(* Content-type: application/vnd.wolfram.mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 8.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 157, 7] NotebookDataLength[ 49346, 1817] NotebookOptionsPosition[ 42312, 1567] NotebookOutlinePosition[ 42655, 1582] CellTagsIndexPosition[ 42612, 1579] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[BoxData[ StyleBox[ RowBox[{"(*", "\:0421\:043f\:0438\:0441\:044a\:0446\:0438", "*)"}], FontFamily->"Courier New", FontSize->24]], "Input", CellChangeTimes->{{3.6228613783466225`*^9, 3.6228613942742505`*^9}, { 3.657264519170847*^9, 3.657264525294197*^9}}, FontFamily->"Courier New"], Cell[CellGroupData[{ Cell[BoxData[{ StyleBox[ RowBox[{"{", RowBox[{"a", ",", "b", ",", "c"}], "}"}], FontSize->24], "\[IndentingNewLine]", StyleBox[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"2", ",", "5"}], "}"}]}], "}"}], FontSize->24], "\[IndentingNewLine]", StyleBox[ RowBox[{"{", RowBox[{"x", ",", "1", ",", "3"}], "}"}], FontSize->24], "\[IndentingNewLine]", StyleBox[ RowBox[{"{", RowBox[{ RowBox[{"x", "==", StyleBox["1", FontFamily->"Courier New"]}], StyleBox[",", FontFamily->"Courier New"], StyleBox[ RowBox[{"y", "==", "3"}], FontFamily->"Courier New"]}], StyleBox["}", FontFamily->"Courier New"]}], FontSize->24]}], "Input", CellChangeTimes->{{3.622861410669879*^9, 3.622861482211605*^9}, { 3.6228686871022043`*^9, 3.6228686923750143`*^9}}, FontFamily->"Courier New"], Cell[BoxData[ RowBox[{"{", RowBox[{"a", ",", "b", ",", "c"}], "}"}]], "Output", CellChangeTimes->{{3.622868615466879*^9, 3.6228686943718176`*^9}, 3.657264533231651*^9, 3.657268104623923*^9}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"2", ",", "5"}], "}"}]}], "}"}]], "Output", CellChangeTimes->{{3.622868615466879*^9, 3.6228686943718176`*^9}, 3.657264533231651*^9, 3.657268104625923*^9}], Cell[BoxData[ RowBox[{"{", RowBox[{"x", ",", "1", ",", "3"}], "}"}]], "Output", CellChangeTimes->{{3.622868615466879*^9, 3.6228686943718176`*^9}, 3.657264533231651*^9, 3.657268104627923*^9}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"x", "\[Equal]", "1"}], ",", RowBox[{"y", "\[Equal]", "3"}]}], "}"}]], "Output", CellChangeTimes->{{3.622868615466879*^9, 3.6228686943718176`*^9}, 3.657264533231651*^9, 3.6572681046289234`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ StyleBox[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "4"}], "}"}], ",", RowBox[{"{", "3", "}"}]}], "}"}], FontFamily->"Courier New", FontSize->24]], "Input", CellChangeTimes->{{3.6228615438005133`*^9, 3.6228615769973717`*^9}}, FontFamily->"Courier New"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "4"}], "}"}], ",", RowBox[{"{", "3", "}"}]}], "}"}]], "Output", CellChangeTimes->{3.6228687338086867`*^9, 3.6572645402150507`*^9, 3.657264929180298*^9, 3.657268140328965*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ StyleBox[ RowBox[{ RowBox[{"{", RowBox[{ "1", ",", "2", ",", "3", ",", "4", ",", "5", ",", "6", ",", "7", ",", "8", ",", "9"}], "}"}], "^", "2"}], FontFamily->"Courier New", FontSize->24]], "Input", CellChangeTimes->{{3.6228617592690916`*^9, 3.6228617875051413`*^9}}, FontFamily->"Courier New"], Cell[BoxData[ RowBox[{"{", RowBox[{ "1", ",", "4", ",", "9", ",", "16", ",", "25", ",", "36", ",", "49", ",", "64", ",", "81"}], "}"}]], "Output", CellChangeTimes->{ 3.622868781965971*^9, {3.657264545734366*^9, 3.6572645483145137`*^9}, 3.657264933017517*^9, 3.6572681573999414`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ StyleBox[ SqrtBox[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"2", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"4", ",", "5"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"6", ",", "7"}], "}"}], ",", "8"}], "}"}]], FontSize->24]], "Input", CellChangeTimes->{{3.6228618708882875`*^9, 3.6228619205275745`*^9}}, FontFamily->"Courier New"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ SqrtBox["2"], ",", SqrtBox["3"]}], "}"}], ",", RowBox[{"{", RowBox[{"2", ",", SqrtBox["5"]}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{ SqrtBox["6"], ",", SqrtBox["7"]}], "}"}], ",", RowBox[{"2", " ", SqrtBox["2"]}]}], "}"}]], "Output", CellChangeTimes->{3.622868858047305*^9, 3.6572649401209235`*^9, 3.6572682373005114`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ StyleBox[ FractionBox["1", RowBox[{"{", RowBox[{"1", ",", "2", ",", "3", ",", "4", ",", "5"}], "}"}]], FontFamily->"Courier New", FontSize->24]], "Input", CellChangeTimes->{{3.6228620324421716`*^9, 3.622862055109011*^9}}, FontFamily->"Courier New"], Cell[BoxData[ RowBox[{"{", RowBox[{"1", ",", FractionBox["1", "2"], ",", FractionBox["1", "3"], ",", FractionBox["1", "4"], ",", FractionBox["1", "5"]}], "}"}]], "Output", CellChangeTimes->{3.6228689311812334`*^9, 3.6572649457602463`*^9, 3.6572682727565393`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ StyleBox[ RowBox[{ RowBox[{"{", RowBox[{"1", ",", "2", ",", "3"}], "}"}], "+", RowBox[{"{", RowBox[{"4", ",", "5", ",", "6"}], "}"}]}], FontFamily->"Courier New", FontSize->24]], "Input", CellChangeTimes->{{3.622862130613144*^9, 3.622862162000399*^9}}, FontFamily->"Courier New"], Cell[BoxData[ RowBox[{"{", RowBox[{"5", ",", "7", ",", "9"}], "}"}]], "Output", CellChangeTimes->{3.622868994174144*^9, 3.657264949240445*^9, 3.6572682837071657`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ StyleBox[ RowBox[{ RowBox[{"{", RowBox[{"1", ",", "2", ",", "3"}], "}"}], "-", RowBox[{"{", RowBox[{"4", ",", "5", ",", "6"}], "}"}]}], FontFamily->"Courier