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Golden ratio | A Wisdom Archive on Golden ratio | | Golden ratio A selection of articles related to Golden ratio | |
| We recommend this article: Golden ratio - 1, and also this: Golden ratio - 2. |
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golden ratio
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| ARTICLES RELATED TO Golden ratio | | | |  Golden ratio: Encyclopedia II - Pi film - Mathematics and π explain the ratio problem ?While the film's characters make several mathematical "goofs", such as saying
* the ratio of a/b is the same as the ratio of a/(a + b) instead of (a+b)/a,
it is notable that Sean Gullette's character, Max, pursues a legitimate scientific goal (though through questionable "scientific" means). As such, π features several references to mathematics and mathematical theories. For instance, Max finds the golden spiral occurring everywhere, including the stock market. Max's belief that diverse systems embodying highly n ...
See also:Pi film, Pi film - Production, Pi film - Plot, Pi film - The game of Go, Pi film - Mathematics and π explain the ratio problem ?, Pi film - Kabbalah and π, Pi film - Soundtrack, Pi film - Quotes Read more here: » Pi film: Encyclopedia II - Pi film - Mathematics and π explain the ratio problem ? |
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| | | | | Golden ratio: Encyclopedia II - Fibonacci number program - Common Lisp
Fibonacci number program - Calculating fibonacci through Lucas' formula.
(defun fib (n)
(cond
((= n 0) 0)
((or (= n 1) (= n 2)) 1)
((= 0 (mod n 2)) (-
(expt (fib (+ (truncate n 2) 1)) 2)
(expt (fib (- (truncate n 2) 1)) 2)))
(t (+ (expt (fib (truncate n 2)) 2)
(expt (fib (+ (truncate n 2) 1)) 2)))))
(fib (parse-integer (second *posix-argv*))) ;
...
See also:Fibonacci number program, Fibonacci number program - Common Lisp, Fibonacci number program - Calculating fibonacci through Lucas' formula, Fibonacci number program - Haskell examples, Fibonacci number program - Lazy infinite list, Fibonacci number program - Perl examples, Fibonacci number program - One example, Fibonacci number program - Binary recursion snippet, Fibonacci number program - Binary recursion with special Perl caching snippet, Fibonacci number program - Iterative snippet, Fibonacci number program - Command line iterative, Fibonacci number program - PostScript example, Fibonacci number program - Iterative, Fibonacci number program - Stack recursion, Fibonacci number program - Python examples, Fibonacci number program - Recursion, Fibonacci number program - Generator, Fibonacci number program - Matrix equation, Fibonacci number program - Scheme examples, Fibonacci number program - Binary recursion snippet, Fibonacci number program - Tail-end recursive snippet, Fibonacci number program - Tail-end recursive snippet, Fibonacci number program - Display all snippet, Fibonacci number program - C/C++/Java example, Fibonacci number program - Recursive snippet, Fibonacci number program - Iterative snippet, Fibonacci number program - Shorter iteration, Fibonacci number program - Ada example, Fibonacci number program - Recursive snippet, Fibonacci number program - Iterative snippet, Fibonacci number program - MatLab example, Fibonacci number program - Recursive snippet, Fibonacci number program - Iterative snippet, Fibonacci number program - PHP scripting language example, Fibonacci number program - Contained snippet, Fibonacci number program - Ruby examples, Fibonacci number program - QBasic/Visual Basic examples, Fibonacci number program - J examples, Fibonacci number program - Double recursion, Fibonacci number program - Single recursion, Fibonacci number program - Iteration, Fibonacci number program - Power of phi, Fibonacci number program - Continued fraction, Fibonacci number program - Taylor series, Fibonacci number program - Sum of binomial coefficients, Fibonacci number program - Matrix power, Fibonacci number program - Operations in Q[√5] and Z[√5] Read more here: » Fibonacci number program: Encyclopedia II - Fibonacci number program - Common Lisp |
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| | | | | | Golden ratio: Encyclopedia II - Fibonacci number program - Haskell examples
Fibonacci number program - Lazy infinite list.
module Main where
import System.Environment
fibo = 1 : 1 : zipWith (+) fibo (tail fibo)
main = do
args <- getArgs
print (fibo !! (read(args!!0)-1))
...
