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  2. Area of a circle - Wikipedia

    en.wikipedia.org/wiki/Area_of_a_circle

    The area of a regular polygon is half its perimeter multiplied by the distance from its center to its sides, and because the sequence tends to a circle, the corresponding formula–that the area is half the circumference times the radius–namely, A = ⁠ 1 / 2 ⁠ × 2πr × r, holds for a circle.

  3. List of formulas in elementary geometry - Wikipedia

    en.wikipedia.org/wiki/List_of_formulas_in...

    Perimeter#Formulas – Path that surrounds an area; List of second moments of area; List of surface-area-to-volume ratios – Surface area per unit volume; List of surface area formulas – Measure of a two-dimensional surface; List of trigonometric identities; List of volume formulas – Quantity of three-dimensional space

  4. List of formulae involving π - Wikipedia

    en.wikipedia.org/wiki/List_of_formulae_involving_π

    where C is the circumference of a circle, d is the diameter, and r is the radius. More generally, = where L and w are, respectively, the perimeter and the width of any curve of constant width. = where A is the area of a circle. More generally, =

  5. Circle - Wikipedia

    en.wikipedia.org/wiki/Circle

    The ratio of a circle's circumference to its diameter is π (pi), an irrational constant approximately equal to 3.141592654. The ratio of a circle's circumference to its radius is 2 π. [a] Thus the circumference C is related to the radius r and diameter d by: = =.

  6. Circular segment - Wikipedia

    en.wikipedia.org/wiki/Circular_segment

    The area formula can be used in calculating the volume of a partially-filled cylindrical tank lying horizontally. In the design of windows or doors with rounded tops, c and h may be the only known values and can be used to calculate R for the draftsman's compass setting.

  7. Pi - Wikipedia

    en.wikipedia.org/wiki/Pi

    The circumference of a circle with radius r is 2πr. [155] The area of a circle with radius r is πr 2. The area of an ellipse with semi-major axis a and semi-minor axis b is πab. [156] The volume of a sphere with radius r is ⁠ 4 / 3 ⁠ πr 3. The surface area of a sphere with radius r is 4πr 2.

  8. Equivalent radius - Wikipedia

    en.wikipedia.org/wiki/Equivalent_radius

    The area-equivalent radius of a 2D object is the radius of a circle with the same area as the object Cross sectional area of a trapezoidal open channel, red highlights the wetted perimeter, where water is in contact with the channel. The hydraulic diameter is the equivalent circular configuration with the same circumference as the wetted perimeter.

  9. Gauss circle problem - Wikipedia

    en.wikipedia.org/wiki/Gauss_circle_problem

    Gauss's circle problem asks how many points there are inside this circle of the form (,) where and are both integers. Since the equation of this circle is given in Cartesian coordinates by x 2 + y 2 = r 2 {\displaystyle x^{2}+y^{2}=r^{2}} , the question is equivalently asking how many pairs of integers m and n there are such that