Search results
Results From The WOW.Com Content Network
A simple fraction (also known as a common fraction or vulgar fraction, where vulgar is Latin for "common") is a rational number written as a / b or , where a and b are both integers. [9] As with other fractions, the denominator ( b) cannot be zero. Examples include 1 2, − 8 5, −8 5, and 8 −5.
The golden ratio's negative −φ and reciprocal φ−1 are the two roots of the quadratic polynomial x2 + x − 1. The golden ratio is also an algebraic number and even an algebraic integer. It has minimal polynomial. x x. This quadratic polynomial has two roots, and.
Definition and divergence[edit] The harmonic series is the infinite series in which the terms are all of the positive unit fractions. It is a divergent series: as more terms of the series are included in partial sums of the series, the values of these partial sums grow arbitrarily large, beyond any finite limit.
In more generality: For all p ≥ 1 and odd h, f p − 1 (2 p h − 1) = 2 × 3 p − 1 h − 1. (Here f p − 1 is function iteration notation.) For all odd h, f(2h − 1) ≤ 3h − 1 / 2 The Collatz conjecture is equivalent to the statement that, for all k in I, there exists an integer n ≥ 1 such that f n (k) = 1. Undecidable ...
Fractions such as 22 / 7 and 355 / 113 are commonly used to approximate π, but no common fraction (ratio of whole numbers) can be its exact value. Because π is irrational, it has an infinite number of digits in its decimal representation , and does not settle into an infinitely repeating pattern of digits.
From Wikipedia, the free encyclopedia. Sum of an (infinite) geometric progression. The geometric series 1/4 + 1/16 + 1/64 + 1/256 + ... shown as areas of purple squares. Each of the purple squares has 1/4 of the area of the next larger square (1/2×1/2= 1/4, 1/4×1/4 = 1/16, etc.). The sum of the areas of the purple squares is one third of the ...
The Drake equation is: [1] where. N = the number of civilizations in the Milky Way galaxy with which communication might be possible (i.e. which are on the current past light cone ); and. R∗ = the average rate of star formation in our Galaxy. fp = the fraction of those stars that have planets.
The gamma function is an important special function in mathematics. Its particular values can be expressed in closed form for integer and half-integer arguments, but no simple expressions are known for the values at rational points in general. Other fractional arguments can be approximated through efficient infinite products, infinite series ...