See also:Fibonacci number program, Fibonacci number program - Common Lisp, Fibonacci number program - Calculating fibonacci through Lucas' formula, Fibonacci number program - Haskell examples, Fibonacci number program - Lazy infinite list, Fibonacci number program - Perl examples, Fibonacci number program - One example, Fibonacci number program - Binary recursion snippet, Fibonacci number program - Binary recursion with special Perl caching snippet, Fibonacci number program - Iterative snippet, Fibonacci number program - Command line iterative, Fibonacci number program - PostScript example, Fibonacci number program - Iterative, Fibonacci number program - Stack recursion, Fibonacci number program - Python examples, Fibonacci number program - Recursion, Fibonacci number program - Generator, Fibonacci number program - Matrix equation, Fibonacci number program - Scheme examples, Fibonacci number program - Binary recursion snippet, Fibonacci number program - Tail-end recursive snippet, Fibonacci number program - Tail-end recursive snippet, Fibonacci number program - Display all snippet, Fibonacci number program - C/C++/Java example, Fibonacci number program - Recursive snippet, Fibonacci number program - Iterative snippet, Fibonacci number program - Shorter iteration, Fibonacci number program - Ada example, Fibonacci number program - Recursive snippet, Fibonacci number program - Iterative snippet, Fibonacci number program - MatLab example, Fibonacci number program - Recursive snippet, Fibonacci number program - Iterative snippet, Fibonacci number program - PHP scripting language example, Fibonacci number program - Contained snippet, Fibonacci number program - Ruby examples, Fibonacci number program - QBasic/Visual Basic examples, Fibonacci number program - J examples, Fibonacci number program - Double recursion, Fibonacci number program - Single recursion, Fibonacci number program - Iteration, Fibonacci number program - Power of phi, Fibonacci number program - Continued fraction, Fibonacci number program - Taylor series, Fibonacci number program - Sum of binomial coefficients, Fibonacci number program - Matrix power, Fibonacci number program - Operations in Q[√5] and Z[√5] Read more here: » Fibonacci number program: Encyclopedia II - Fibonacci number program - Haskell examples |
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| | | | | | Golden ratio: Encyclopedia II - Proportion architecture - Sacred Proportions Among the Cistercians, Gothic, Renaissance, Egyptian, Semitic, Babylonian, Arab, Greek and Roman traditions; the harmonic proportions, human proportions, cosmological/astronomical proportions and orientations, and various aspects of sacred geometry (Vesica Piscis, the Pentagram, Golden Ratio and small whole-number ratios) were all applied as part of the practice of Architectural design.
Proportion architecture - Feng Shui.
Part of the practice of Feng Shui is a proportional system based on the double tatami mat. Feng Shui also includes within it the ideas of cosmic orienta ...
See also:Proportion architecture, Proportion architecture - Sacred Proportions, Proportion architecture - Feng Shui, Proportion architecture - Classical Orders, Proportion architecture - Vitruvian Proportion, Proportion architecture - Renaissance Orders, Proportion architecture - Le Modulor, Proportion architecture - The Plastic Number Read more here: » Proportion architecture: Encyclopedia II - Proportion architecture - Sacred Proportions |
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| | | | | Golden ratio: Encyclopedia II - Fibonacci number program - PostScript example
Fibonacci number program - Iterative.
20 % how many Fibonacci numbers to print
1 dup
3 -1 roll
{
dup
3 -1 roll
dup
4 1 roll
add
3 -1 roll
=
}
repeat
Fibonacci number program - Stack recursion.
This example uses recursion on the stack.
% the procedure
/fib
{
dup dup 1 eq exch 0 eq or not
{
dup 1 sub fib
exch 2 sub fib
add
} if
} def
% prints the first twenty fib numbers
/ntimes 20 de ...
