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GoldenRatio




Mathematica Notation

Traditional Notation









Constants > GoldenRatio > Continued fraction representations





http://functions.wolfram.com/02.02.10.0001.01









  


  








Input Form





GoldenRatio == 1 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + \[Ellipsis]))))








Standard Form





Cell[BoxData[RowBox[List["GoldenRatio", "\[Equal]", " ", RowBox[List["1", "+", FractionBox["1", RowBox[List["1", "+", FractionBox["1", RowBox[List["1", "+", FractionBox["1", RowBox[List["1", "+", FractionBox["1", RowBox[List["1", "+", "\[Ellipsis]"]]]]]]]]]]]]]]]]]]








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> <mn> 1 </mn> <mo> + </mo> <mfrac> <mn> 1 </mn> <mstyle scriptlevel='0'> <mrow> <mn> 1 </mn> <mo> + </mo> <mfrac> <mn> 1 </mn> <mstyle scriptlevel='0'> <mrow> <mn> 1 </mn> <mo> + </mo> <mfrac> <mn> 1 </mn> <mstyle scriptlevel='0'> <mrow> <mn> 1 </mn> <mo> + </mo> <mfrac> <mn> 1 </mn> <mstyle scriptlevel='0'> <mrow> <mn> 1 </mn> <mo> + </mo> <mo> &#8230; </mo> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <ci> GoldenRatio </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <ci> &#8230; </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", "GoldenRatio", "]"]], "\[RuleDelayed]", RowBox[List["1", "+", FractionBox["1", RowBox[List["1", "+", FractionBox["1", RowBox[List["1", "+", FractionBox["1", RowBox[List["1", "+", FractionBox["1", RowBox[List["1", "+", "\[Ellipsis]"]]]]]]]]]]]]]]]]]]


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





2001-10-29