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GoldenRatio




Mathematica Notation

Traditional Notation









Constants > GoldenRatio > Representations through more general functions > Through other functions





http://functions.wolfram.com/02.02.26.0001.01









  


  








Input Form





GoldenRatio == (1/2) (Fibonacci[1] Sqrt[5] + Sqrt[5 Fibonacci[1]^2 - 4])








Standard Form





Cell[BoxData[RowBox[List["GoldenRatio", "\[Equal]", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["Fibonacci", "[", "1", "]"]], " ", SqrtBox["5"]]], "+", SqrtBox[RowBox[List[RowBox[List["5", " ", SuperscriptBox[RowBox[List["Fibonacci", "[", "1", "]"]], "2"]]], "-", "4"]]]]], ")"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <semantics> <mi> &#981; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Phi]&quot;, Function[GoldenRatio]] </annotation> </semantics> <mo> &#10869; </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msqrt> <mn> 5 </mn> </msqrt> <mo> &#8290; </mo> <msub> <semantics> <mi> F </mi> <annotation encoding='Mathematica'> TagBox[&quot;F&quot;, Fibonacci] </annotation> </semantics> <mn> 1 </mn> </msub> </mrow> <mo> + </mo> <msqrt> <mrow> <mrow> <mn> 5 </mn> <mo> &#8290; </mo> <msubsup> <semantics> <mi> F </mi> <annotation encoding='Mathematica'> TagBox[&quot;F&quot;, Fibonacci] </annotation> </semantics> <mn> 1 </mn> <mn> 2 </mn> </msubsup> </mrow> <mo> - </mo> <mn> 4 </mn> </mrow> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <ci> GoldenRatio </ci> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <apply> <times /> <apply> <power /> <cn type='integer'> 5 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ci> Fibonacci </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 5 </cn> <apply> <power /> <apply> <ci> Fibonacci </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -4 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", "GoldenRatio", "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["Fibonacci", "[", "1", "]"]], " ", SqrtBox["5"]]], "+", SqrtBox[RowBox[List[RowBox[List["5", " ", SuperscriptBox[RowBox[List["Fibonacci", "[", "1", "]"]], "2"]]], "-", "4"]]]]], ")"]]]]]]]]


Date Added to functions.wolfram.com (modification date)





2001-10-29