New", FontSize->24]], "Input", CellChangeTimes->{ 3.6228622125288877`*^9, {3.6572683205472727`*^9, 3.6572683336740236`*^9}}, FontFamily->"Courier New"], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"-", "3"}], ",", RowBox[{"-", "3"}], ",", RowBox[{"-", "3"}]}], "}"}]], "Output", CellChangeTimes->{ 3.6228690247033978`*^9, 3.657264957435914*^9, {3.657268302577245*^9, 3.6572683366261926`*^9}}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ StyleBox[ RowBox[{ RowBox[{"{", RowBox[{"1", ",", "2", ",", "3"}], "}"}], "*", RowBox[{"{", RowBox[{"4", ",", "5", ",", "6"}], "}"}]}], FontFamily->"Courier New", FontSize->24]], "Input", CellChangeTimes->{3.622862234290926*^9}, FontFamily->"Courier New"], Cell[BoxData[ RowBox[{"{", RowBox[{"4", ",", "10", ",", "18"}], "}"}]], "Output", CellChangeTimes->{3.622869045591834*^9, 3.657268343450583*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ StyleBox[ RowBox[{ RowBox[{"{", RowBox[{"1", ",", "2", ",", "3"}], "}"}], RowBox[{"{", RowBox[{"4", ",", "5", ",", "6"}], "}"}]}], FontFamily->"Courier New", FontSize->24]], "Input", CellChangeTimes->{3.622862250327754*^9}, FontFamily->"Courier New"], Cell[BoxData[ RowBox[{"{", RowBox[{"4", ",", "10", ",", "18"}], "}"}]], "Output", CellChangeTimes->{3.6228690741398845`*^9, 3.657264960306078*^9, 3.657268358034417*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ StyleBox[ RowBox[{ RowBox[{"{", RowBox[{"1", ",", "2", ",", "3"}], "}"}], "/", RowBox[{"{", RowBox[{"4", ",", "5", ",", "6"}], "}"}]}], FontFamily->"Courier New", FontSize->24]], "Input", CellChangeTimes->{ 3.6228622772222013`*^9, {3.622869163902442*^9, 3.6228691742452602`*^9}}, FontFamily->"Courier New"], Cell[BoxData[ RowBox[{"{", RowBox[{ FractionBox["1", "4"], ",", FractionBox["2", "5"], ",", FractionBox["1", "2"]}], "}"}]], "Output", CellChangeTimes->{ 3.6228691180539618`*^9, {3.6228691668196473`*^9, 3.622869175118862*^9}, 3.6572649644143133`*^9, 3.657268381263746*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ StyleBox[ RowBox[{"2", "^", RowBox[{"{", RowBox[{ "0", ",", "1", ",", "2", ",", "3", ",", "4", ",", "5", ",", "6", ",", "7", ",", "8", ",", "9", ",", "10"}], "}"}]}], FontFamily->"Courier New", FontSize->24]], "Input", CellChangeTimes->{{3.6228623306054955`*^9, 3.622862361259549*^9}}, FontFamily->"Courier New"], Cell[BoxData[ RowBox[{"{", RowBox[{ "1", ",", "2", ",", "4", ",", "8", ",", "16", ",", "32", ",", "64", ",", "128", ",", "256", ",", "512", ",", "1024"}], "}"}]], "Output", CellChangeTimes->{3.6228692434011817`*^9, 3.657264976686015*^9, 3.6572683910653067`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ StyleBox[ RowBox[{"Cos", "[", RowBox[{"{", RowBox[{"0", ",", RowBox[{"Pi", "/", "4"}], ",", RowBox[{"Pi", "/", "2"}], ",", RowBox[{"3", RowBox[{"Pi", "/", "4"}]}], ",", "Pi"}], "}"}], "]"}], FontSize->24]], "Input", CellChangeTimes->{{3.6228624184804497`*^9, 3.622862467105735*^9}}, FontFamily->"Courier New"], Cell[BoxData[ RowBox[{"{", RowBox[{"1", ",", FractionBox["1", SqrtBox["2"]], ",", "0", ",", RowBox[{"-", FractionBox["1", SqrtBox["2"]]}], ",", RowBox[{"-", "1"}]}], "}"}]], "Output", CellChangeTimes->{3.6228693049120903`*^9, 3.657264987905657*^9, 3.6572684306125684`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ StyleBox[ RowBox[{ RowBox[{"Log", "[", RowBox[{"{", RowBox[{"1", ",", "2", ",", "3", ",", "4", ",", "5"}], "}"}], "]"}], "//", "N"}], FontSize->24]], "Input", CellChangeTimes->{{3.6228693798556213`*^9, 3.622869411991678*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ "0.`", ",", "0.6931471805599453`", ",", "1.0986122886681098`", ",", "1.3862943611198906`", ",", "1.6094379124341003`"}], "}"}]], "Output", CellChangeTimes->{{3.6228694020544605`*^9, 3.6228694129588795`*^9}, 3.657264992474918*^9, 3.6572684522738075`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ StyleBox[ RowBox[{"aa", "=", RowBox[{"{", RowBox[{"2", ",", "x", ",", "y", ",", RowBox[{"{", RowBox[{"a", ",", "b"}], "}"}]}], "}"}]}], FontFamily->"Courier New", FontSize->24]], "Input", CellChangeTimes->{{3.622862565541908*^9, 3.6228625724527197`*^9}, { 3.622862605119177*^9, 3.6228626145571938`*^9}}, FontFamily->"Courier New"], Cell[BoxData[ RowBox[{"{", RowBox[{"2", ",", "x", ",", "y", ",", RowBox[{"{", RowBox[{"a", ",", "b"}], "}"}]}], "}"}]], "Output", CellChangeTimes->{3.622869508368647*^9, 3.657264996436145*^9, 3.6572684977324076`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ StyleBox[ RowBox[{"Length", "[", "aa", "]"}], FontFamily->"Courier New", FontSize->24]], "Input", CellChangeTimes->{{3.6228626435108447`*^9, 3.6228626691572895`*^9}}, FontFamily->"Courier New"], Cell[BoxData["4"], "Output", CellChangeTimes->{3.62286956689995*^9, 3.6572650010144067`*^9, 3.657268512180234*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ StyleBox[ RowBox[{"aa", "[", RowBox[{"[", "2", "]"}], "]"}], FontFamily->"Courier New", FontSize->24]], "Input", CellChangeTimes->{{3.622862710918563*^9, 3.6228627110433636`*^9}, { 3.62286274314822*^9, 3.6228627482338285`*^9}}, FontFamily->"Courier New"], Cell[BoxData["x"], "Output", CellChangeTimes->{3.6228696541353035`*^9, 3.6572650095128927`*^9, 3.6572685743867917`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ StyleBox[ RowBox[{"aa", "[", RowBox[{"[", "3", "]"}], "]"}], FontFamily->"Courier New", FontSize->24]], "Input", CellChangeTimes->{3.622862793723509*^9}, FontFamily->"Courier New"], Cell[BoxData["y"], "Output", CellChangeTimes->{3.62286966920493*^9, 3.6572650126720734`*^9, 