Search results
Results from the WOW.Com Content Network
It was covered under the now-expired U.S. patent 5,732,138, titled "Method for seeding a pseudo-random number generator with a cryptographic hash of a digitization of a chaotic system." by Landon Curt Noll, Robert G. Mende, and Sanjeev Sisodiya. From 1997 to 2001, [2] there was a website at lavarand.sgi.com demonstrating the technique.
Farey sequences are very useful to find rational approximations of irrational numbers. [13] For example, the construction by Eliahou [ 14 ] of a lower bound on the length of non-trivial cycles in the 3 x +1 process uses Farey sequences to calculate a continued fraction expansion of the number log 2 (3) .
Some irrational numbers (as well as all the rationals) are the root of a polynomial with integer coefficients, such as the square root √2 = 1.414 ...
In Wonders of Numbers Pickover described the history of schizophrenic numbers thus: The construction and discovery of schizophrenic numbers was prompted by a claim (posted in the Usenet newsgroup sci.math) that the digits of an irrational number chosen at random would not be expected to display obvious patterns in the first 100 digits. It was ...
The number shows the iteration step; after 300 iterations, the original image returns. Sample mapping on a picture of a pair of cherries. The image is 74 pixels wide, and takes 114 iterations to be restored, although it appears upside-down at the halfway point (the 57th iteration).
The powers of two whose exponents are powers of two, , form an irrationality sequence.However, although Sylvester's sequence. 2, 3, 7, 43, 1807, 3263443, ... (in which each term is one more than the product of all previous terms) also grows doubly exponentially, it does not form an irrationality sequence.
In mathematics, an irrational number is any real number that is not a rational number, i.e., one that cannot be written as a fraction a / b with a and b integers and b not zero. This is also known as being incommensurable, or without common measure. The irrational numbers are precisely those numbers whose expansion in any given base (decimal ...
In fact, every real number can be written as the limit of a sequence of rational numbers (e.g. via its decimal expansion, also see completeness of the real numbers). As another example, π is the limit of the sequence (3, 3.1, 3.14, 3.141, 3.1415, ...), which is increasing.