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  2. Eccentricity (mathematics) - Wikipedia

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

    For example, on a triaxial ellipsoid, the meridional eccentricity is that of the ellipse formed by a section containing both the longest and the shortest axes (one of which will be the polar axis), and the equatorial eccentricity is the eccentricity of the ellipse formed by a section through the centre, perpendicular to the polar axis (i.e. in ...

  3. Elliptic coordinate system - Wikipedia

    en.wikipedia.org/wiki/Elliptic_coordinate_system

    Ellipsoidal coordinates are a formal extension of elliptic coordinates into 3-dimensions, which is based on confocal ellipsoids, hyperboloids of one and two sheets. Note that (ellipsoidal) Geographic coordinate system is a different concept from above.

  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. Counting points on elliptic curves - Wikipedia

    en.wikipedia.org/wiki/Counting_points_on...

    Let E be the curve y 2 = x 3 + x + 1 over . To count points on E, we make a list of the possible values of x, then of the quadratic residues of x mod 5 (for lookup purpose only), then of x 3 + x + 1 mod 5, then of y of x 3 + x + 1 mod 5. This yields the points on E.

  6. Parametric equation - Wikipedia

    en.wikipedia.org/wiki/Parametric_equation

    Here (X c, Y c) is the center of the ellipse, and φ is the angle between the x-axis and the major axis of the ellipse. Both parameterizations may be made rational by using the tangent half-angle formula and setting tan ⁡ t 2 = u . {\textstyle \tan {\frac {t}{2}}=u\,.}

  7. Elliptic curve - Wikipedia

    en.wikipedia.org/wiki/Elliptic_curve

    Redoing the same with P 1, that is to say P 1 = 2P 2 + Q 2, then P 2 = 2P 3 + Q 3, etc. finally expresses P as an integral linear combination of points Q i and of points whose height is bounded by a fixed constant chosen in advance: by the weak Mordell–Weil theorem and the second property of the height function P is thus expressed as an ...

  8. Ellipsoid - Wikipedia

    en.wikipedia.org/wiki/Ellipsoid

    The lower part of the diagram shows that F 1 and F 2 are the foci of the ellipse in the xy-plane, too. Hence, it is confocal to the given ellipse and the length of the string is l = 2r x + (a − c). Solving for r x yields r x = ⁠ 1 / 2 ⁠ (l − a + c); furthermore r 2 y = r 2 x − c 2.

  9. Orthoptic (geometry) - Wikipedia

    en.wikipedia.org/wiki/Orthoptic_(geometry)

    If a tangent contains the point (x 0, y 0), off the parabola, then the equation = + = holds, which has two solutions m 1 and m 2 corresponding to the two tangents passing (x 0, y 0). The free term of a reduced quadratic equation is always the product of its solutions.