3.657268580077117*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ StyleBox[ RowBox[{"aa", "[", RowBox[{"[", "4", "]"}], "]"}], FontFamily->"Courier New", FontSize->24]], "Input", CellChangeTimes->{3.622862817887951*^9}, FontFamily->"Courier New"], Cell[BoxData[ RowBox[{"{", RowBox[{"a", ",", "b"}], "}"}]], "Output", CellChangeTimes->{3.6228696803433495`*^9, 3.657265016441289*^9, 3.6572685857284403`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ StyleBox[ RowBox[{ RowBox[{"aa", "[", RowBox[{"[", "4", "]"}], "]"}], "[", RowBox[{"[", "2", "]"}], "]"}], FontFamily->"Courier New", FontSize->24]], "Input", CellChangeTimes->{{3.6228628441271973`*^9, 3.622862848058404*^9}}, FontFamily->"Courier New"], Cell[BoxData["b"], "Output", CellChangeTimes->{3.6228696986421814`*^9, 3.6572650547454796`*^9, 3.6572686257177277`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ StyleBox[ RowBox[{"aa", "[", RowBox[{"[", RowBox[{"4", ",", "2"}], "]"}], "]"}], FontFamily->"Courier New", FontSize->24]], "Input", CellChangeTimes->{3.622862888025674*^9}, FontFamily->"Courier New"], Cell[BoxData["b"], "Output", CellChangeTimes->{3.62286972625423*^9, 3.6572650573116264`*^9, 3.657268679407799*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ StyleBox[ RowBox[{"aa", "[", RowBox[{"[", RowBox[{"{", RowBox[{"1", ",", "3"}], "}"}], "]"}], "]"}], FontFamily->"Courier New", FontSize->24]], "Input", CellChangeTimes->{{3.622862966509412*^9, 3.6228629735138245`*^9}, { 3.6228630043862786`*^9, 3.622863011624691*^9}}, FontFamily->"Courier New"], Cell[BoxData[ RowBox[{"{", RowBox[{"2", ",", "y"}], "}"}]], "Output", CellChangeTimes->{3.62286978320993*^9, 3.6572650646130443`*^9, 3.6572687164659185`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ StyleBox[ RowBox[{"aa", "[", RowBox[{"[", RowBox[{"1", ";;", "3"}], "]"}], "]"}], FontFamily->"Courier New", FontSize->24]], "Input", CellChangeTimes->{{3.622863070639595*^9, 3.6228630824800158`*^9}}, FontFamily->"Courier New"], Cell[BoxData[ RowBox[{"{", RowBox[{"2", ",", "x", ",", "y"}], "}"}]], "Output", CellChangeTimes->{3.622869830478013*^9, 3.6572687491527877`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ StyleBox[ RowBox[{"First", "[", "aa", "]"}], FontFamily->"Courier New", FontSize->24]], "Input", CellChangeTimes->{{3.6228631475321302`*^9, 3.6228631528049393`*^9}}, FontFamily->"Courier New"], Cell[BoxData["2"], "Output", CellChangeTimes->{3.622869878354497*^9, 3.657265083792141*^9, 3.657268775579299*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ StyleBox[ RowBox[{"Last", "[", "aa", "]"}], FontFamily->"Courier New", FontSize->24]], "Input", CellChangeTimes->{{3.622863202428626*^9, 3.622863202927827*^9}}, FontFamily->"Courier New"], Cell[BoxData[ RowBox[{"{", RowBox[{"a", ",", "b"}], "}"}]], "Output", CellChangeTimes->{3.6228698859673104`*^9, 3.65726508848341*^9, 3.6572687804565783`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ StyleBox[ RowBox[{"bb", "=", RowBox[{"{", RowBox[{"1", ",", RowBox[{"{", RowBox[{"2", ",", RowBox[{"{", RowBox[{"3", ",", RowBox[{"{", RowBox[{"4", ",", "5"}], "}"}], ",", "6"}], "}"}]}], "}"}], ",", "7"}], "}"}]}], FontFamily->"Courier New", FontSize->24]], "Input", CellChangeTimes->{{3.622863240133893*^9, 3.622863288681178*^9}}, FontFamily->"Courier New"], Cell[BoxData[ RowBox[{"{", RowBox[{"1", ",", RowBox[{"{", RowBox[{"2", ",", RowBox[{"{", RowBox[{"3", ",", RowBox[{"{", RowBox[{"4", ",", "5"}], "}"}], ",", "6"}], "}"}]}], "}"}], ",", "7"}], "}"}]], "Output", CellChangeTimes->{3.622869951705826*^9, 3.657265093263683*^9, 3.65726879885363*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ StyleBox[ RowBox[{"bb", "[", RowBox[{"[", RowBox[{"2", ",", "2", ",", "2", ",", "1"}], "]"}], "]"}], FontFamily->"Courier New", FontSize->24]], "Input", CellChangeTimes->{{3.6228633089612136`*^9, 3.6228633615489063`*^9}}, FontFamily->"Courier New"], Cell[BoxData["4"], "Output", CellChangeTimes->{3.622870004433919*^9, 3.6572651127908*^9, 3.6572688620582457`*^9}] }, Open ]], Cell[BoxData[""], "Input", CellChangeTimes->{{3.622864342392829*^9, 3.6228643558712525`*^9}}, FontFamily->"Courier New"], Cell[CellGroupData[{ Cell[BoxData[ StyleBox[ RowBox[{"Range", "[", "10", "]"}], FontFamily->"Courier New", FontSize->24]], "Input", CellChangeTimes->{{3.62286458210485*^9, 3.622864599545681*^9}, { 3.6228704741663437`*^9, 3.6228704947271795`*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ "1", ",", "2", ",", "3", ",", "4", ",", "5", ",", "6", ",", "7", ",", "8", ",", "9", ",", "10"}], "}"}]], "Output", CellChangeTimes->{ 3.6228700916380715`*^9, {3.6228704756795464`*^9, 3.622870495850382*^9}, 3.6572651169660387`*^9, 3.657268872413838*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{"Range", "[", RowBox[{"1.2", ",", "12.3", ",", RowBox[{"1", "/", "2"}]}], "]"}]}]], "Input", CellChangeTimes->{{3.6572702472574744`*^9, 3.657270269976774*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ "1.2`", ",", "1.7`", ",", "2.2`", ",", "2.7`", ",", "3.2`", ",", "3.7`", ",", "4.2`", ",", "4.7`", ",", "5.2`", ",", "5.7`", ",", "6.2`", ",", "6.7`", ",", "7.2`", ",", "7.7`", ",", "8.2`", ",", "8.7`", ",", "9.2`", ",", "9.7`", ",", "10.2`", ",", "10.7`", ",", "11.2`", ",", "11.7`", ",", "12.2`"}], "}"}]], "Output", CellChangeTimes->{3.657270275255076*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ StyleBox[ RowBox[{"Range", "[", RowBox[{"2", ",", "10"}], "]"}], FontFamily->"Courier New", FontSize->24]], "Input", CellChangeTimes->{{3.6228646410261536`*^9, 