See also:Fibonacci number program, Fibonacci number program - Common Lisp, Fibonacci number program - Calculating fibonacci through Lucas' formula, Fibonacci number program - Haskell examples, Fibonacci number program - Lazy infinite list, Fibonacci number program - Perl examples, Fibonacci number program - One example, Fibonacci number program - Binary recursion snippet, Fibonacci number program - Binary recursion with special Perl caching snippet, Fibonacci number program - Iterative snippet, Fibonacci number program - Command line iterative, Fibonacci number program - PostScript example, Fibonacci number program - Iterative, Fibonacci number program - Stack recursion, Fibonacci number program - Python examples, Fibonacci number program - Recursion, Fibonacci number program - Generator, Fibonacci number program - Matrix equation, Fibonacci number program - Scheme examples, Fibonacci number program - Binary recursion snippet, Fibonacci number program - Tail-end recursive snippet, Fibonacci number program - Tail-end recursive snippet, Fibonacci number program - Display all snippet, Fibonacci number program - C/C++/Java example, Fibonacci number program - Recursive snippet, Fibonacci number program - Iterative snippet, Fibonacci number program - Shorter iteration, Fibonacci number program - Ada example, Fibonacci number program - Recursive snippet, Fibonacci number program - Iterative snippet, Fibonacci number program - MatLab example, Fibonacci number program - Recursive snippet, Fibonacci number program - Iterative snippet, Fibonacci number program - PHP scripting language example, Fibonacci number program - Contained snippet, Fibonacci number program - Ruby examples, Fibonacci number program - QBasic/Visual Basic examples, Fibonacci number program - J examples, Fibonacci number program - Double recursion, Fibonacci number program - Single recursion, Fibonacci number program - Iteration, Fibonacci number program - Power of phi, Fibonacci number program - Continued fraction, Fibonacci number program - Taylor series, Fibonacci number program - Sum of binomial coefficients, Fibonacci number program - Matrix power, Fibonacci number program - Operations in Q[√5] and Z[√5] Read more here: » Fibonacci number program: Encyclopedia II - Fibonacci number program - PostScript example |
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| | | | | Golden ratio: Encyclopedia II - Numeral system - Types of numeral systems The simplest numeral system is the unary numeral system, in which every natural number is represented by a corresponding number of symbols. If the symbol ′ is chosen, for example, then the number seven would be represented by ′′′′′′′. The unary system is normally only useful for small numbers. It has some uses in theoretical computer science. Elias gamma coding is commonly used in da ...
See also:Numeral system, Numeral system - Types of numeral systems, Numeral system - History, Numeral system - Bases used, Numeral system - Positional systems in detail, Numeral system - Change of radix, Numeral system - Generalized variable-length integers, Numeral system - Reference Read more here: » Numeral system: Encyclopedia II - Numeral system - Types of numeral systems |
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| | | | | Golden ratio: Encyclopedia II - Fibonacci number program - Ada example
Fibonacci number program - Recursive snippet.
function fib(n : integer) return integer is
begin
if n < 2 then
return n;
else
return fib(n-1) + fib(n-2);
end if;
end fib;
Fibonacci number program - Iterative snippet.
function fib(n : integer) return integer is
first : integer := 0;
second : integer := 1;
tmp : integer;
begin
for i in 1..n loop
tmp := first + second;
first := second;
...
See also:Fibonacci number program, Fibonacci number program - Common Lisp, Fibonacci number program - Calculating fibonacci through Lucas' formula, Fibonacci number program - Haskell examples, Fibonacci number program - Lazy infinite list, Fibonacci number program - Perl examples, Fibonacci number program - One example, Fibonacci number program - Binary recursion snippet, Fibonacci number program - Binary recursion with special Perl caching snippet, Fibonacci number program - Iterative snippet, Fibonacci number program - Command line iterative, Fibonacci number program - PostScript example, Fibonacci number program - Iterative, Fibonacci number program - Stack recursion, Fibonacci number program - Python examples, Fibonacci number program - Recursion, Fibonacci number program - Generator, Fibonacci number program - Matrix equation, Fibonacci number program - Scheme examples, Fibonacci number program - Binary recursion snippet, Fibonacci number program - Tail-end recursive snippet, Fibonacci number program - Tail-end recursive snippet, Fibonacci number program - Display all snippet, Fibonacci number program - C/C++/Java example, Fibonacci number program - Recursive snippet, Fibonacci number program - Iterative snippet, Fibonacci number program - Shorter iteration, Fibonacci number program - Ada example, Fibonacci number program - Recursive snippet, Fibonacci number program - Iterative snippet, Fibonacci number program - MatLab example, Fibonacci number program - Recursive snippet, Fibonacci number program - Iterative snippet, Fibonacci number program - PHP scripting language example, Fibonacci number program - Contained snippet, Fibonacci number program - Ruby examples, Fibonacci number program - QBasic/Visual Basic examples, Fibonacci number program - J examples, Fibonacci number program - Double recursion, Fibonacci number program - Single recursion, Fibonacci number program - Iteration, Fibonacci number program - Power of phi, Fibonacci number program - Continued fraction, Fibonacci number program - Taylor series, Fibonacci number program - Sum of binomial coefficients, Fibonacci number program - Matrix power, Fibonacci number program - Operations in Q[√5] and Z[√5] Read more here: » Fibonacci number program: Encyclopedia II - Fibonacci number program - Ada example |
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| | | | | Golden ratio: Encyclopedia II - Fibonacci number program - MatLab example
Fibonacci number program - Recursive snippet.
