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Pi




Mathematica Notation

Traditional Notation









Constants > Pi > Representations through more general functions > Through other functions





http://functions.wolfram.com/02.03.26.0012.01









  


  








Input Form





Pi == -320 ArcTan[1/4000300] - 128 ArcTan[1/500150] - 64 ArcTan[1/62575] - 64 ArcTan[1/50105] - 32 ArcTan[1/4030] - 16 ArcTan[1/515] - 4 ArcTan[1/239] + 640 ArcTan[1/200]








Standard Form





Cell[BoxData[RowBox[List["\[Pi]", "\[Equal]", RowBox[List[RowBox[List[RowBox[List["-", "320"]], " ", RowBox[List["ArcTan", "[", FractionBox["1", "4000300"], "]"]]]], "-", RowBox[List["128", " ", RowBox[List["ArcTan", "[", FractionBox["1", "500150"], "]"]]]], "-", RowBox[List["64", " ", RowBox[List["ArcTan", "[", FractionBox["1", "62575"], "]"]]]], "-", RowBox[List["64", " ", RowBox[List["ArcTan", "[", FractionBox["1", "50105"], "]"]]]], "-", RowBox[List["32", " ", RowBox[List["ArcTan", "[", FractionBox["1", "4030"], "]"]]]], "-", RowBox[List["16", " ", RowBox[List["ArcTan", "[", FractionBox["1", "515"], "]"]]]], "-", RowBox[List["4", " ", RowBox[List["ArcTan", "[", FractionBox["1", "239"], "]"]]]], "+", RowBox[List["640", " ", RowBox[List["ArcTan", "[", FractionBox["1", "200"], "]"]]]]]]]]]]








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> <mrow> <mn> 640 </mn> <mo> &#8290; </mo> <mrow> <msup> <mi> tan </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mfrac> <mn> 1 </mn> <mn> 200 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mrow> <msup> <mi> tan </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mfrac> <mn> 1 </mn> <mn> 239 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 16 </mn> <mo> &#8290; </mo> <mrow> <msup> <mi> tan </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mfrac> <mn> 1 </mn> <mn> 515 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 32 </mn> <mo> &#8290; </mo> <mrow> <msup> <mi> tan </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mfrac> <mn> 1 </mn> <mn> 4030 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 64 </mn> <mo> &#8290; </mo> <mrow> <msup> <mi> tan </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mfrac> <mn> 1 </mn> <mn> 50105 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 64 </mn> <mo> &#8290; </mo> <mrow> <msup> <mi> tan </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mfrac> <mn> 1 </mn> <mn> 62575 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 128 </mn> <mo> &#8290; </mo> <mrow> <msup> <mi> tan </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mfrac> <mn> 1 </mn> <mn> 500150 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 320 </mn> <mo> &#8290; </mo> <mrow> <msup> <mi> tan </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mfrac> <mn> 1 </mn> <mn> 4000300 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <pi /> <apply> <plus /> <apply> <times /> <cn type='integer'> 640 </cn> <apply> <arctan /> <cn type='rational'> 1 <sep /> 200 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <arctan /> <cn type='rational'> 1 <sep /> 239 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 16 </cn> <apply> <arctan /> <cn type='rational'> 1 <sep /> 515 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 32 </cn> <apply> <arctan /> <cn type='rational'> 1 <sep /> 4030 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 64 </cn> <apply> <arctan /> <cn type='rational'> 1 <sep /> 50105 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 64 </cn> <apply> <arctan /> <cn type='rational'> 1 <sep /> 62575 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 128 </cn> <apply> <arctan /> <cn type='rational'> 1 <sep /> 500150 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 320 </cn> <apply> <arctan /> <cn type='rational'> 1 <sep /> 4000300 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", "\[Pi]", "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["-", "320"]], " ", RowBox[List["ArcTan", "[", FractionBox["1", "4000300"], "]"]]]], "-", RowBox[List["128", " ", RowBox[List["ArcTan", "[", FractionBox["1", "500150"], "]"]]]], "-", RowBox[List["64", " ", RowBox[List["ArcTan", "[", FractionBox["1", "62575"], "]"]]]], "-", RowBox[List["64", " ", RowBox[List["ArcTan", "[", FractionBox["1", "50105"], "]"]]]], "-", RowBox[List["32", " ", RowBox[List["ArcTan", "[", FractionBox["1", "4030"], "]"]]]], "-", RowBox[List["16", " ", RowBox[List["ArcTan", "[", FractionBox["1", "515"], "]"]]]], "-", RowBox[List["4", " ", RowBox[List["ArcTan", "[", FractionBox["1", "239"], "]"]]]], "+", RowBox[List["640", " ", RowBox[List["ArcTan", "[", FractionBox["1", "200"], "]"]]]]]]]]]]


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





2002-12-18