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  2. Ellipse - Wikipedia

    en.wikipedia.org/wiki/Ellipse

    An ellipse has a simple algebraic solution for its area, but for its perimeter (also known as circumference), integration is required to obtain an exact solution. Analytically , the equation of a standard ellipse centered at the origin with width 2 a {\displaystyle 2a} and height 2 b {\displaystyle 2b} is: x 2 a 2 + y 2 b 2 = 1. {\displaystyle ...

  3. Kepler's laws of planetary motion - Wikipedia

    en.wikipedia.org/wiki/Kepler's_laws_of_planetary...

    The area of the ellipse is = ... A derivation of Kepler's third law of planetary motion is a standard topic in engineering mechanics classes. See, ...

  4. Method of exhaustion - Wikipedia

    en.wikipedia.org/wiki/Method_of_exhaustion

    The area bounded by the intersection of a line and a parabola is 4/3 that of the triangle having the same base and height (the quadrature of the parabola); The area of an ellipse is proportional to a rectangle having sides equal to its major and minor axes;

  5. List of second moments of area - Wikipedia

    en.wikipedia.org/wiki/List_of_second_moments_of_area

    The following is a list of second moments of area of some shapes. The second moment of area , also known as area moment of inertia, is a geometrical property of an area which reflects how its points are distributed with respect to an arbitrary axis.

  6. 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.

  7. Area of a circle - Wikipedia

    en.wikipedia.org/wiki/Area_of_a_circle

    The square gets sent to a rectangle circumscribing the ellipse. The ratio of the area of the circle to the square is π /4, which means the ratio of the ellipse to the rectangle is also π /4. Suppose a and b are the lengths of the major and minor axes of the ellipse. Since the area of the rectangle is ab, the area of the ellipse is π ab/4.

  8. Radius of curvature - Wikipedia

    en.wikipedia.org/wiki/Radius_of_curvature

    In an ellipse with major axis 2a and minor axis 2b, the vertices on the major axis have the smallest radius of curvature of any points, =; and the vertices on the minor axis have the largest radius of curvature of any points, R = ⁠ a 2 / b ⁠.

  9. Semi-major and semi-minor axes - Wikipedia

    en.wikipedia.org/wiki/Semi-major_and_semi-minor_axes

    The semi-minor axis of an ellipse runs from the center of the ellipse (a point halfway between and on the line running between the foci) to the edge of the ellipse. The semi-minor axis is half of the minor axis. The minor axis is the longest line segment perpendicular to the major axis that connects two points on the ellipse's edge.