Template:Golden ratio

The following documentation is located at Template:Golden ratio/doc. [<Edit> Template:Golden ratio/doc]
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The {{Golden ratio}} (or {{phi}}) mathematical constant function template returns the positive root $\scriptstyle {\tfrac {1+{\sqrt {5}}}{2}}\,$ or negative root $\scriptstyle {\tfrac {1-{\sqrt {5}}}{2}}\,$ of $\scriptstyle x^{2}-x-1\,=\,0\,$, 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.

Usage

{{Golden ratio|+ or -}} or {{phi|+ or -}}

to get the positive root (+) or negative root (-) of $\scriptstyle x^{2}-x-1\,=\,0\,$, or

{{Golden ratio}} or {{phi}}

to get the Golden ratio (positive root (+) of $\scriptstyle x^{2}-x-1\,=\,0\,$ 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|phi}}

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}}