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Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> ($CellContext`base = Graphics[ Style[ Line[{{0, 0}, {$CellContext`b$$, 0}}], Thick, Blue]]; $CellContext`r = $CellContext`b$$/ 2; $CellContext`leftsideRect = Graphics[ Style[ Line[{{0, 0}, {0, 5 - 2 $CellContext`r}}], Thick, Blue]]; $CellContext`rightsideRect = Graphics[ Style[ Line[{{2 $CellContext`r, 0}, { 2 $CellContext`r, 5 - 2 $CellContext`r}}], Thick, Blue]]; $CellContext`topRect = Plot[5 - 2 $CellContext`r, {$CellContext`x, 0, 2 $CellContext`r}, PlotStyle -> {Thick, Blue}, Filling -> 0, FillingStyle -> RGBColor[0.25, 0.75, 0.25], AxesOrigin -> {0, 0}, AxesLabel -> {"x", None}]; $CellContext`rectArea[ Pattern[$CellContext`b, Blank[]]] := ($CellContext`b/2) (10 - 2 $CellContext`b); $CellContext`leftsideRightTri = Graphics[ Style[ Line[{{0, 0}, { 0, 10 (($CellContext`b$$ - 5)/($CellContext`b$$ - 10))}}], Thick, Blue]]; $CellContext`topRightTri = Plot[10 (($CellContext`b$$ - 5)/($CellContext`b$$ - 10)) - 10 (($CellContext`b$$ - 5)/($CellContext`b$$^2 - 10 $CellContext`b$$)) $CellContext`x, {$CellContext`x, 0, 2 $CellContext`r}, PlotStyle -> {Thick, Blue}, Filling -> 0, FillingStyle -> RGBColor[0.25, 0.75, 0.25], AxesOrigin -> {0, 0}, AxesLabel -> {"x", None}]; $CellContext`rightTriArea[ Pattern[$CellContext`b, Blank[]]] := 5 $CellContext`b (($CellContext`b - 5)/($CellContext`b - 10)); $CellContext`leftsideIsosc = Plot[(Sqrt[( 5 - $CellContext`r)^2 - $CellContext`r^2]/$CellContext`r) \ $CellContext`x, {$CellContext`x, 0, $CellContext`r}, PlotStyle -> {Thick, Blue}, Filling -> 0, FillingStyle -> RGBColor[0.25, 0.75, 0.25], AxesOrigin -> {0, 0}, AxesLabel -> {"x", None}]; $CellContext`rightsideIsosc = Plot[2 Sqrt[(5 - $CellContext`r)^2 - $CellContext`r^2] - ( Sqrt[(5 - $CellContext`r)^2 - $CellContext`r^2]/$CellContext`r) \ $CellContext`x, {$CellContext`x, $CellContext`r, 2 $CellContext`r}, PlotStyle -> {Thick, Blue}, Filling -> 0, FillingStyle -> RGBColor[0.25, 0.75, 0.25], AxesOrigin -> {0, 0}, AxesLabel -> {"x", None}]; $CellContext`isoscArea[ Pattern[$CellContext`b, Blank[]]] := ($CellContext`b/2) Sqrt[(5 - $CellContext`b/2)^2 - ($CellContext`b/ 2)^2]; $CellContext`leftsideNorman = Graphics[ Style[ Line[{{0, 0}, {0, (10 - (2 + Pi) $CellContext`r)/2}}], Thick, Blue]]; $CellContext`rightsideNorman = Graphics[ Style[ Line[{{2 $CellContext`r, 0}, { 2 $CellContext`r, (10 - (2 + Pi) $CellContext`r)/2}}], Thick, Blue]]; $CellContext`topNorman = Plot[(10 - (2 + Pi) $CellContext`r)/2 + Sqrt[$CellContext`r^2 - ($CellContext`x - $CellContext`r)^2], \ {$CellContext`x, 0, 2 $CellContext`r}, PlotStyle -> {Thick, Blue}, Filling -> 0, FillingStyle -> RGBColor[0.25, 0.75, 0.25], AxesOrigin -> {0, 0}, AxesLabel -> {"x", None}]; $CellContext`normanArea[ Pattern[$CellContext`b, Blank[]]] := 5 $CellContext`b - ((2 + Pi/2)/ 4) $CellContext`b^2; $CellContext`leftsideHouse = Graphics[ Style[ Line[{{0, 0}, {0, 5 - 3 $CellContext`r}}], Thick, Blue]]; $CellContext`rightsideHouse = Graphics[ Style[ Line[{{2 $CellContext`r, 0}, { 2 $CellContext`r, 