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  2. List of formulas in elementary geometry - Wikipedia

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

    The basic quantities describing a sphere (meaning a 2-sphere, a 2-dimensional surface inside 3-dimensional space) will be denoted by the following variables r {\displaystyle r} is the radius, C = 2 π r {\displaystyle C=2\pi r} is the circumference (the length of any one of its great circles ),

  3. 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.

  4. Circle - Wikipedia

    en.wikipedia.org/wiki/Circle

    The circle is the shape with the largest area for a given length of perimeter (see Isoperimetric inequality). The circle is a highly symmetric shape: every line through the centre forms a line of reflection symmetry, and it has rotational symmetry around the centre for every angle.

  5. List of centroids - Wikipedia

    en.wikipedia.org/wiki/List_of_centroids

    Shape Figure ¯ ¯ Area rectangle area: General triangular area + + [1] Isosceles-triangular area: Right-triangular area: Circular area: Quarter-circular area [2]: Semicircular area [3]: Circular sector

  6. List of formulae involving π - Wikipedia

    en.wikipedia.org/wiki/List_of_formulae_involving_π

    where A is the area of an epicycloid with the smaller circle of radius r and the larger circle of radius kr (), assuming the initial point lies on the larger circle. A = ( − 1 ) k + 3 8 π a 2 {\displaystyle A={\frac {(-1)^{k}+3}{8}}\pi a^{2}}

  7. Regular polygon - Wikipedia

    en.wikipedia.org/wiki/Regular_polygon

    All vertices of a regular polygon lie on a common circle (the circumscribed circle); i.e., they are concyclic points. That is, a regular polygon is a cyclic polygon. Together with the property of equal-length sides, this implies that every regular polygon also has an inscribed circle or incircle that is

  8. Pi - Wikipedia

    en.wikipedia.org/wiki/Pi

    The area of the circle equals π times the shaded area. The area of the unit circle is π. [152] π appears in formulae for areas and volumes of geometrical shapes based on circles, such as ellipses, spheres, cones, and tori. Below are some of the more common formulae that involve π. [153] The circumference of a circle with radius r is 2πr. [154]

  9. List of mathematical shapes - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical_shapes

    Peak, an (n-3)-dimensional element For example, in a polyhedron (3-dimensional polytope), a face is a facet, an edge is a ridge, and a vertex is a peak. Vertex figure : not itself an element of a polytope, but a diagram showing how the elements meet.