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The Mandelbrot set within a continuously colored environment. The Mandelbrot set (/ ˈmændəlbroʊt, - brɒt /) [1][2] is a two-dimensional set with a relatively simple definition that exhibits great complexity, especially as it is magnified. It is popular for its aesthetic appeal and fractal structures. The set is defined in the complex plane ...
Look-and-say sequence. The lines show the growth of the numbers of digits in the look-and-say sequences with starting points 23 (red), 1 (blue), 13 (violet), 312 (green). These lines (when represented in a logarithmic vertical scale) tend to straight lines whose slopes coincide with Conway's constant. In mathematics, the look-and-say sequence ...
The Catalan numbers can be interpreted as a special case of the Bertrand's ballot theorem. Specifically, is the number of ways for a candidate A with n + 1 votes to lead candidate B with n votes. The two-parameter sequence of non-negative integers is a generalization of the Catalan numbers.
Scott Flansburg (born December 28, 1963) is an American dubbed "The Human Calculator" and listed in the Guinness Book of World Records for speed of mental calculation. He is the annual host and ambassador for The National Counting Bee, a math educator, and media personality. He has published the books Math Magic and Math Magic for Your Kids.
Formula for primes. In number theory, a formula for primes is a formula generating the prime numbers, exactly and without exception. Formulas for calculating primes do exist; however, they are computationally very slow. A number of constraints are known, showing what such a "formula" can and cannot be.
Pascal's calculator (also known as the arithmetic machine or Pascaline) is a mechanical calculator invented by Blaise Pascal in 1642. Pascal was led to develop a calculator by the laborious arithmetical calculations required by his father's work as the supervisor of taxes in Rouen. [2] He designed the machine to add and subtract two numbers ...
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A hexagonal number is a figurate number. The n th hexagonal number hn is the number of distinct dots in a pattern of dots consisting of the outlines of regular hexagons with sides up to n dots, when the hexagons are overlaid so that they share one vertex. The formula for the n th hexagonal number. {\displaystyle h_ {n}=2n^ {2}-n=n (2n-1 ...