5 - 3 $CellContext`r}}], Thick, Blue]]; $CellContext`lefttopHouse = Plot[5 - 3 $CellContext`r + Sqrt[3] $CellContext`x, {$CellContext`x, 0, $CellContext`r}, PlotStyle -> {Thick, Blue}, Filling -> 0, FillingStyle -> RGBColor[0.25, 0.75, 0.25], AxesOrigin -> {0, 0}, AxesLabel -> {"x", None}]; $CellContext`righttopHouse = Plot[5 + (2 Sqrt[3] - 3) $CellContext`r - Sqrt[3] $CellContext`x, {$CellContext`x, $CellContext`r, 2 $CellContext`r}, PlotStyle -> {Thick, Blue}, Filling -> 0, FillingStyle -> RGBColor[0.25, 0.75, 0.25], AxesOrigin -> {0, 0}, AxesLabel -> {"x", None}]; $CellContext`houseArea[ Pattern[$CellContext`b, Blank[]]] := $CellContext`b (5 - (3/2) $CellContext`b) + Sqrt[3] $CellContext`b; Switch[$CellContext`fig$$, $CellContext`rect, $CellContext`figure = \ {$CellContext`topRect, $CellContext`leftsideRect, $CellContext`rightsideRect, \ $CellContext`base}; $CellContext`maxb = 5; $CellContext`areaFunc = $CellContext`rectArea; \ $CellContext`areaPlot = Plot[ $CellContext`areaFunc[$CellContext`x], {$CellContext`x, 0, $CellContext`maxb}, PlotRange -> {{0, 5}, Automatic}, PlotLabel -> Style[ Row[{"area of rectangle"}], 18], ImageSize -> 250], $CellContext`rightTri, $CellContext`figure = \ {$CellContext`topRightTri, $CellContext`leftsideRightTri, $CellContext`base}; \ $CellContext`maxb = 5; $CellContext`areaFunc = $CellContext`rightTriArea; \ $CellContext`areaPlot = ($CellContext`areaPlot = Plot[ $CellContext`areaFunc[$CellContext`x], {$CellContext`x, 0, $CellContext`maxb}, PlotRange -> {{0, 5}, Automatic}, PlotLabel -> Style[ Row[{"area of right triangle"}], 18], ImageSize -> 250]), $CellContext`isosc, $CellContext`figure = \ {$CellContext`leftsideIsosc, $CellContext`rightsideIsosc, $CellContext`base}; \ $CellContext`maxb = 5; $CellContext`areaFunc = $CellContext`isoscArea; \ $CellContext`areaPlot = Plot[ $CellContext`areaFunc[$CellContext`x], {$CellContext`x, 0, $CellContext`maxb}, PlotRange -> {{0, 5}, Automatic}, PlotLabel -> Style[ Row[{"area of isosceles triangle"}], 18], ImageSize -> 250], $CellContext`norm, $CellContext`figure = \ {$CellContext`topNorman, $CellContext`base, $CellContext`leftsideNorman, \ $CellContext`rightsideNorman}; $CellContext`maxb = 20/(2 + Pi); If[$CellContext`b$$ > $CellContext`maxb, $CellContext`b$$ = 2]; $CellContext`areaFunc = $CellContext`normanArea; \ $CellContext`areaPlot = Plot[ $CellContext`areaFunc[$CellContext`x], {$CellContext`x, 0, $CellContext`maxb}, PlotRange -> {{0, 5}, Automatic}, PlotLabel -> Style[ Row[{"area of Norman window"}], 18], ImageSize -> 250], $CellContext`house, $CellContext`figure = \ {$CellContext`lefttopHouse, $CellContext`righttopHouse, \ $CellContext`leftsideHouse, $CellContext`rightsideHouse, $CellContext`base}; \ $CellContext`maxb = 10/3; If[$CellContext`b$$ > $CellContext`maxb, $CellContext`b$$ = 2]; $CellContext`areaFunc = $CellContext`houseArea; \ $CellContext`areaPlot = Plot[ $CellContext`areaFunc[$CellContext`x], {$CellContext`x, 0, $CellContext`maxb}, PlotRange -> {{0, 5}, Automatic}, PlotLabel -> Style[ Row[{"area of side of house"}], 18], ImageSize -> 