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  2. Eccentricity (mathematics) - Wikipedia

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

    In mathematics, the eccentricity of a conic section is a non-negative real number that uniquely characterizes its shape. One can think of the eccentricity as a measure of how much a conic section deviates from being circular. In particular: The eccentricity of a circle is 0. The eccentricity of an ellipse which is not a circle is between 0 and 1.

  3. Perimeter of an ellipse - Wikipedia

    en.wikipedia.org/wiki/Perimeter_of_an_ellipse

    An ellipse has two axes and two foci. Unlike most other elementary shapes, such as the circle and square, there is no algebraic equation to determine the perimeter of an ellipse. Throughout history, a large number of equations for approximations and estimates have been made for the perimeter of an ellipse.

  4. Ellipse - Wikipedia

    en.wikipedia.org/wiki/Ellipse

    An ellipse (red) obtained as the intersection of a cone with an inclined plane. Ellipse: notations Ellipses: examples with increasing eccentricity. In mathematics, an ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant.

  5. Confocal conic sections - Wikipedia

    en.wikipedia.org/wiki/Confocal_conic_sections

    A pencil of confocal ellipses and hyperbolas is specified by choice of linear eccentricity c (the x-coordinate of one focus) and can be parametrized by the semi-major axis a (the x-coordinate of the intersection of a specific conic in the pencil and the x-axis). When 0 < a < c the conic is a hyperbola; when c < a the conic is an ellipse.

  6. Roundness - Wikipedia

    en.wikipedia.org/wiki/Roundness

    Roundness = ⁠ Perimeter 2 / 4 π × Area ⁠. This ratio will be 1 for a circle and greater than 1 for non-circular shapes. Another definition is the inverse of that: Roundness = ⁠ 4 π × Area / Perimeter 2 ⁠, which is 1 for a perfect circle and goes down as far as 0 for highly non-circular shapes.

  7. Conic constant - Wikipedia

    en.wikipedia.org/wiki/Conic_constant

    The constant is given by =, where e is the eccentricity of the conic section. The equation for a conic section with apex at the origin and tangent to the y axis is y 2 − 2 R x + ( K + 1 ) x 2 = 0 {\displaystyle y^{2}-2Rx+(K+1)x^{2}=0}

  8. Elliptic integral - Wikipedia

    en.wikipedia.org/wiki/Elliptic_integral

    For an ellipse with semi-major axis a and semi-minor axis b and eccentricity e = √ 1 − b 2 /a 2, the complete elliptic integral of the second kind E(e) is equal to one quarter of the circumference C of the ellipse measured in units of the semi-major axis a. In other words: = ().

  9. Orbital eccentricity - Wikipedia

    en.wikipedia.org/wiki/Orbital_eccentricity

    For elliptical orbits, a simple proof shows that ⁡ gives the projection angle of a perfect circle to an ellipse of eccentricity e. For example, to view the eccentricity of the planet Mercury (e = 0.2056), one must simply calculate the inverse sine to find the projection angle of 11.86 degrees. Then, tilting any circular object by that angle ...