function F = fibonacci_recursive(n)
if n < 2
F = n;
else
F = fibonacci_recursive(n-1) + fibonacci_recursive(n-2);
end
Fibonacci number program - Iterative snippet.
function F = fibonacci_iterative(n)
first = 0;
second = 1;
third = 0;
for q = 1:n,
third = first + second ...
See also:Fibonacci number program, Fibonacci number program - Common Lisp, Fibonacci number program - Calculating fibonacci through Lucas' formula, Fibonacci number program - Haskell examples, Fibonacci number program - Lazy infinite list, Fibonacci number program - Perl examples, Fibonacci number program - One example, Fibonacci number program - Binary recursion snippet, Fibonacci number program - Binary recursion with special Perl caching snippet, Fibonacci number program - Iterative snippet, Fibonacci number program - Command line iterative, Fibonacci number program - PostScript example, Fibonacci number program - Iterative, Fibonacci number program - Stack recursion, Fibonacci number program - Python examples, Fibonacci number program - Recursion, Fibonacci number program - Generator, Fibonacci number program - Matrix equation, Fibonacci number program - Scheme examples, Fibonacci number program - Binary recursion snippet, Fibonacci number program - Tail-end recursive snippet, Fibonacci number program - Tail-end recursive snippet, Fibonacci number program - Display all snippet, Fibonacci number program - C/C++/Java example, Fibonacci number program - Recursive snippet, Fibonacci number program - Iterative snippet, Fibonacci number program - Shorter iteration, Fibonacci number program - Ada example, Fibonacci number program - Recursive snippet, Fibonacci number program - Iterative snippet, Fibonacci number program - MatLab example, Fibonacci number program - Recursive snippet, Fibonacci number program - Iterative snippet, Fibonacci number program - PHP scripting language example, Fibonacci number program - Contained snippet, Fibonacci number program - Ruby examples, Fibonacci number program - QBasic/Visual Basic examples, Fibonacci number program - J examples, Fibonacci number program - Double recursion, Fibonacci number program - Single recursion, Fibonacci number program - Iteration, Fibonacci number program - Power of phi, Fibonacci number program - Continued fraction, Fibonacci number program - Taylor series, Fibonacci number program - Sum of binomial coefficients, Fibonacci number program - Matrix power, Fibonacci number program - Operations in Q[√5] and Z[√5] Read more here: » Fibonacci number program: Encyclopedia II - Fibonacci number program - MatLab example |
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| | | | | Golden ratio: Encyclopedia II - Numeral system - Positional systems in detail Also see Positional notation.
In a positional base-b numeral system (with b a positive natural number known as the radix), b basic symbols (or digits) corresponding to the first b natural numbers including zero are used. To generate the rest of the numerals, the position of the symbol in the figure is used. The symbol in the last position has its own value, and as it moves to the left its value is multiplied by b.
For example, in the decimal system (base 10), the numeral 4327 means (4×103) + (3×102) + (2×101 ...