250]]; $CellContext`pointOnCurve = Graphics[{ PointSize[Large], RGBColor[0.25, 0.75, 0.25], Point[{$CellContext`b$$, $CellContext`areaFunc[$CellContext`b$$]}]}]; Text[ Pane[ Row[{ Show[$CellContext`figure, Axes -> True, PlotRange -> {{0, 5}, {0, 5}}, AspectRatio -> 1, ImageSize -> 300], "", Column[{ Show[$CellContext`areaPlot, $CellContext`pointOnCurve], "", Style[ Row[{ Style["x", Italic], " = ", If[ MachineNumberQ[$CellContext`b$$], NumberForm[$CellContext`b$$, {6, 4}], $CellContext`b$$]}], 24], Style[ Row[{"area = ", If[ MachineNumberQ[ $CellContext`areaFunc[$CellContext`b$$]], NumberForm[ $CellContext`areaFunc[$CellContext`b$$], {6, 4}], $CellContext`areaFunc[$CellContext`b$$]]}], 24]}]}], ImageSize -> {560, 320}]]), "Specifications" :> {{{$CellContext`fig$$, $CellContext`rect, "figure"}, {$CellContext`rect -> "rectangle", $CellContext`rightTri -> "right triangle", $CellContext`isosc -> "isosceles triangle", $CellContext`norm -> "Norman window", $CellContext`house -> "side of house"}, ControlType -> PopupMenu}, {{$CellContext`b$$, 2, "length of base, x"}, 0.0001, Dynamic[$CellContext`maxb]}}, "Options" :> {TrackedSymbols -> True}, "DefaultOptions" :> {ControllerLinking -> True}], ImageSizeCache->{603., {217.34375, 222.65625}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellChangeTimes->{ 3.35696210375764*^9, {3.460933496692086*^9, 3.460933514031743*^9}}, CellID->254165686] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "ManipulateCaptionSection"], Cell["\<\ This Demonstration illustrates a common type of max-min problem from a \ Calculus I course\[LongDash]that of finding the maximum area of a geometric \ figure of fixed perimeter. The figures available are a rectangle, a right \ triangle, an isosceles triangle, a Norman window (a rectangle topped by a \ semicircle), and a \"side view of a house\" (a rectangle topped by an \ equilateral triangle). The perimeter is 10 units for each figure.\ \>", "ManipulateCaption", CellChangeTimes->{ 3.35696210375764*^9, {3.4604739655857573`*^9, 3.4604739885528374`*^9}, { 3.4604740214583597`*^9, 3.4604740254753723`*^9}, {3.4604741412653756`*^9, 3.4604741507217674`*^9}, {3.460474182185763*^9, 3.46047430371198*^9}, { 3.460495198483939*^9, 3.4604952415774136`*^9}}] }, Open ]], Cell[CellGroupData[{ Cell["", "ThumbnailSection"], Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`b$$ = 2., $CellContext`fig$$ = $CellContext`norm, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{{ Hold[$CellContext`fig$$], $CellContext`norm, "figure"}, {$CellContext`rect -> "rectangle", $CellContext`rightTri -> "right triangle", $CellContext`isosc -> "isosceles triangle", $CellContext`norm -> "Norman window", $CellContext`house -> "side of house"}}, {{ Hold[$CellContext`b$$], 2., "length of base, x"}, 0.0001, Dynamic[$CellContext`maxb]}}, Typeset`size$$ = {560., {159., 164.