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Template:Golden ratio/doc
From OeisWiki
The {{Golden ratio}} (or {{phi}}) mathematical constant function template returns the positive root or negative root of , the positive root (+) being the Golden ratio, which is returned if no argument is given. An error message is returned if an argument other than + or - is given.
The Golden ratio is used in Binet's closed-form formulae for the Fibonacci numbers and Lucas numbers.
Contents
Usage
- {{Golden ratio|+ or -}} or {{phi|+ or -}}
to get the positive root (+) or negative root (-) of , or
- {{Golden ratio}} or {{phi}}
to get the Golden ratio (positive root (+) of as default).
Valid input
- + (default) or - as argument.
Examples
Examples with valid input
Code Result {{phi}} 1.6180339887499 {{Golden ratio}} 1.6180339887499 {{phi|+}} 1.6180339887499 {{Golden ratio|+}} 1.6180339887499 {{phi|-}} −0.61803398874989 {{Golden ratio|-}} −0.61803398874989
Examples with invalid input
Code Result {{Golden ratio|*}} Golden ratio error: Argument must be + or - {{Golden ratio|phi}} Golden ratio error: Argument must be + or -
Code
{{#switch: {{{1|+}}} | + = {{expr| (1+5^(1/2))/2 }} | - = {{expr| (1-5^(1/2))/2 }} | {{error| Golden ratio error: Argument must be + or - }} }}
See also
- {{Fibonacci}}
- {{Lucas}}
- {{Golden ratio}} or {{phi}}