3.6228646421649556`*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ "2", ",", "3", ",", "4", ",", "5", ",", "6", ",", "7", ",", "8", ",", "9", ",", "10"}], "}"}]], "Output", CellChangeTimes->{3.6228701456141663`*^9, 3.6572688982503157`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ StyleBox[ RowBox[{"Range", "[", RowBox[{"2", ",", "10", ",", RowBox[{"1", "/", "2"}]}], "]"}], FontFamily->"Courier New", FontSize->24]], "Input", CellChangeTimes->{{3.6228646852366314`*^9, 3.622864687529835*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{"2", ",", FractionBox["5", "2"], ",", "3", ",", FractionBox["7", "2"], ",", "4", ",", FractionBox["9", "2"], ",", "5", ",", FractionBox["11", "2"], ",", "6", ",", FractionBox["13", "2"], ",", "7", ",", FractionBox["15", "2"], ",", "8", ",", FractionBox["17", "2"], ",", "9", ",", FractionBox["19", "2"], ",", "10"}], "}"}]], "Output", CellChangeTimes->{3.6572689158733234`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"{", RowBox[{"2", ",", FractionBox["5", "2"], ",", "3", ",", FractionBox["7", "2"], ",", "4", ",", FractionBox["9", "2"], ",", "5", ",", FractionBox["11", "2"], ",", "6", ",", FractionBox["13", "2"], ",", "7", ",", FractionBox["15", "2"], ",", "8", ",", FractionBox["17", "2"], ",", "9", ",", FractionBox["19", "2"], ",", "10"}], "}"}]], "Input", CellChangeTimes->{3.657265127270628*^9}], Cell[BoxData[ RowBox[{"{", RowBox[{"2", ",", FractionBox["5", "2"], ",", "3", ",", FractionBox["7", "2"], ",", "4", ",", FractionBox["9", "2"], ",", "5", ",", FractionBox["11", "2"], ",", "6", ",", FractionBox["13", "2"], ",", "7", ",", FractionBox["15", "2"], ",", "8", ",", FractionBox["17", "2"], ",", "9", ",", FractionBox["19", "2"], ",", "10"}], "}"}]], "Output", CellChangeTimes->{3.6572651273426323`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ StyleBox[ RowBox[{"Range", "[", RowBox[{"2", ",", "10.2", ",", RowBox[{"1", "/", "2"}]}], "]"}], FontFamily->"Courier New", FontSize->24]], "Input", CellChangeTimes->{{3.622864726295903*^9, 3.622864727231905*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{"2", ",", FractionBox["5", "2"], ",", "3", ",", FractionBox["7", "2"], ",", "4", ",", FractionBox["9", "2"], ",", "5", ",", FractionBox["11", "2"], ",", "6", ",", FractionBox["13", "2"], ",", "7", ",", FractionBox["15", "2"], ",", "8", ",", FractionBox["17", "2"], ",", "9", ",", FractionBox["19", "2"], ",", "10"}], "}"}]], "Output", CellChangeTimes->{3.6228702425527368`*^9, 3.657269010253722*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ StyleBox[ RowBox[{"Table", "[", RowBox[{ RowBox[{"k", "^", "2"}], ",", RowBox[{"{", RowBox[{"k", ",", "10"}], "}"}]}], "]"}], FontFamily->"Courier New", FontSize->24]], "Input", CellChangeTimes->{{3.6228648435925093`*^9, 3.6228649051034174`*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ "1", ",", "4", ",", "9", ",", "16", ",", "25", ",", "36", ",", "49", ",", "64", ",", "81", ",", "100"}], "}"}]], "Output", CellChangeTimes->{3.6228703208336744`*^9, 3.6572651355050993`*^9, 3.65726906214469*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ StyleBox[ RowBox[{"Table", "[", RowBox[{ RowBox[{"k", "^", "2"}], ",", RowBox[{"{", RowBox[{"k", ",", "1", ",", "10"}], "}"}]}], "]"}], FontFamily->"Courier New", FontSize->24], "\[IndentingNewLine]"}]], "Input", CellChangeTimes->{{3.6572690664019337`*^9, 3.657269080654749*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ "1", ",", "4", ",", "9", ",", "16", ",", "25", ",", "36", ",", "49", ",", "64", ",", "81", ",", "100"}], "}"}]], "Output", CellChangeTimes->{3.6572690831708927`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ StyleBox[ RowBox[{"Table", "[", RowBox[{ RowBox[{"k", "^", "2"}], ",", RowBox[{"{", RowBox[{"k", ",", "2", ",", "10"}], "}"}]}], "]"}], FontFamily->"Courier New", FontSize->24]], "Input", CellChangeTimes->{{3.622864925399053*^9, 3.6228649265846553`*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ "4", ",", "9", ",", "16", ",", "25", ",", "36", ",", "49", ",", "64", ",", "81", ",", "100"}], "}"}]], "Output", CellChangeTimes->{3.6228703939198027`*^9, 3.6572651392803144`*^9, 3.6572690960016265`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ StyleBox[ RowBox[{"Table", "[", RowBox[{ RowBox[{"k", "^", "2"}], ",", RowBox[{"{", RowBox[{"k", ",", "2", ",", "10", ",", RowBox[{"1", "/", "2"}]}], "}"}]}], "]"}], FontFamily->"Courier New", FontSize->24]], "Input", CellChangeTimes->{{3.6228649409366803`*^9, 3.6228649481750927`*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{"4", ",", FractionBox["25", "4"], ",", "9", ",", FractionBox["49", "4"], ",", "16", ",", FractionBox["81", "4"], ",", "25", ",", FractionBox["121", "4"], ",", "36", ",", FractionBox["169", "4"], ",", "49", ",", FractionBox["225", "4"], ",", "64", ",", FractionBox["289", "4"], ",", "81", ",", FractionBox["361", "4"], ",", "100"}], "}"}]], "Output", CellChangeTimes->{3.62287040376342*^9, 3.657269116777815*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ StyleBox[ RowBox[{"Table", "[", RowBox[{ RowBox[{"Table", "[", RowBox[{ RowBox[{"i", "-", "j"}], ",", RowBox[{"{", RowBox[{"i", ",", "4"}], "}"}]}], "]"}], ",", RowBox[{"{", RowBox[{"j", ",", "4"}], "}"}]}], "]"}], FontFamily->"Courier New", FontSize->24]], "Input", CellChangeTimes->{{3.622864999311983*^9, 