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = True, $CellContext`fig$455784$$ = False, $CellContext`b$455785$$ = 0}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`b$$ = 2., $CellContext`fig$$ = $CellContext`norm}, "ControllerVariables" :> { Hold[$CellContext`fig$$, $CellContext`fig$455784$$, False], Hold[$CellContext`b$$, $CellContext`b$455785$$, 0]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> ($CellContext`base = Graphics[ Style[ Line[{{0, 0}, {$CellContext`b$$, 0}}], Thick, Blue]]; $CellContext`r = $CellContext`b$$/ 2; $CellContext`leftsideRect = Graphics[ Style[ Line[{{0, 0}, {0, 5 - 2 $CellContext`r}}], Thick, Blue]]; $CellContext`rightsideRect = Graphics[ Style[ Line[{{2 $CellContext`r, 0}, { 2 $CellContext`r, 5 - 2 $CellContext`r}}], Thick, Blue]]; $CellContext`topRect = Plot[ 5 - 2 $CellContext`r, {$CellContext`x, 0, 2 $CellContext`r}, PlotStyle -> {Thick, Blue}, Filling -> 0, FillingStyle -> RGBColor[0.25, 0.75, 0.25], AxesOrigin -> {0, 0}, AxesLabel -> {"x", None}]; $CellContext`rectArea[ Pattern[$CellContext`b, Blank[]]] := ($CellContext`b/2) (10 - 2 $CellContext`b); $CellContext`leftsideRightTri = Graphics[ Style[ Line[{{0, 0}, { 0, 10 (($CellContext`b$$ - 5)/($CellContext`b$$ - 10))}}], Thick, Blue]]; $CellContext`topRightTri = Plot[10 (($CellContext`b$$ - 5)/($CellContext`b$$ - 10)) - 10 (($CellContext`b$$ - 5)/($CellContext`b$$^2 - 10 $CellContext`b$$)) $CellContext`x, {$CellContext`x, 0, 2 $CellContext`r}, PlotStyle -> {Thick, Blue}, Filling -> 0, FillingStyle -> RGBColor[0.25, 0.75, 0.25], AxesOrigin -> {0, 0}, AxesLabel -> {"x", None}]; $CellContext`rightTriArea[ Pattern[$CellContext`b, Blank[]]] := 5 $CellContext`b (($CellContext`b - 5)/($CellContext`b - 10)); $CellContext`leftsideIsosc = Plot[(Sqrt[( 5 - $CellContext`r)^2 - $CellContext`r^2]/$CellContext`r) \ $CellContext`x, {$CellContext`x, 0, $CellContext`r}, PlotStyle -> {Thick, Blue}, Filling -> 0, FillingStyle -> RGBColor[0.25, 0.75, 0.25], AxesOrigin -> {0, 0}, AxesLabel -> {"x", None}]; $CellContext`rightsideIsosc = Plot[2 Sqrt[(5 - $CellContext`r)^2 - $CellContext`r^2] - ( Sqrt[(5 - $CellContext`r)^2 - $CellContext`r^2]/$CellContext`r) \ $CellContext`x, {$CellContext`x, $CellContext`r, 2 $CellContext`r}, PlotStyle -> {Thick, Blue}, Filling -> 0, FillingStyle -> RGBColor[0.25, 0.75, 0.25], AxesOrigin -> {0, 0}, AxesLabel -> {"x", None}]; $CellContext`isoscArea[ Pattern[$CellContext`b, Blank[]]] := ($CellContext`b/2) Sqrt[(5 - $CellContext`b/2)^2 - ($CellContext`b/ 2)^2]; $CellContext`leftsideNorman = Graphics[ Style[ Line[{{0, 0}, {0, (10 - (2 + Pi) $CellContext`r)/2}}], Thick, Blue]]; $CellContext`rightsideNorman = Graphics[ Style[ Line[{{2 $CellContext`r, 0}, { 2 $CellContext`r, (10 - (2 + Pi) $CellContext`r)/2}}], Thick, Blue]]; $CellContext`topNorman = Plot[(10 - (2 + Pi) $CellContext`r)/2 + Sqrt[$CellContext`r^2 - ($CellContext`x - $CellContext`r)^2], \ {$CellContext`x, 0, 2 $CellContext`r}, PlotStyle -> {Thick, Blue}, Filling -> 0, FillingStyle -> RGBColor[0.25, 0.75, 0.25], AxesOrigin -> {0, 0}, AxesLabel -> {"x", None}]; $CellContext`normanArea[ Pattern[$CellContext`b, Blank[]]] := 5 $CellContext`b - ((2 + Pi/2)/ 4) $CellContext`b^2; $CellContext`leftsideHouse = Graphics[ Style[ Line[{{0, 0}, {0, 5 - 3 $CellContext`r}}], Thick, Blue]]; $CellContext`rightsideHouse = Graphics[ Style[ Line[{{2 $CellContext`r, 0}, { 2 $CellContext`r, 5 - 3 $CellContext`r}}], Thick, Blue]]; $CellContext`lefttopHouse = Plot[5 - 3 $CellContext`r + Sqrt[3] $CellContext`x, {$CellContext`x, 0, $CellContext`r}, PlotStyle -> {Thick, Blue}, Filling -> 0, FillingStyle -> RGBColor[0.25, 0.75, 0.25], AxesOrigin -> {0, 0}, AxesLabel -> {"x", None}]; $CellContext`righttopHouse = Plot[5 + (2 Sqrt[3] - 3) $CellContext`r - Sqrt[3] $CellContext`x, {$CellContext`x, $CellContext`r, 2 $CellContext`r}, PlotStyle -> {Thick, Blue}, Filling -> 0, FillingStyle -> RGBColor[0.25, 0.75, 0.25], AxesOrigin -> {0, 0}, AxesLabel -> {"x", None}]; $CellContext`houseArea[ Pattern[$CellContext`b, Blank[]]] := $CellContext`b (5 - (3/2) $CellContext`b) + Sqrt[3] $CellContext`b; Switch[$CellContext`fig$$, $CellContext`rect, $CellContext`figure = \ {$CellContext`topRect, $CellContext`leftsideRect, $CellContext`rightsideRect, \ $CellContext`base}; $CellContext`maxb = 5; $CellContext`areaFunc = $CellContext`rectArea; \ $CellContext`areaPlot = Plot[ $CellContext`areaFunc[$CellContext`x], {$CellContext`x, 0, $CellContext`maxb}, PlotRange -> {{0, 5}, Automatic}, PlotLabel -> Style[ Row[{"area of rectangle"}], 18], ImageSize -> 250], $CellContext`rightTri, $CellContext`figure = \ {$CellContext`topRightTri, $CellContext`leftsideRightTri, $CellContext`base}; \ $CellContext`maxb = 5; $CellContext`areaFunc = $CellContext`rightTriArea; \ $CellContext`areaPlot = ($CellContext`areaPlot = Plot[ $CellContext`areaFunc[$CellContext`x], {$CellContext`x, 0, $CellContext`maxb}, PlotRange -> {{0, 5}, Automatic}, PlotLabel -> Style[ Row[{"area of right triangle"}], 18], ImageSize -> 250]), $CellContext`isosc, $CellContext`figure = \ {$CellContext`leftsideIsosc, $CellContext`rightsideIsosc, $CellContext`base}; \ $CellContext`maxb = 5; $CellContext`areaFunc = $CellContext`isoscArea; \ $CellContext`areaPlot = Plot[ $CellContext`areaFunc[$CellContext`x], {$CellContext`x, 0, $CellContext`maxb}, PlotRange -> {{0, 5}, Automatic}, PlotLabel -> Style[ Row[{"area of isosceles triangle"}], 18], ImageSize -> 250], $CellContext`norm, $CellContext`figure = \ {$CellContext`topNorman, $CellContext`base, $CellContext`leftsideNorman, \ $CellContext`rightsideNorman}; $CellContext`maxb = 20/(2 + Pi); If[$CellContext`b$$ > $CellContext`maxb, $CellContext`b$$ = 2]; $CellContext`areaFunc = $CellContext`normanArea; \ $CellContext`areaPlot = Plot[ $CellContext`areaFunc[$CellContext`x], {$CellContext`x, 0, $CellContext`maxb}, PlotRange -> {{0, 5}, Automatic}, PlotLabel -> Style[ Row[{"area of Norman window"}], 18], ImageSize -> 250], $CellContext`house, $CellContext`figure = \ {$CellContext`lefttopHouse, $CellContext`righttopHouse, \ $CellContext`leftsideHouse, $CellContext`rightsideHouse, $CellContext`base}; \ $CellContext`maxb = 10/3; If[$CellContext`b$$ > $CellContext`maxb, $CellContext`b$$ = 2]; $CellContext`areaFunc = $CellContext`houseArea; \ $CellContext`areaPlot = Plot[ $CellContext`areaFunc[$CellContext`x], {$CellContext`x, 0, $CellContext`maxb}, PlotRange -> {{0, 