The Mathematical Magic of the Fibonacci Numbers. This page looks at some patterns in the Fibonacci numbers themselves, from the digits in the numbers to their factors and multiples and which are prime numbers.
There is an unexpected pattern in the initial digits too. We also relate Fibonacci numbers to Pascal's triangle via the original rabbit problem that Fibonacci used to introduce the series we now call by his name. We can also make the Fibonacci numbers appear in a decimal fraction, introduce you to an easily learned number magic trick that only works with Fibonacci-like series numbers, see how Pythagoras' Theorem and right-angled triangles such as 3-4-5 have connections with the Fibonacci numbers and then give you lots of hints and suggestions for finding more number patterns of your own.
Take a look at the Fibonacci Numbers List or, better, see this list in another browser window, then you can refer to this page and the list together. 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987 ..More.. 1.1 The Final Digits or. Ulam spiral. Ulam spiral of size 200×200. Black dots represent prime numbers. Diagonal, vertical, and horizontal lines with a high density of prime numbers are clearly visible. The Ulam spiral, or prime spiral (in other languages also called the Ulam Cloth) is a simple method of visualizing the prime numbers that reveals the apparent tendency of certain quadratic polynomials to generate unusually large numbers of primes.
It was discovered by the mathematician Stanislaw Ulam in 1963, while he was doodling during the presentation of a "long and very boring paper" at a scientific meeting. Shortly afterwards, in an early application of computer graphics, Ulam with collaborators Myron Stein and Mark Wells used MANIAC II at Los Alamos Scientific Laboratory to produce pictures of the spiral for numbers up to 65,000. In an addendum to the Scientific American column, Gardner mentions work of the herpetologist Laurence M.
Construction[edit] All prime numbers, except for the number 2, are odd numbers. What's Special About This Number? What's Special About This Number?
If you know a distinctive fact about a number not listed here, please e-mail me. primes graphs digits sums of powers bases combinatorics powers/polygonal Fibonacci geometry repdigits algebra perfect/amicable pandigital matrices divisors games/puzzles 0 is the additive identity . 1 is the multiplicative identity . 2 is the only even prime . 3 is the number of spatial dimensions we live in. 4 is the smallest number of colors sufficient to color all planar maps. 5 is the number of Platonic solids . 6 is the smallest perfect number . 7 is the smallest number of sides of a regular polygon that is not constructible by straightedge and compass. 8 is the largest cube in the Fibonacci sequence . 9 is the maximum number of cubes that are needed to sum to any positive integer . 10 is the base of our number system. 11 is the largest known multiplicative persistence . 12 is the smallest abundant number .