3.622865057562485*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "1", ",", "2", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "0", ",", "1", ",", "2"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "2"}], ",", RowBox[{"-", "1"}], ",", "0", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "3"}], ",", RowBox[{"-", "2"}], ",", RowBox[{"-", "1"}], ",", "0"}], "}"}]}], "}"}]], "Output", CellChangeTimes->{3.6228705349440503`*^9, 3.6572651578573775`*^9, 3.6572692148774257`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ StyleBox[ RowBox[{"%", "//", "MatrixForm"}], FontFamily->"Courier New", FontSize->24]], "Input", CellChangeTimes->{{3.622865114237385*^9, 3.622865122302599*^9}}], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"0", "1", "2", "3"}, { RowBox[{"-", "1"}], "0", "1", "2"}, { RowBox[{"-", "2"}], RowBox[{"-", "1"}], "0", "1"}, { RowBox[{"-", "3"}], RowBox[{"-", "2"}], RowBox[{"-", "1"}], "0"} }, GridBoxAlignment->{ "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}], Function[BoxForm`e$, MatrixForm[BoxForm`e$]]]], "Output", CellChangeTimes->{3.6572692682144766`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ StyleBox[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"0", "1", "2", "3"}, { RowBox[{"-", "1"}], "0", "1", "2"}, { RowBox[{"-", "2"}], RowBox[{"-", "1"}], "0", "1"}, { RowBox[{"-", "3"}], RowBox[{"-", "2"}], RowBox[{"-", "1"}], "0"} }, GridBoxAlignment->{ "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}], Function[BoxForm`e$, MatrixForm[BoxForm`e$]]], FontFamily->"Courier New", FontSize->24, FontWeight->"Plain"]], "Input", CellChangeTimes->{3.6228705558636875`*^9}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "1", ",", "2", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "0", ",", "1", ",", "2"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "2"}], ",", RowBox[{"-", "1"}], ",", "0", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "3"}], ",", RowBox[{"-", "2"}], ",", RowBox[{"-", "1"}], ",", "0"}], "}"}]}], "}"}]], "Output", CellChangeTimes->{3.657265178797575*^9, 3.6572692816922474`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ StyleBox[ RowBox[{"Table", "[", RowBox[{ RowBox[{"j", "-", "i"}], ",", RowBox[{"{", RowBox[{"i", ",", "4"}], "}"}], ",", RowBox[{"{", RowBox[{"j", ",", "4"}], "}"}]}], "]"}], FontFamily->"Courier New", FontSize->24]], "Input", CellChangeTimes->{{3.622865168073079*^9, 3.6228651999439354`*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "1", ",", "2", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "0", ",", "1", ",", "2"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "2"}], ",", RowBox[{"-", "1"}], ",", "0", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "3"}], ",", RowBox[{"-", "2"}], ",", RowBox[{"-", "1"}], ",", "0"}], "}"}]}], "}"}]], "Output", CellChangeTimes->{3.622870630993419*^9, 3.657265181925754*^9, 3.6572693137070785`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ StyleBox[ RowBox[{"%", "//", "MatrixForm"}], FontFamily->"Courier New", FontSize->24]], "Input"], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"0", "1", "2", "3"}, { RowBox[{"-", "1"}], "0", "1", "2"}, { RowBox[{"-", "2"}], RowBox[{"-", "1"}], "0", "1"}, { RowBox[{"-", "3"}], RowBox[{"-", "2"}], RowBox[{"-", "1"}], "0"} }, GridBoxAlignment->{ "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}], Function[BoxForm`e$, MatrixForm[BoxForm`e$]]]], "Output", CellChangeTimes->{3.6572693187793684`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ StyleBox[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"0", "1", "2", "3"}, { RowBox[{"-", "1"}], "0", "1", "2"}, { RowBox[{"-", "2"}], RowBox[{"-", "1"}], "0", "1"}, { RowBox[{"-", "3"}], RowBox[{"-", "2"}], RowBox[{"-", "1"}], "0"} }, GridBoxAlignment->{ "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, "RowsIndexed" -> {}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}], Function[BoxForm`e$, MatrixForm[BoxForm`e$]]], FontFamily->"Courier New", FontSize->24, FontWeight->"Plain"]], "Input", CellChangeTimes->{3.622870643551441*^9}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "1", ",", "2", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "1"}], ",", "0", ",", "1", ",", "2"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "2"}], ",", RowBox[{"-", "1"}], ",", "0", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"-", "3"}], ",", RowBox[{"-", "2"}], ",", RowBox[{"-", "1"}], ",", "0"}], "}"}]}], "}"}]], "Output", CellChangeTimes->{3.6572651883261204`*^9}] }, Open ]], Cell[BoxData[ StyleBox[ RowBox[{ RowBox[{"f", "[", "x_", "]"}], ":=", RowBox[{ RowBox[{"2", "x"}], "+", "1"}]}], FontFamily->"Courier New", FontSize->24]], "Input", CellChangeTimes->{{3.6228655347985234`*^9, 3.6228655649533763`*^9}, { 3.6228657425752883`*^9, 3.6228657904517727`*^9}}], Cell[BoxData[ StyleBox[ RowBox[{"NestList", "[", RowBox[{"f", ",", "1", ",", "9"}], "]"}], FontFamily->"Courier New", FontSize->24]], "Input", CellChangeTimes->{{3.622865608461853*^9, 3.622865660409944*^9}, { 3.6228657678161325`*^9, 