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Pi




Mathematica Notation

Traditional Notation









Constants > Pi > Continued fraction representations





http://functions.wolfram.com/02.03.10.0008.01









  


  








Input Form





4/Pi == 1 + 1/(2 + 9/(2 + 25/(2 + 49/(2 + 81/(2 + 121/(2 + \[Ellipsis]))))))








Standard Form





Cell[BoxData[RowBox[List[FractionBox["4", "\[Pi]"], "\[Equal]", RowBox[List["1", "+", FractionBox["1", StyleBox[RowBox[List["2", "+", FractionBox["9", StyleBox[RowBox[List["2", "+", FractionBox["25", StyleBox[RowBox[List["2", "+", FractionBox["49", StyleBox[RowBox[List["2", "+", FractionBox["81", StyleBox[RowBox[List["2", "+", FractionBox["121", StyleBox[RowBox[List["2", "+", "\[Ellipsis]"]], Rule[ScriptLevel, 0]]]]], Rule[ScriptLevel, 0]]]]], Rule[ScriptLevel, 0]]]]], Rule[ScriptLevel, 0]]]]], Rule[ScriptLevel, 0]]]]], Rule[ScriptLevel, 0]]]]]]]]]








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> 4 </mn> <mi> &#960; </mi> </mfrac> <mo> &#10869; </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mfrac> <mn> 1 </mn> <mstyle scriptlevel='0'> <mrow> <mn> 2 </mn> <mo> + </mo> <mfrac> <mn> 9 </mn> <mstyle scriptlevel='0'> <mrow> <mn> 2 </mn> <mo> + </mo> <mfrac> <mn> 25 </mn> <mstyle scriptlevel='0'> <mrow> <mn> 2 </mn> <mo> + </mo> <mfrac> <mn> 49 </mn> <mstyle scriptlevel='0'> <mrow> <mn> 2 </mn> <mo> + </mo> <mfrac> <mn> 81 </mn> <mstyle scriptlevel='0'> <mrow> <mn> 2 </mn> <mo> + </mo> <mfrac> <mn> 121 </mn> <mstyle scriptlevel='0'> <mrow> <mn> 2 </mn> <mo> + </mo> <mo> &#8230; </mo> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <pi /> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> 9 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> 25 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> 49 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> 81 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> 121 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 2 </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> <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", "[", FractionBox["4", "\[Pi]"], "]"]], "\[RuleDelayed]", RowBox[List["1", "+", FractionBox["1", RowBox[List["2", "+", FractionBox["9", RowBox[List["2", "+", FractionBox["25", RowBox[List["2", "+", FractionBox["49", RowBox[List["2", "+", FractionBox["81", RowBox[List["2", "+", FractionBox["121", RowBox[List["2", "+", "\[Ellipsis]"]]]]]]]]]]]]]]]]]]]]]]]]


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





2001-10-29