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  2. Carlyle circle - Wikipedia

    en.wikipedia.org/wiki/Carlyle_circle

    Carlyle circle of the quadratic equation x 2 − sx + p = 0. Given the quadratic equation x 2 − sx + p = 0. the circle in the coordinate plane having the line segment joining the points A(0, 1) and B(s, p) as a diameter is called the Carlyle circle of the quadratic equation. [1] [2] [3]

  3. Quadratic mean diameter - Wikipedia

    en.wikipedia.org/wiki/Quadratic_mean_diameter

    For n trees, QMD is calculated using the quadratic mean formula: where is the diameter at breast height of the i th tree. Compared to the arithmetic mean, QMD assigns greater weight to larger trees – QMD is always greater than or equal to arithmetic mean for a given set of trees.

  4. Smallest-circle problem - Wikipedia

    en.wikipedia.org/wiki/Smallest-circle_problem

    Chakraborty and Chaudhuri [11] propose a linear-time method for selecting a suitable initial circle and a pair of boundary points on that circle. Each step of the algorithm includes as one of the two boundary points a new vertex of the convex hull, so if the hull has h vertices this method can be implemented to run in time O(nh).

  5. Straightedge and compass construction - Wikipedia

    en.wikipedia.org/wiki/Straightedge_and_compass...

    Creating the one point or two points in the intersection of two circles (if they intersect). For example, starting with just two distinct points, we can create a line or either of two circles (in turn, using each point as centre and passing through the other point). If we draw both circles, two new points are created at their intersections.

  6. Quadric - Wikipedia

    en.wikipedia.org/wiki/Quadric

    A quadratic set is a set of points of a projective space with the same geometric properties as a quadric: every line intersects a quadratic set in at most two points or is contained in the set. See also

  7. Polynomial interpolation - Wikipedia

    en.wikipedia.org/wiki/Polynomial_interpolation

    Left to right steps indicate addition whereas right to left steps indicate subtraction; If the slope of a step is positive, the term to be used is the product of the difference and the factor immediately below it. If the slope of a step is negative, the term to be used is the product of the difference and the factor immediately above it.

  8. Descartes' theorem - Wikipedia

    en.wikipedia.org/wiki/Descartes'_theorem

    Kissing circles. Given three mutually tangent circles (black), there are, in general, two possible answers (red) as to what radius a fourth tangent circle can have.In geometry, Descartes' theorem states that for every four kissing, or mutually tangent circles, the radii of the circles satisfy a certain quadratic equation.

  9. Circle - Wikipedia

    en.wikipedia.org/wiki/Circle

    The sum of the squared lengths of any two chords intersecting at right angles at a given point is the same as that of any other two perpendicular chords intersecting at the same point and is given by 8r 2 − 4p 2, where r is the circle radius, and p is the distance from the centre point to the point of intersection.