3.62286579449218*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"{", RowBox[{"1", ",", RowBox[{"f", "[", "1", "]"}], ",", RowBox[{"f", "[", RowBox[{"f", "[", "1", "]"}], "]"}], ",", RowBox[{"f", "[", RowBox[{"f", "[", RowBox[{"f", "[", "1", "]"}], "]"}], "]"}], ",", RowBox[{"f", "[", RowBox[{"f", "[", RowBox[{"f", "[", RowBox[{"f", "[", "1", "]"}], "]"}], "]"}], "]"}], ",", RowBox[{"f", "[", RowBox[{"f", "[", RowBox[{"f", "[", RowBox[{"f", "[", RowBox[{"f", "[", "1", "]"}], "]"}], "]"}], "]"}], "]"}], ",", RowBox[{"f", "[", RowBox[{"f", "[", RowBox[{"f", "[", RowBox[{"f", "[", RowBox[{"f", "[", RowBox[{"f", "[", "1", "]"}], "]"}], "]"}], "]"}], "]"}], "]"}], ",", RowBox[{"f", "[", RowBox[{"f", "[", RowBox[{"f", "[", RowBox[{"f", "[", RowBox[{"f", "[", RowBox[{"f", "[", RowBox[{"f", "[", "1", "]"}], "]"}], "]"}], "]"}], "]"}], "]"}], "]"}], ",", RowBox[{"f", "[", RowBox[{"f", "[", RowBox[{"f", "[", RowBox[{"f", "[", RowBox[{"f", "[", RowBox[{"f", "[", RowBox[{"f", "[", RowBox[{"f", "[", "1", "]"}], "]"}], "]"}], "]"}], "]"}], "]"}], "]"}], "]"}], ",", RowBox[{"f", "[", RowBox[{"f", "[", RowBox[{"f", "[", RowBox[{"f", "[", RowBox[{"f", "[", RowBox[{"f", "[", RowBox[{"f", "[", RowBox[{"f", "[", RowBox[{"f", "[", "1", "]"}], "]"}], "]"}], "]"}], "]"}], "]"}], "]"}], "]"}], "]"}]}], "}"}]], "Input", CellChangeTimes->{3.6572694123527207`*^9}], Cell[BoxData[ RowBox[{"{", RowBox[{ "1", ",", "3", ",", "7", ",", "15", ",", "31", ",", "63", ",", "127", ",", "255", ",", "511", ",", "1023"}], "}"}]], "Output", CellChangeTimes->{3.657269412401724*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ StyleBox[ RowBox[{"Flatten", "[", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], ",", "3", ",", "4", ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"5", ",", "6"}], "}"}], ",", "7"}], "}"}], ",", "8"}], "}"}], "]"}], FontFamily->"Courier New", FontSize->24]], "Input", CellChangeTimes->{{3.6228659007907662`*^9, 3.622865968307685*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ "1", ",", "2", ",", "3", ",", "4", ",", "5", ",", "6", ",", "7", ",", "8"}], "}"}]], "Output", CellChangeTimes->{3.6228710822866116`*^9, 3.657265244842353*^9, 3.657269487607025*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ StyleBox[ RowBox[{"Append", "[", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], ",", "3"}], "]"}], FontFamily->"Courier New", FontSize->24]], "Input", CellChangeTimes->{{3.622866087881895*^9, 3.6228661131227393`*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{"1", ",", "2", ",", "3"}], "}"}]], "Output", CellChangeTimes->{3.622871190489402*^9, 3.6572652548189235`*^9, 3.6572695302934666`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ StyleBox[ RowBox[{"Prepend", "[", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "2"}], "}"}], ",", "0"}], "]"}], FontFamily->"Courier New", FontSize->24]], "Input", CellChangeTimes->{{3.6228661525440083`*^9, 3.6228661631052265`*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{"0", ",", "1", ",", "2"}], "}"}]], "Output", CellChangeTimes->{3.6228712113466387`*^9, 3.657265257957103*^9, 3.6572695478644714`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ StyleBox[ RowBox[{ RowBox[{"a", "=", RowBox[{"215", "/", "111"}]}], "\[IndentingNewLine]", "\[IndentingNewLine]"}], FontFamily->"Courier New", FontSize->24]], "Input", CellChangeTimes->{{3.6228662823986363`*^9, 3.6228662971874623`*^9}, 3.6228712951343856`*^9}], Cell[BoxData[ FractionBox["215", "111"]], "Output", CellChangeTimes->{3.622871299159193*^9, 3.657265262397357*^9, 3.657269563646374*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ StyleBox[ RowBox[{"Union", "[", RowBox[{ RowBox[{"{", RowBox[{"a", ",", "2"}], "}"}], ",", RowBox[{"{", RowBox[{"v", ",", "8"}], "}"}], ",", RowBox[{"{", RowBox[{"h", ",", "s"}], "}"}]}], "]"}], FontFamily->"Courier New", FontSize->24]], "Input", CellChangeTimes->{{3.622866318965101*^9, 3.622866385327617*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ FractionBox["215", "111"], ",", "2", ",", "8", ",", "h", ",", "s", ",", "v"}], "}"}]], "Output", CellChangeTimes->{3.6228713438532715`*^9, 3.6572695900488844`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ StyleBox[ RowBox[{"Join", "[", RowBox[{ RowBox[{"{", RowBox[{"a", ",", "2"}], "}"}], ",", RowBox[{"{", RowBox[{"v", ",", "8"}], "}"}], ",", RowBox[{"{", RowBox[{"h", ",", "s"}], "}"}]}], "]"}], FontFamily->"Courier New", FontSize->24]], "Input", CellChangeTimes->{{3.6228664339217024`*^9, 3.6228664479929276`*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ FractionBox["215", "111"], ",", "2", ",", "v", ",", "8", ",", "h", ",", "s"}], "}"}]], "Output", CellChangeTimes->{3.622871400543771*^9, 3.657269616057372*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ StyleBox[ RowBox[{"Union", "[", RowBox[{ RowBox[{"{", RowBox[{"a", ",", "2"}], "}"}], ",", RowBox[{"{", RowBox[{"v", ",", "8"}], "}"}], ",", RowBox[{"{", RowBox[{"h", ",", "s", ",", "v"}], "}"}]}], "]"}], FontFamily->"Courier New", FontSize->24]], "Input", CellChangeTimes->{{3.622866502655423*^9, 3.6228665032170243`*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ FractionBox["215", "111"], ",", "2", ",", "8", ",", "h", ",", "s", ",", "v"}], "}"}]], "Output", CellChangeTimes->{3.6228714481862545`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ StyleBox[ RowBox[{"Join", "[", RowBox[{ RowBox[{"{", RowBox[{"a", ",", "2"}], "}"}], ",", RowBox[{"{", RowBox[{"v", ",", "8"}], "}"}], ",", RowBox[{"{", RowBox[{"h", ",", "s", ",", "v"}], "}"}]}], "]"}], FontFamily->"Courier New", FontSize->24]], "Input", CellChangeTimes->{{3.6228665329350767`*^9, 3.6228665335434775`*^9}, { 3.6228714740667*^9, 3.622871487529524*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ FractionBox["215", "111"], ",", "2", ",", "v", ",", "8", ",", "h", ",", "s", ",", "v"}], "}"}]], "Output", CellChangeTimes->{{3.62287145712507*^9, 3.6228714881379247`*^9}}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ StyleBox[ RowBox[{"points", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"2", "i"}], ",", RowBox[{"5", "-", "i"}]}], "}"}], ",", RowBox[{"{", RowBox[{"i", ",", "8"}], "}"}]}], "]"}]}], FontFamily->"Courier