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  2. List of formulas in elementary geometry - Wikipedia

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

    Shape Area Perimeter/Circumference ... Circle or : where is the ... This is a list of volume formulas of basic shapes: [4]: 405–406 ...

  3. Area of a circle - Wikipedia

    en.wikipedia.org/wiki/Area_of_a_circle

    Another proof that uses triangles considers the area enclosed by a circle to be made up of an infinite number of triangles (i.e. the triangles each have an angle of d𝜃 at the center of the circle), each with an area of ⁠ 1 / 2 ⁠ · r 2 · d𝜃 (derived from the expression for the area of a triangle: ⁠ 1 / 2 ⁠ · a · b · sin𝜃 ...

  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. Dividing a circle into areas - Wikipedia

    en.wikipedia.org/wiki/Dividing_a_circle_into_areas

    The lemma establishes an important property for solving the problem. By employing an inductive proof, one can arrive at a formula for f(n) in terms of f(n − 1).. Proof. In the figure the dark lines are connecting points 1 through 4 dividing the circle into 8 total regions (i.e., f(4) = 8).

  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. Area - Wikipedia

    en.wikipedia.org/wiki/Area

    The formula for the surface area of a sphere was first obtained by Archimedes in his work On the Sphere and Cylinder. The formula is: [6] A = 4πr 2 (sphere), where r is the radius of the sphere. As with the formula for the area of a circle, any derivation of this formula inherently uses methods similar to calculus.

  9. 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}}