( x ) {\displaystyle y=f(x)} over an interval [ a , b ].

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