New", FontSize->24]], "Input", CellChangeTimes->{{3.622866806403557*^9, 3.622866862438855*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"2", ",", "4"}], "}"}], ",", RowBox[{"{", RowBox[{"4", ",", "3"}], "}"}], ",", RowBox[{"{", RowBox[{"6", ",", "2"}], "}"}], ",", RowBox[{"{", RowBox[{"8", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"10", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"12", ",", RowBox[{"-", "1"}]}], "}"}], ",", RowBox[{"{", RowBox[{"14", ",", RowBox[{"-", "2"}]}], "}"}], ",", RowBox[{"{", RowBox[{"16", ",", RowBox[{"-", "3"}]}], "}"}]}], "}"}]], "Output", CellChangeTimes->{3.622871726365943*^9, 3.6572696792419863`*^9}] }, Open ]], Cell[BoxData[ StyleBox[ RowBox[{ RowBox[{ RowBox[{"addpairs", "[", RowBox[{"{", RowBox[{"x_", ",", "y_"}], "}"}], "]"}], ":=", RowBox[{"x", "+", "y"}]}], "\[IndentingNewLine]"}], FontFamily->"Courier New", FontSize->24]], "Input", CellChangeTimes->{{3.6228668820012894`*^9, 3.6228669531218147`*^9}, { 3.622871861836581*^9, 3.6228718832710185`*^9}}], Cell[CellGroupData[{ Cell[BoxData[ StyleBox[ RowBox[{"Map", "[", RowBox[{"addpairs", ",", "points"}], "]"}], FontFamily->"Courier New", FontSize->24]], "Input", CellChangeTimes->{{3.622866963183832*^9, 3.6228669923558836`*^9}, { 3.6228718772182083`*^9, 3.6228718862974243`*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ "6", ",", "7", ",", "8", ",", "9", ",", "10", ",", "11", ",", "12", ",", "13"}], "}"}]], "Output", CellChangeTimes->{3.6228718063472834`*^9, 3.62287187859101*^9, 3.6572697849740334`*^9}] }, Open ]], Cell[BoxData[ StyleBox[ RowBox[{ RowBox[{"vol", "[", RowBox[{"r_", ",", "h_"}], "]"}], ":=", RowBox[{"Pi", " ", RowBox[{"r", "^", "2"}], " ", "h"}]}], FontFamily->"Courier New", FontSize->24]], "Input", CellChangeTimes->{{3.6228670740376267`*^9, 3.6228671204009085`*^9}}], Cell[BoxData[ StyleBox[ RowBox[{"mes", ":=", RowBox[{"{", RowBox[{"3.5", ",", "4.5"}], "}"}]}], FontFamily->"Courier New", FontSize->24]], "Input", CellChangeTimes->{{3.622867134191333*^9, 3.6228671683251925`*^9}}], Cell[CellGroupData[{ Cell[BoxData[ StyleBox[ RowBox[{"vol", "[", RowBox[{ RowBox[{"mes", "[", RowBox[{"[", "1", "]"}], "]"}], ",", RowBox[{"mes", "[", RowBox[{"[", "2", "]"}], "]"}]}], "]"}], FontFamily->"Courier New", FontSize->24]], "Input", CellChangeTimes->{{3.6228671916160336`*^9, 3.6228672033160543`*^9}}], Cell[BoxData["173.18029502913734`"], "Output", CellChangeTimes->{3.622872061580332*^9, 3.6572700610948267`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ StyleBox[ RowBox[{"Apply", "[", RowBox[{"vol", ",", "mes"}], "]"}], FontSize->24]], "Input", CellChangeTimes->{{3.6228672262636943`*^9, 3.622867240256919*^9}}], Cell[BoxData["173.18029502913734`"], "Output", CellChangeTimes->{3.6228721187232323`*^9, 3.6572700836281157`*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ StyleBox[ RowBox[{"Apply", "[", RowBox[{"Plus", ",", RowBox[{"{", RowBox[{ "2", ",", "3", ",", "4", ",", "5", ",", "6", ",", "7", ",", "8", ",", "9"}], "}"}]}], "]"}], FontFamily->"Courier New", FontSize->24]], "Input", CellChangeTimes->{{3.6228672888666043`*^9, 3.622867302797429*^9}}], Cell[BoxData["44"], "Output", CellChangeTimes->{3.6228722090317907`*^9, 3.657270119162148*^9}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ StyleBox[ RowBox[{"Apply", "[", RowBox[{"Times", ",", RowBox[{"{", RowBox[{ "2", ",", "3", ",", "4", ",", "5", ",", "6", ",", "7", ",", "8", ",", "9"}], "}"}]}], "]"}], FontFamily->"Courier New", FontSize->24]], "Input", CellChangeTimes->{{3.622872244849454*^9, 3.6228722464406567`*^9}}], Cell[BoxData["362880"], "Output", CellChangeTimes->{3.622872247735459*^9, 3.6572701260425415`*^9}] }, Open ]] }, WindowSize->{1091, 631}, WindowMargins->{{0, Automatic}, {Automatic, 0}}, FrontEndVersion->"8.0 for Microsoft Windows (64-bit) (November 7, 2010)", StyleDefinitions->"Default.nb" ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[557, 20, 297, 7, 42, "Input"], Cell[CellGroupData[{ Cell[879, 31, 923, 33, 112, "Input"], Cell[1805, 66, 199, 4, 30, "Output"], Cell[2007, 72, 287, 8, 30, "Output"], Cell[2297, 82, 199, 4, 30, "Output"], Cell[2499, 88, 253, 6, 30, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[2789, 99, 421, 14, 42, "Input"], Cell[3213, 115, 373, 11, 30, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[3623, 131, 335, 10, 42, "Input"], Cell[3961, 143, 299, 7, 30, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[4297, 155, 444, 15, 50, "Input"], Cell[4744, 172, 499, 19, 37, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[5280, 196, 280, 8, 76, "Input"], Cell[5563, 206, 286, 8, 47, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[5886, 219, 319, 10, 42, "Input"], Cell[6208, 231, 174, 4, 30, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[6419, 240, 350, 11, 42, "Input"], Cell[6772, 253, 261, 8, 30, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[7070, 266, 295, 10, 42, "Input"], Cell[7368, 278, 149, 3, 30, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[7554, 286, 290, 10, 42, "Input"], Cell[7847, 298, 176, 4, 30, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[8060, 307, 348, 11, 42, "Input"], Cell[8411, 320, 294, 8, 47, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[8742, 333, 354, 10, 42, "Input"], Cell[9099, 345, 275, 6, 30, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[9411, 356, 364, 11, 42, "Input"], Cell[9778, 369, 308, 10, 50, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[10123, 384, 263, 8, 