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In mathematics, a cube root of a number x is a number y such that y3 = x. All nonzero real numbers have exactly one real cube root and a pair of complex conjugate cube roots, and all nonzero complex numbers have three distinct complex cube roots. For example, the real cube root of 8, denoted , is 2, because 23 = 8, while the other cube roots of ...
The cube root law is an observation in political science that the number of members of a unicameral legislature, or of the lower house of a bicameral legislature, is about the cube root of the population being represented. [1] The rule was devised by Estonian political scientist Rein Taagepera in his 1972 paper "The size of national assemblies".
The other roots of the equation are obtained either by changing of cube root or, equivalently, by multiplying the cube root by a primitive cube root of unity, that is . This formula for the roots is always correct except when p = q = 0 , with the proviso that if p = 0 , the square root is chosen so that C ≠ 0 .
The cube of a number or any other mathematical expression is denoted by a superscript 3, for example 23 = 8 or (x + 1)3 . The cube is also the number multiplied by its square : n3 = n × n2 = n × n × n. The cube function is the function x ↦ x3 (often denoted y = x3) that maps a number to its cube. It is an odd function, as.
Individual polygons are named (and sometimes classified) according to the number of sides, combining a Greek -derived numerical prefix with the suffix -gon, e.g. pentagon, dodecagon. The triangle, quadrilateral and nonagon are exceptions, although the regular forms trigon, tetragon, and enneagon are sometimes encountered as well.
Triangular numbers are a type of figurate number, other examples being square numbers and cube numbers. The n th triangular number is the number of dots in the triangular arrangement with n dots on each side, and is equal to the sum of the n natural numbers from 1 to n.
Spiral of Theodorus. The spiral of Theodorus up to the triangle with a hypotenuse of. In geometry, the spiral of Theodorus (also called the square root spiral, Pythagorean spiral, or Pythagoras's snail) [1] is a spiral composed of right triangles, placed edge-to-edge. It was named after Theodorus of Cyrene .
A method analogous to piece-wise linear approximation but using only arithmetic instead of algebraic equations, uses the multiplication tables in reverse: the square root of a number between 1 and 100 is between 1 and 10, so if we know 25 is a perfect square (5 × 5), and 36 is a perfect square (6 × 6), then the square root of a number greater ...