GoldenRatio == Sqrt[1 + Sqrt[1 + Sqrt[1 + Sqrt[1 + \[Ellipsis]]]]]

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<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> <msqrt> <mrow> <mn> 1 </mn> <mo> + </mo> <msqrt> <mrow> <mn> 1 </mn> <mo> + </mo> <msqrt> <mrow> <mn> 1 </mn> <mo> + </mo> <msqrt> <mrow> <mn> 1 </mn> <mo> + </mo> <mo> &#8230; </mo> </mrow> </msqrt> </mrow> </msqrt> </mrow> </msqrt> </mrow> </msqrt> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <ci> GoldenRatio </ci> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <ci> &#8230; </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </annotation-xml> </semantics> </math>

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

2001-10-29