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Area#Area formulas – Size of a two-dimensional surface; 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
Diagram illustrating three basic geometric sequences of the pattern 1(r n−1) up to 6 iterations deep.The first block is a unit block and the dashed line represents the infinite sum of the sequence, a number that it will forever approach but never touch: 2, 3/2, and 4/3 respectively.
A formula is an entity constructed using the symbols and formation rules of a given logical language. [5] For example, determining the volume of a sphere requires a significant amount of integral calculus or its geometrical analogue, the method of exhaustion ; [ 6 ] but, having done this once in terms of some parameter (the radius for example ...
The convergence of a geometric series can be described depending on the value of a common ratio, see § Convergence of the series and its proof. Grandi's series is an example of a divergent series that can be expressed as 1 − 1 + 1 − 1 + ⋯ {\displaystyle 1-1+1-1+\cdots } , where the initial term is 1 {\displaystyle 1} and the common ratio ...
The number π (/ p aɪ / ⓘ; spelled out as "pi") is a mathematical constant, approximately equal to 3.14159, that is the ratio of a circle's circumference to its diameter.It appears in many formulae across mathematics and physics, and some of these formulae are commonly used for defining π, to avoid relying on the definition of the length of a curve.
The point D is the harmonic conjugate of C with respect to A and B precisely if the cross-ratio of the quadruple is −1, called the harmonic ratio. The cross-ratio can therefore be regarded as measuring the quadruple's deviation from this ratio; hence the name anharmonic ratio. The cross-ratio is preserved by linear fractional transformations.
A common compactness measure is the isoperimetric quotient, the ratio of the area of the shape to the area of a circle (the most compact shape) having the same perimeter. . In the plane, this is equivalent to the Polsby–Popper t
This formula can be derived by partitioning the n-sided polygon into n congruent isosceles triangles, and then noting that the apothem is the height of each triangle, and that the area of a triangle equals half the base times the height. The following formulations are all equivalent:
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