See also:Numeral system, Numeral system - Types of numeral systems, Numeral system - History, Numeral system - Bases used, Numeral system - Positional systems in detail, Numeral system - Change of radix, Numeral system - Generalized variable-length integers, Numeral system - Reference Read more here: » Numeral system: Encyclopedia II - Numeral system - Positional systems in detail |
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| | | | | Golden ratio: Encyclopedia II - Fibonacci number program - PHP scripting language example
Fibonacci number program - Contained snippet.
function generate_fibonacci_sequence( $length, $method = 0 ) {
# ----
if( $method == 0 ):
// -- standard addition - limited by the capacity (int)
for( $l = array(1,1), $i = 2, $x = 0; $i < $length; $i++ )
$l[] = $l[$x++] + $l[$x];
elseif( $method == 1 ):
// -- arbitrary precision addition - more process inten ...
See also:Fibonacci number program, Fibonacci number program - Common Lisp, Fibonacci number program - Calculating fibonacci through Lucas' formula, Fibonacci number program - Haskell examples, Fibonacci number program - Lazy infinite list, Fibonacci number program - Perl examples, Fibonacci number program - One example, Fibonacci number program - Binary recursion snippet, Fibonacci number program - Binary recursion with special Perl caching snippet, Fibonacci number program - Iterative snippet, Fibonacci number program - Command line iterative, Fibonacci number program - PostScript example, Fibonacci number program - Iterative, Fibonacci number program - Stack recursion, Fibonacci number program - Python examples, Fibonacci number program - Recursion, Fibonacci number program - Generator, Fibonacci number program - Matrix equation, Fibonacci number program - Scheme examples, Fibonacci number program - Binary recursion snippet, Fibonacci number program - Tail-end recursive snippet, Fibonacci number program - Tail-end recursive snippet, Fibonacci number program - Display all snippet, Fibonacci number program - C/C++/Java example, Fibonacci number program - Recursive snippet, Fibonacci number program - Iterative snippet, Fibonacci number program - Shorter iteration, Fibonacci number program - Ada example, Fibonacci number program - Recursive snippet, Fibonacci number program - Iterative snippet, Fibonacci number program - MatLab example, Fibonacci number program - Recursive snippet, Fibonacci number program - Iterative snippet, Fibonacci number program - PHP scripting language example, Fibonacci number program - Contained snippet, Fibonacci number program - Ruby examples, Fibonacci number program - QBasic/Visual Basic examples, Fibonacci number program - J examples, Fibonacci number program - Double recursion, Fibonacci number program - Single recursion, Fibonacci number program - Iteration, Fibonacci number program - Power of phi, Fibonacci number program - Continued fraction, Fibonacci number program - Taylor series, Fibonacci number program - Sum of binomial coefficients, Fibonacci number program - Matrix power, Fibonacci number program - Operations in Q[√5] and Z[√5] Read more here: » Fibonacci number program: Encyclopedia II - Fibonacci number program - PHP scripting language example |
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| | | | | | Golden ratio: Encyclopedia II - Numeral system - Generalized variable-length integers More general is using a notation (here written little-endian) like a0a1a2 for a0 + a1b1 + a2b1b2, etc.
This is used in punycode, one aspect of which is the representation of a sequence of non-negative integers of arbitrary size in the form of a sequence without delimiters, of "digits" from a collection of 36: a-z and 0-9, representing 0-25 and 26-35 respectively. A digit lowe ...
See also:Numeral system, Numeral system - Types of numeral systems, Numeral system - History, Numeral system - Bases used, Numeral system - Positional systems in detail, Numeral system - Change of radix, Numeral system - Generalized variable-length integers, Numeral system - Reference Read more here: » Numeral system: Encyclopedia II - Numeral system - Generalized variable-length integers |
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| | | | | Golden ratio: Encyclopedia II - Numeral system - History Tallies carved from wood and stone have been used since prehistoric times. Stone age cultures, including ancient American Indian groups, used tallies for gambling with horses, slaves, personal services and trade-goods.
The earliest known written tallies appear in the ruins of the Sumerian empire, using clay tablets impressed with a sharp stick and baked. The Sumerians had quite an exotic system based on counts to 60, used in astronomical and other calculations. This system was imported and used by every Mediterranean nation that u ...
See also:Numeral system, Numeral system - Types of numeral systems, Numeral system - History, Numeral system - Bases used, Numeral system - Positional systems in detail, Numeral system - Change of radix, Numeral system - Generalized variable-length integers, Numeral system - Reference Read more here: » Numeral system: Encyclopedia II - Numeral system - History |
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| | | | | Golden ratio: Encyclopedia II - Numeral system - Bases used The base-10 system is the one most commonly used today. It is assumed to have originated because humans have ten fingers.
