(* Content-type: application/vnd.wolfram.mathematica *)

(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)

(* CreatedBy='Mathematica 9.0' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       157,          7]
NotebookDataLength[      7132,        303]
NotebookOptionsPosition[      5554,        240]
NotebookOutlinePosition[      5909,        256]
CellTagsIndexPosition[      5866,        253]
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{

Cell[CellGroupData[{
Cell["Geometric Mean", "Title"],

Cell[CellGroupData[{

Cell["Author", "Subsection"],

Cell["\<\
Eric W. Weisstein
June 21, 2004\
\>", "Text"],

Cell[TextData[{
 "This notebook downloaded from ",
 ButtonBox["http://mathworld.wolfram.com/notebooks/SpecialFunctions/\
GeometricMean.nb",
  BaseStyle->"Hyperlink",
  ButtonData:>{
    URL["http://mathworld.wolfram.com/notebooks/SpecialFunctions/\
GeometricMean.nb"], None}],
 "."
}], "Text"],

Cell[TextData[{
 "For more information, see Eric's ",
 StyleBox["MathWorld",
  FontSlant->"Italic"],
 " entry ",
 ButtonBox["http://mathworld.wolfram.com/GeometricMean.html",
  BaseStyle->"Hyperlink",
  ButtonData:>{
    URL["http://mathworld.wolfram.com/GeometricMean.html"], None}],
 "."
}], "Text"],

Cell["\<\
\[Copyright]2005 Wolfram Research, Inc. except for portions noted otherwise\
\>", "Text"]
}, Open  ]],

Cell[CellGroupData[{

Cell["Initialization", "Subsection"],

Cell[BoxData[
 RowBox[{"<<", "Statistics`DescriptiveStatistics`"}]], "Input",
 InitializationCell->True]
}, Open  ]],

Cell[CellGroupData[{

Cell["Code", "Subsection"],

Cell[BoxData[
 RowBox[{
  RowBox[{"MyGeometricMean", "[", "l_List", "]"}], ":=", 
  RowBox[{
   RowBox[{"(", 
    RowBox[{"Times", "@@", "l"}], ")"}], "^", 
   RowBox[{"(", 
    RowBox[{"1", "/", 
     RowBox[{"Length", "[", "l", "]"}]}], ")"}]}]}]], "Input",
 InitializationCell->True]
}, Open  ]],

Cell[CellGroupData[{

Cell["Examples", "Section"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Table", "[", 
  RowBox[{
   RowBox[{"Subtract", "@@", 
    RowBox[{"Through", "[", 
     RowBox[{
      RowBox[{"{", 
       RowBox[{"GeometricMean", ",", "MyGeometricMean"}], "}"}], "[", 
      RowBox[{"Array", "[", 
       RowBox[{"x", ",", "n"}], "]"}], "]"}], "]"}]}], ",", 
   RowBox[{"{", 
    RowBox[{"n", ",", "10"}], "}"}]}], "]"}]], "Input"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
  "0", ",", "0", ",", "0", ",", "0", ",", "0", ",", "0", ",", "0", ",", "0", 
   ",", "0", ",", "0"}], "}"}]], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"GeometricMean", "[", 
  RowBox[{"{", 
   RowBox[{
    SubscriptBox["x", "1"], ",", 
    SubscriptBox["x", "2"]}], "}"}], "]"}]], "Input"],

Cell[BoxData[
 SqrtBox[
  RowBox[{
   SubscriptBox["x", "1"], " ", 
   SubscriptBox["x", "2"]}]]], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"GeometricMean", "[", 
  RowBox[{"{", 
   RowBox[{
    SubscriptBox["x", "1"], ",", 
    SubscriptBox["x", "2"], ",", 
    SubscriptBox["x", "3"]}], "}"}], "]"}]], "Input"],

