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  2. List of centroids - Wikipedia

    en.wikipedia.org/wiki/List_of_centroids

    Quarter-circular area [2] ... The points on the circle + = and above the axis = Arc of circle: The points on the curve (in polar coordinates ...

  3. Arc length - Wikipedia

    en.wikipedia.org/wiki/Arc_length

    For example, consider the problem of finding the length of a quarter of the unit circle by numerically integrating the arc length integral. The upper half of the unit circle can be parameterized as y = 1 − x 2 . {\displaystyle y={\sqrt {1-x^{2}}}.}

  4. List of second moments of area - Wikipedia

    en.wikipedia.org/wiki/List_of_second_moments_of_area

    Regular polygons; Description Figure Second moment of area Comment A filled regular (equiliteral) triangle with a side length of a = = [6] The result is valid for both a horizontal and a vertical axis through the centroid, and therefore is also valid for an axis with arbitrary direction that passes through the origin.

  5. List of formulae involving π - Wikipedia

    en.wikipedia.org/wiki/List_of_formulae_involving_π

    The buckling formula: = ... (integrating a quarter of a circle with a radius of two + = to ... (Riemann sum to evaluate the area of the unit circle) ...

  6. Golden spiral - Wikipedia

    en.wikipedia.org/wiki/Golden_spiral

    A Fibonacci spiral approximates the golden spiral using quarter-circle arcs inscribed in squares derived from the Fibonacci sequence. A golden spiral with initial radius 1 is the locus of points of polar coordinates ( r , θ ) {\displaystyle (r,\theta )} satisfying r = φ 2 θ / π , {\displaystyle r=\varphi ^{2\theta /\pi },} where φ ...

  7. Circular segment - Wikipedia

    en.wikipedia.org/wiki/Circular_segment

    The arc length, from the familiar geometry of a circle, is s = θ R {\displaystyle s={\theta }R} The area a of the circular segment is equal to the area of the circular sector minus the area of the triangular portion (using the double angle formula to get an equation in terms of θ {\displaystyle \theta } ):

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  9. Area of a circle - Wikipedia

    en.wikipedia.org/wiki/Area_of_a_circle

    The transformation sends the circle to an ellipse by stretching or shrinking the horizontal and vertical diameters to the major and minor axes of the ellipse. 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