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  2. Semicircle - Wikipedia

    en.wikipedia.org/wiki/Semicircle

    For a semicircle with a diameter of a + b, the length of its radius is the arithmetic mean of a and b (since the radius is half of the diameter). The geometric mean can be found by dividing the diameter into two segments of lengths a and b, and then connecting their common endpoint to the semicircle with a segment perpendicular to the diameter ...

  3. List of centroids - Wikipedia

    en.wikipedia.org/wiki/List_of_centroids

    a = the radius of the base circle h = the height of the paboloid from the base cicle's center to the edge Solid ellipsoid: a, b, c = the principal semi-axes of the ...

  4. Circle - Wikipedia

    en.wikipedia.org/wiki/Circle

    Radius: a line segment joining the centre of a circle with any single point on the circle itself; or the length of such a segment, which is half (the length of) a diameter. Usually, the radius is denoted r {\displaystyle r} and required to be a positive number.

  5. 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.

  6. Archimedean circle - Wikipedia

    en.wikipedia.org/wiki/Archimedean_circle

    In geometry, an Archimedean circle is any circle constructed from an arbelos that has the same radius as each of Archimedes' twin circles. If the arbelos is normed such that the diameter of its outer (largest) half circle has a length of 1 and r denotes the radius of any of the inner half circles, then the radius ρ of such an Archimedean ...

  7. 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

  8. Equivalent radius - Wikipedia

    en.wikipedia.org/wiki/Equivalent_radius

    The authalic radius is an surface area-equivalent radius for solid figures such as an ellipsoid. The osculating circle and osculating sphere define curvature -equivalent radii at a particular point of tangency for plane figures and solid figures, respectively.

  9. Incircle and excircles - Wikipedia

    en.wikipedia.org/wiki/Incircle_and_excircles

    Any line through a triangle that splits both the triangle's area and its perimeter in half goes through the triangle's incenter (the center of its incircle). There are either one, two, or three of these for any given triangle. [15] The incircle radius is no greater than one-ninth the sum of the altitudes. [16]: 289