42, "Input"], Cell[10389, 394, 304, 6, 30, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[10730, 405, 377, 11, 42, "Input"], Cell[11110, 418, 233, 6, 30, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[11380, 429, 216, 6, 42, "Input"], Cell[11599, 437, 118, 2, 30, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[11754, 444, 283, 8, 42, "Input"], Cell[12040, 454, 123, 2, 30, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[12200, 461, 207, 7, 42, "Input"], Cell[12410, 470, 118, 2, 30, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[12565, 477, 207, 7, 42, "Input"], Cell[12775, 486, 166, 4, 30, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[12978, 495, 287, 9, 42, "Input"], Cell[13268, 506, 123, 2, 30, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[13428, 513, 232, 8, 42, "Input"], Cell[13663, 523, 118, 2, 30, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[13818, 530, 335, 10, 42, "Input"], Cell[14156, 542, 165, 4, 30, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[14358, 551, 259, 8, 42, "Input"], Cell[14620, 561, 149, 3, 30, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[14806, 569, 215, 6, 42, "Input"], Cell[15024, 577, 117, 2, 30, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[15178, 584, 210, 6, 42, "Input"], Cell[15391, 592, 165, 4, 30, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[15593, 601, 448, 15, 42, "Input"], Cell[16044, 618, 344, 11, 30, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[16425, 634, 280, 8, 42, "Input"], Cell[16708, 644, 117, 2, 30, "Output"] }, Open ]], Cell[16840, 649, 122, 2, 31, "Input"], Cell[CellGroupData[{ Cell[16987, 655, 235, 6, 42, "Input"], Cell[17225, 663, 306, 7, 30, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[17568, 675, 226, 5, 52, "Input"], Cell[17797, 682, 418, 8, 30, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[18252, 695, 211, 6, 42, "Input"], Cell[18466, 703, 219, 5, 30, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[18722, 713, 244, 7, 42, "Input"], Cell[18969, 722, 449, 11, 47, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[19455, 738, 446, 11, 47, "Input"], Cell[19904, 751, 449, 11, 47, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[20390, 767, 244, 7, 42, "Input"], Cell[20637, 776, 471, 11, 47, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[21145, 792, 287, 9, 42, "Input"], Cell[21435, 803, 260, 6, 30, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[21732, 814, 338, 10, 59, "Input"], Cell[22073, 826, 212, 5, 30, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[22322, 836, 295, 9, 42, "Input"], Cell[22620, 847, 253, 6, 30, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[22910, 858, 334, 10, 42, "Input"], Cell[23247, 870, 483, 11, 47, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[23767, 886, 399, 13, 42, "Input"], Cell[24169, 901, 590, 18, 30, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[24796, 924, 183, 5, 42, "Input"], Cell[24982, 931, 835, 26, 72, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[25854, 962, 939, 30, 127, "Input"], Cell[26796, 994, 561, 17, 30, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[27394, 1016, 345, 11, 42, "Input"], Cell[27742, 1029, 586, 18, 30, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[28365, 1052, 117, 4, 42, "Input"], Cell[28485, 1058, 835, 26, 72, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[29357, 1089, 937, 30, 127, "Input"], Cell[30297, 1121, 539, 17, 30, "Output"] }, Open ]], Cell[30851, 1141, 305, 9, 42, "Input"], Cell[31159, 1152, 269, 7, 42, "Input"], Cell[CellGroupData[{ Cell[31453, 1163, 1639, 51, 52, "Input"], Cell[33095, 1216, 214, 5, 30, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[33346, 1226, 432, 14, 42, "Input"], Cell[33781, 1242, 230, 6, 30, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[34048, 1253, 260, 8, 42, "Input"], Cell[34311, 1263, 176, 4, 30, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[34524, 1272, 263, 8, 42, "Input"], Cell[34790, 1282, 176, 4, 30, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[35003, 1291, 298, 9, 111, "Input"], Cell[35304, 1302, 141, 3, 47, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[35482, 1310, 369, 12, 42, "Input"], Cell[35854, 1324, 211, 5, 47, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[36102, 1334, 372, 12, 42, "Input"], Cell[36477, 1348, 207, 5, 47, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[36721, 1358, 381, 12, 42, "Input"], Cell[37105, 1372, 187, 5, 47, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[37329, 1382, 429, 13, 42, "Input"], Cell[37761, 1397, 220, 5, 47, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[38018, 1407, 393, 13, 42, "Input"], Cell[38414, 1422, 658, 22, 30, "Output"] }, Open ]], Cell[39087, 1447, 383, 11, 77, "Input"], Cell[CellGroupData[{ Cell[39495, 1462, 271, 7, 42, "Input"], Cell[39769, 1471, 236, 6, 30, "Output"] }, Open ]], Cell[40020, 1480, 296, 9, 42, "Input"], Cell[40319, 1491, 231, 7, 42, "Input"], Cell[CellGroupData[{ Cell[40575, 1502, 324, 10, 42, "Input"], Cell[40902, 1514, 112, 1, 30, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[41051, 1520, 183, 5, 42, "Input"], Cell[41237, 1527, 114, 1, 30, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[41388, 1533, 335, 10, 42, "Input"], Cell[41726, 1545, 95, 1, 30, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[41858, 1551, 336, 10, 42, "Input"], Cell[42197, 1563, 99, 1, 30, "Output"] }, Open ]] } ] *) (* End of internal cache information *)