A base-eight system was devised by the Yuki of Northern California, who used the spaces between the fingers to count. There is also linguistic evidence which suggests that the Bronze Age Proto-Indo Europeans (from whom most European and Indic languages descend) might have replaced a base 8 system (or a system which could only count up to 8) with a base 10 system. The evidence is that the word for 9, newan, a ...
See also:Numeral system, Numeral system - Types of numeral systems, Numeral system - History, Numeral system - Bases used, Numeral system - Positional systems in detail, Numeral system - Change of radix, Numeral system - Generalized variable-length integers, Numeral system - Reference Read more here: » Numeral system: Encyclopedia II - Numeral system - Bases used |
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| | | | | Golden ratio: Encyclopedia II - Fibonacci number program - Perl examples
Fibonacci number program - One example.
#! /usr/bin/perl
use bigint;
my ($a, $b) = (0, 1);
for (;;) {
print "$a\n";
($a, $b) = ($b, $a+$b);
}
Fibonacci number program - Binary recursion snippet.
sub fibo;
sub fibo {$_ [0] < 2 ? $_ [0] : fibo ($_ [0] - 1) + fibo ($_ [0] - 2)}
Runs in Θ(F(n)) time, which is Ω(1.6n).
Fibonacci number program - Binary recursion with special Perl caching snippet.
use Memoize;
memoize 'fibo';
sub fibo;
sub fibo {$_ [0] & ...
See also:Fibonacci number program, Fibonacci number program - Common Lisp, Fibonacci number program - Calculating fibonacci through Lucas' formula, Fibonacci number program - Haskell examples, Fibonacci number program - Lazy infinite list, Fibonacci number program - Perl examples, Fibonacci number program - One example, Fibonacci number program - Binary recursion snippet, Fibonacci number program - Binary recursion with special Perl caching snippet, Fibonacci number program - Iterative snippet, Fibonacci number program - Command line iterative, Fibonacci number program - PostScript example, Fibonacci number program - Iterative, Fibonacci number program - Stack recursion, Fibonacci number program - Python examples, Fibonacci number program - Recursion, Fibonacci number program - Generator, Fibonacci number program - Matrix equation, Fibonacci number program - Scheme examples, Fibonacci number program - Binary recursion snippet, Fibonacci number program - Tail-end recursive snippet, Fibonacci number program - Tail-end recursive snippet, Fibonacci number program - Display all snippet, Fibonacci number program - C/C++/Java example, Fibonacci number program - Recursive snippet, Fibonacci number program - Iterative snippet, Fibonacci number program - Shorter iteration, Fibonacci number program - Ada example, Fibonacci number program - Recursive snippet, Fibonacci number program - Iterative snippet, Fibonacci number program - MatLab example, Fibonacci number program - Recursive snippet, Fibonacci number program - Iterative snippet, Fibonacci number program - PHP scripting language example, Fibonacci number program - Contained snippet, Fibonacci number program - Ruby examples, Fibonacci number program - QBasic/Visual Basic examples, Fibonacci number program - J examples, Fibonacci number program - Double recursion, Fibonacci number program - Single recursion, Fibonacci number program - Iteration, Fibonacci number program - Power of phi, Fibonacci number program - Continued fraction, Fibonacci number program - Taylor series, Fibonacci number program - Sum of binomial coefficients, Fibonacci number program - Matrix power, Fibonacci number program - Operations in Q[√5] and Z[√5] Read more here: » Fibonacci number program: Encyclopedia II - Fibonacci number program - Perl examples |
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| | | | | Golden ratio: Encyclopedia II - Recurrence relation - Example: Fibonacci numbers The Fibonacci numbers are defined using a linear recurrence relation:
and has solution (letting be the golden ratio)
The initial conditions are:
Therefore, the sequence of Fibonacci numbers is:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89 ...
...
