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GoldenRatio




Mathematica Notation

Traditional Notation









Constants > GoldenRatio > Identities > Functional identities





http://functions.wolfram.com/02.02.17.0007.01









  


  








Input Form





GoldenRatio^GoldenRatio^(2 + GoldenRatio) == GoldenRatio^(GoldenRatio^GoldenRatio (1 + GoldenRatio)) == GoldenRatio^GoldenRatio^(1 + GoldenRatio^2) == GoldenRatio^GoldenRatio^(2 + GoldenRatio)








Standard Form





Cell[BoxData[RowBox[List[SuperscriptBox["GoldenRatio", SuperscriptBox["GoldenRatio", RowBox[List["2", "+", "GoldenRatio"]]]], "\[Equal]", SuperscriptBox["GoldenRatio", RowBox[List[SuperscriptBox["GoldenRatio", "GoldenRatio"], " ", RowBox[List["(", RowBox[List["1", "+", "GoldenRatio"]], ")"]]]]], "\[Equal]", SuperscriptBox["GoldenRatio", SuperscriptBox["GoldenRatio", RowBox[List["1", "+", SuperscriptBox["GoldenRatio", "2"]]]]], "\[Equal]", SuperscriptBox["GoldenRatio", SuperscriptBox["GoldenRatio", RowBox[List["2", "+", "GoldenRatio"]]]]]]]]








MathML Form







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










Rule Form





Cell[BoxData[RowBox[List[SuperscriptBox["GoldenRatio", SuperscriptBox["GoldenRatio", RowBox[List["2", "+", "GoldenRatio"]]]], "\[Equal]", SuperscriptBox["GoldenRatio", RowBox[List[SuperscriptBox["GoldenRatio", "GoldenRatio"], " ", RowBox[List["(", RowBox[List["1", "+", "GoldenRatio"]], ")"]]]]], "\[Equal]", SuperscriptBox["GoldenRatio", SuperscriptBox["GoldenRatio", RowBox[List["1", "+", SuperscriptBox["GoldenRatio", "2"]]]]], "\[Equal]", SuperscriptBox["GoldenRatio", SuperscriptBox["GoldenRatio", RowBox[List["2", "+", "GoldenRatio"]]]]]]]]










Contributed by





Udaya Chinthaka Jayatilake


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





2007-05-02