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Pi




Mathematica Notation

Traditional Notation









Constants > Pi > Product representations





http://functions.wolfram.com/02.03.08.0006.01









  


  








Input Form





2/Pi == (Sqrt[2]/2) (Sqrt[2 + Sqrt[2]]/2) (Sqrt[2 + Sqrt[2 + Sqrt[2]]]/2) (Sqrt[2 + Sqrt[2 + Sqrt[2 + Sqrt[2]]]]/2) \[Ellipsis]








Standard Form





Cell[BoxData[RowBox[List[FractionBox["2", "\[Pi]"], "\[Equal]", RowBox[List[FractionBox[SqrtBox["2"], "2"], "\[Times]", FractionBox[SqrtBox[RowBox[List["2", "+", SqrtBox["2"]]]], "2"], "\[Times]", FractionBox[SqrtBox[RowBox[List["2", "+", SqrtBox[RowBox[List["2", "+", SqrtBox["2"]]]]]]], "2"], "\[Times]", FractionBox[SqrtBox[RowBox[List["2", "+", SqrtBox[RowBox[List["2", "+", SqrtBox[RowBox[List["2", "+", SqrtBox["2"]]]]]]]]]], "2"], "\[Times]", "\[Ellipsis]"]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mfrac> <mn> 2 </mn> <mi> &#960; </mi> </mfrac> <mo> &#10869; </mo> <mrow> <mfrac> <msqrt> <mn> 2 </mn> </msqrt> <mn> 2 </mn> </mfrac> <mo> &#215; </mo> <mfrac> <msqrt> <mrow> <mn> 2 </mn> <mo> + </mo> <msqrt> <mn> 2 </mn> </msqrt> </mrow> </msqrt> <mn> 2 </mn> </mfrac> <mo> &#215; </mo> <mfrac> <msqrt> <mrow> <mn> 2 </mn> <mo> + </mo> <msqrt> <mrow> <mn> 2 </mn> <mo> + </mo> <msqrt> <mn> 2 </mn> </msqrt> </mrow> </msqrt> </mrow> </msqrt> <mn> 2 </mn> </mfrac> <mo> &#215; </mo> <mfrac> <msqrt> <mrow> <mn> 2 </mn> <mo> + </mo> <msqrt> <mrow> <mn> 2 </mn> <mo> + </mo> <msqrt> <mrow> <mn> 2 </mn> <mo> + </mo> <msqrt> <mn> 2 </mn> </msqrt> </mrow> </msqrt> </mrow> </msqrt> </mrow> </msqrt> <mn> 2 </mn> </mfrac> <mo> &#215; </mo> <mo> &#8230; </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <pi /> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <power /> <apply> <plus /> <cn type='integer'> 2 </cn> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <power /> <apply> <plus /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 2 </cn> <apply> <power /> <cn type='integer'> 2 </cn> <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> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <power /> <apply> <plus /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 2 </cn> <apply> <power /> <cn type='integer'> 2 </cn> <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> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <ci> &#8230; </ci> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", FractionBox["2", "\[Pi]"], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List["2", "+", SqrtBox["2"]]]], " ", SqrtBox[RowBox[List["2", "+", SqrtBox[RowBox[List["2", "+", SqrtBox["2"]]]]]]], " ", SqrtBox[RowBox[List["2", "+", SqrtBox[RowBox[List["2", "+", SqrtBox[RowBox[List["2", "+", SqrtBox["2"]]]]]]]]]], " ", "\[Ellipsis]"]], RowBox[List["2", " ", "2", " ", "2", " ", "2"]]]]]]]


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





2001-10-29