See also:Recurrence relation, Recurrence relation - Linear homogeneous recurrence relations with constant coefficients, Recurrence relation - Solving linear recurrence relations, Recurrence relation - Solving inhomogeneous recurrence relations, Recurrence relation - Example: Fibonacci numbers, Recurrence relation - Relationship to differential equations Read more here: » Recurrence relation: Encyclopedia II - Recurrence relation - Example: Fibonacci numbers |
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| | | | | Golden ratio: Encyclopedia II - Fibonacci number program - Python examples
Fibonacci number program - Recursion.
def fib(n):
if n < 2:
return n
else:
return fib(n - 1) + fib(n - 2)
Fibonacci number program - Generator.
def fib():
a, b = 0, 1
while True:
yield a
a, b = b, a + b
Fibonacci number program - Matrix equation.
def mul(A, B):
a, b, c = A
d, e, f = B
return a*d + b*e, a*e + b*f, b*e + c*f
def pow(A, n):
if n == 1: return A ...
See also:Fibonacci number program, Fibonacci number program - Common Lisp, Fibonacci number program - Calculating fibonacci through Lucas' formula, Fibonacci number program - Haskell examples, Fibonacci number program - Lazy infinite list, Fibonacci number program - Perl examples, Fibonacci number program - One example, Fibonacci number program - Binary recursion snippet, Fibonacci number program - Binary recursion with special Perl caching snippet, Fibonacci number program - Iterative snippet, Fibonacci number program - Command line iterative, Fibonacci number program - PostScript example, Fibonacci number program - Iterative, Fibonacci number program - Stack recursion, Fibonacci number program - Python examples, Fibonacci number program - Recursion, Fibonacci number program - Generator, Fibonacci number program - Matrix equation, Fibonacci number program - Scheme examples, Fibonacci number program - Binary recursion snippet, Fibonacci number program - Tail-end recursive snippet, Fibonacci number program - Tail-end recursive snippet, Fibonacci number program - Display all snippet, Fibonacci number program - C/C++/Java example, Fibonacci number program - Recursive snippet, Fibonacci number program - Iterative snippet, Fibonacci number program - Shorter iteration, Fibonacci number program - Ada example, Fibonacci number program - Recursive snippet, Fibonacci number program - Iterative snippet, Fibonacci number program - MatLab example, Fibonacci number program - Recursive snippet, Fibonacci number program - Iterative snippet, Fibonacci number program - PHP scripting language example, Fibonacci number program - Contained snippet, Fibonacci number program - Ruby examples, Fibonacci number program - QBasic/Visual Basic examples, Fibonacci number program - J examples, Fibonacci number program - Double recursion, Fibonacci number program - Single recursion, Fibonacci number program - Iteration, Fibonacci number program - Power of phi, Fibonacci number program - Continued fraction, Fibonacci number program - Taylor series, Fibonacci number program - Sum of binomial coefficients, Fibonacci number program - Matrix power, Fibonacci number program - Operations in Q[√5] and Z[√5] Read more here: » Fibonacci number program: Encyclopedia II - Fibonacci number program - Python examples |
| |
| | | | | Golden ratio: Encyclopedia II - Recurrence relation - Example: Fibonacci numbers The Fibonacci numbers are defined using the linear recurrence relation
whose solution is
where
denotes the golden ratio. Therefore, the sequence of Fibonacci numbers is:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89 ...
...
See also:Recurrence relation, Recurrence relation - Linear homogeneous recurrence relations with constant coefficients, Recurrence relation - Solving linear recurrence relations, Recurrence relation - Solving inhomogeneous recurrence relations, Recurrence relation - Example: Fibonacci numbers, Recurrence relation - Relationship to differential equations Read more here: » Recurrence relation: Encyclopedia II - Recurrence relation - Example: Fibonacci numbers |
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| | | | | | Golden ratio: Encyclopedia II - Fibonacci number program - Scheme examples
Fibonacci number program - Binary recursion snippet.
(define fibo
(lambda (x)
(if (< x 2)
x
(+ (fibo (- x 1)) (fibo (- x 2)))))))
Runs in Θ(F(n)) time, which is Ω(1.6n).
Fibonacci number program - Tail-end recursive snippet.
(define (fibo x)
(define (fibo-iter x a b)
(if (= x 0)
a
(fibo-iter (- x 1) b (+ a b))))
(fibo-iter x 0 1))
Runs in Θ(n) time.
F ...
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