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Pi




Mathematica Notation

Traditional Notation









Constants > Pi > Continued fraction representations





http://functions.wolfram.com/02.03.10.0001.01









  


  








Input Form





Pi == 3 + 1/ (7 + 1/(15 + 1/(1 + 1/(292 + 1/(1 + 1/(1 + 1/(1 + 1/(2 + 1/(1 + 1/(3 + 1/(1 + 1/(14 + 1/(2 + 1/(1 + 1/(1 + 1/(2 + \[Ellipsis]))))))))))))))))








Standard Form





Cell[BoxData[RowBox[List["\[Pi]", "\[Equal]", RowBox[List["3", "+", RowBox[List["1", "/", RowBox[List["(", RowBox[List["7", "+", RowBox[List["1", "/", RowBox[List["(", RowBox[List["15", "+", RowBox[List["1", "/", RowBox[List["(", RowBox[List["1", "+", FractionBox["1", RowBox[List["292", "+", FractionBox["1", RowBox[List["1", "+", FractionBox["1", RowBox[List["1", "+", FractionBox["1", RowBox[List["1", "+", FractionBox["1", RowBox[List["2", "+", FractionBox["1", RowBox[List["1", "+", FractionBox["1", RowBox[List["3", "+", FractionBox["1", RowBox[List["1", "+", FractionBox["1", RowBox[List["14", "+", FractionBox["1", RowBox[List["2", "+", FractionBox["1", RowBox[List["1", "+", FractionBox["1", RowBox[List["1", "+", FractionBox["1", RowBox[List["2", "+", "\[Ellipsis]"]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mi> &#960; </mi> <mo> &#10869; </mo> <mrow> <mn> 3 </mn> <mo> + </mo> <mrow> <mn> 1 </mn> <mo> / </mo> <mrow> <mo> ( </mo> <mstyle scriptlevel='0'> <mrow> <mn> 7 </mn> <mo> + </mo> <mrow> <mn> 1 </mn> <mo> / </mo> <mrow> <mo> ( </mo> <mstyle scriptlevel='0'> <mrow> <mn> 15 </mn> <mo> + </mo> <mrow> <mn> 1 </mn> <mo> / </mo> <mrow> <mo> ( </mo> <mstyle scriptlevel='0'> <mrow> <mn> 1 </mn> <mo> + </mo> <mrow> <mn> 1 </mn> <mo> / </mo> <mrow> <mo> ( </mo> <mstyle scriptlevel='0'> <mrow> <mn> 292 </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> 2 </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> 3 </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> 14 </mn> <mo> + </mo> <mfrac> <mn> 1 </mn> <mstyle scriptlevel='0'> <mrow> <mn> 2 </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> 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> </mstyle> </mfrac> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mfrac> </mrow> </mstyle> </mfrac> </mrow> </mstyle> <mo> ) </mo> </mrow> </mrow> </mrow> </mstyle> <mo> ) </mo> </mrow> </mrow> </mrow> </mstyle> <mo> ) </mo> </mrow> </mrow> </mrow> </mstyle> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <pi /> <apply> <plus /> <cn type='integer'> 3 </cn> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 7 </cn> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 15 </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'> 292 </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'> 2 </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'> 3 </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'> 14 </cn> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 2 </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'> 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> <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> <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", "[", "\[Pi]", "]"]], "\[RuleDelayed]", RowBox[List["3", "+", FractionBox["1", RowBox[List["7", "+", FractionBox["1", RowBox[List["15", "+", FractionBox["1", RowBox[List["1", "+", FractionBox["1", RowBox[List["292", "+", FractionBox["1", RowBox[List["1", "+", FractionBox["1", RowBox[List["1", "+", FractionBox["1", RowBox[List["1", "+", FractionBox["1", RowBox[List["2", "+", FractionBox["1", RowBox[List["1", "+", FractionBox["1", RowBox[List["3", "+", FractionBox["1", RowBox[List["1", "+", FractionBox["1", RowBox[List["14", "+", FractionBox["1", RowBox[List["2", "+", FractionBox["1", RowBox[List["1", "+", FractionBox["1", RowBox[List["1", "+", FractionBox["1", RowBox[List["2", "+", "\[Ellipsis]"]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]


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





2001-10-29