Cell[BoxData[
 SuperscriptBox[
  RowBox[{"(", 
   RowBox[{
    SubscriptBox["x", "1"], " ", 
    SubscriptBox["x", "2"], " ", 
    SubscriptBox["x", "3"]}], ")"}], 
  RowBox[{"1", "/", "3"}]]], "Output"]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell[TextData[{
 "Relationship to ",
 Cell[BoxData[
  FormBox["A", TraditionalForm]]],
 " and ",
 Cell[BoxData[
  FormBox["H", TraditionalForm]]]
}], "Section"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"With", "[", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"n", "=", "2"}], "}"}], ",", 
   RowBox[{"Eliminate", "[", 
    RowBox[{
     RowBox[{"Thread", "[", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"G", ",", "H", ",", "A"}], "}"}], "\[Equal]", 
       RowBox[{
        RowBox[{"Through", "[", 
         RowBox[{
          RowBox[{"{", 
           RowBox[{"GeometricMean", ",", "HarmonicMean", ",", "Mean"}], "}"}],
           "[", 
          RowBox[{"Array", "[", 
           RowBox[{"x", ",", "n"}], "]"}], "]"}], "]"}], "^", "n"}]}], "]"}], 
     ",", 
     RowBox[{"Array", "[", 
      RowBox[{"x", ",", "n"}], "]"}]}], "]"}]}], "\[IndentingNewLine]", 
  "]"}]], "Input"],

Cell[BoxData[
 RowBox[{
  RowBox[{"A", " ", "H"}], "\[Equal]", 
  SuperscriptBox["G", "2"]}]], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Solve", "[", 
  RowBox[{
   RowBox[{
    RowBox[{"G", "^", "2"}], "\[Equal]", 
    RowBox[{"A", " ", "H"}]}], ",", "H"}], "]"}]], "Input"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"{", 
   RowBox[{"H", "\[Rule]", 
    FractionBox[
     SuperscriptBox["G", "2"], "A"]}], "}"}], "}"}]], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"With", "[", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{"n", "=", "3"}], "}"}], ",", 
   RowBox[{"Eliminate", "[", 
    RowBox[{
     RowBox[{"Thread", "[", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"g", ",", "h", ",", "a"}], "}"}], "\[Equal]", 
       RowBox[{
        RowBox[{"Through", "[", 
         RowBox[{
          RowBox[{"{", 
           RowBox[{"GeometricMean", ",", "HarmonicMean", ",", "Mean"}], "}"}],
           "[", 
          RowBox[{"Array", "[", 
           RowBox[{"x", ",", "n"}], "]"}], "]"}], "]"}], "^", "n"}]}], "]"}], 
     ",", 
     RowBox[{"Array", "[", 
      RowBox[{"x", ",", "n"}], "]"}]}], "]"}]}], "\[IndentingNewLine]", 
  "]"}]], "Input"],

Cell[BoxData["$Aborted"], "Output"]
}, Open  ]]
}, Open  ]]
}, Open  ]]
},
WindowSize->{740, 867},
WindowMargins->{{412, Automatic}, {-12, Automatic}},
FrontEndVersion->"9.0 for Mac OS X x86 (32-bit, 64-bit Kernel) (March 5, \
2013)",
StyleDefinitions->"Default.nb"
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[CellGroupData[{
Cell[579, 22, 31, 0, 92, "Title"],
Cell[CellGroupData[{
Cell[635, 26, 28, 0, 44, "Subsection"],
Cell[666, 28, 55, 3, 49, "Text"],
Cell[724, 33, 293, 9, 49, "Text"],
Cell[1020, 44, 301, 10, 49, "Text"],
Cell[1324, 56, 99, 2, 30, "Text"]
}, Open  ]],
Cell[CellGroupData[{
Cell[1460, 63, 36, 0, 44, "Subsection"],
Cell[1499, 65, 104, 2, 28, "Input",
 InitializationCell->True]
}, Open  ]],
Cell[CellGroupData[{
Cell[1640, 72, 26, 0, 44, "Subsection"],
Cell[1669, 74, 286, 9, 28, "Input",
 InitializationCell->True]
}, Open  ]],
Cell[CellGroupData[{
Cell[1992, 88, 27, 0, 80, "Section"],
Cell[CellGroupData[{
Cell[2044, 92, 375, 11, 46, "Input"],
Cell[2422, 105, 160, 4, 28, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[2619, 114, 161, 5, 28, "Input"],
Cell[2783, 121, 108, 4, 39, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[2928, 130, 195, 6, 28, "Input"],
Cell[3126, 138, 203, 7, 32, "Output"]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[3378, 151, 160, 7, 82, "Section"],
Cell[CellGroupData[{
Cell[3563, 162, 707, 22, 97, "Input"],
Cell[4273, 186, 104, 3, 32, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[4414, 194, 162, 5, 25, "Input"],
Cell[4579, 201, 153, 5, 41, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[4769, 211, 707, 22, 89, "Input"],
Cell[5479, 235, 35, 0, 70, "Output"]
}, Open  ]]
}, Open  ]]
}, Open  ]]
}
]
*)

(* End of internal cache information *)