5}, Automatic}, PlotLabel -> Style[ Row[{"area of side of house"}], 18], ImageSize -> 250]]; $CellContext`pointOnCurve = Graphics[{ PointSize[Large], RGBColor[0.25, 0.75, 0.25], Point[{$CellContext`b$$, $CellContext`areaFunc[$CellContext`b$$]}]}]; Text[ Pane[ Row[{ Show[$CellContext`figure, Axes -> True, PlotRange -> {{0, 5}, {0, 5}}, AspectRatio -> 1, ImageSize -> 300], "", Column[{ Show[$CellContext`areaPlot, $CellContext`pointOnCurve], "", Style[ Row[{ Style["x", Italic], " = ", If[ MachineNumberQ[$CellContext`b$$], NumberForm[$CellContext`b$$, {6, 4}], $CellContext`b$$]}], 24], Style[ Row[{"area = ", If[ MachineNumberQ[ $CellContext`areaFunc[$CellContext`b$$]], NumberForm[ $CellContext`areaFunc[$CellContext`b$$], {6, 4}], $CellContext`areaFunc[$CellContext`b$$]]}], 24]}]}], ImageSize -> {560, 320}]]), "Specifications" :> {{{$CellContext`fig$$, $CellContext`norm, "figure"}, {$CellContext`rect -> "rectangle", $CellContext`rightTri -> "right triangle", $CellContext`isosc -> "isosceles triangle", $CellContext`norm -> "Norman window", $CellContext`house -> "side of house"}, ControlType -> PopupMenu}, {{$CellContext`b$$, 2., "length of base, x"}, 0.0001, Dynamic[$CellContext`maxb]}}, "Options" :> {TrackedSymbols -> True}, "DefaultOptions" :> {ControllerLinking -> True}], ImageSizeCache->{603., {217.34375, 222.65625}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellID->1562353806] }, Open ]], Cell[CellGroupData[{ Cell["", "SnapshotsSection"], Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`b$$ = 3, $CellContext`fig$$ = $CellContext`rect, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{{ Hold[$CellContext`fig$$], $CellContext`rect, "figure"}, {$CellContext`rect -> "rectangle", $CellContext`rightTri -> "right triangle", $CellContext`isosc -> "isosceles triangle", $CellContext`norm -> "Norman window", $CellContext`house -> "side of house"}}, {{ Hold[$CellContext`b$$], 3, "length of base, x"}, 0.0001, Dynamic[$CellContext`maxb]}}, Typeset`size$$ = {560., {159., 164.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = True, $CellContext`fig$455839$$ = False, $CellContext`b$455840$$ = 0}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`b$$ = 3, $CellContext`fig$$ = $CellContext`rect}, "ControllerVariables" :> { Hold[$CellContext`fig$$, $CellContext`fig$455839$$, False], Hold[$CellContext`b$$, $CellContext`b$455840$$, 0]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> ($CellContext`base = Graphics[ Style[ Line[{{0, 0}, {$CellContext`b$$, 0}}], Thick, Blue]]; $CellContext`r = $CellContext`b$$/ 2; $CellContext`leftsideRect = Graphics[ Style[ Line[{{0, 0}, {0, 5 - 2 $CellContext`r}}], Thick, Blue]]; $CellContext`rightsideRect = Graphics[ Style[ Line[{{2 $CellContext`r, 0}, { 2 $CellContext`r, 5 - 2 $CellContext`r}}], Thick, Blue]]; $CellContext`topRect = Plot[5 - 2 $CellContext`r, {$CellContext`x, 0, 2 $CellContext`r}, PlotStyle -> {Thick, Blue}, Filling -> 0, FillingStyle -> RGBColor[0.25, 0.75, 0.25], AxesOrigin -> {0, 0}, AxesLabel -> {"x", None}]; $CellContext`rectArea[ Pattern[$CellContext`b, Blank[]]] := ($CellContext`b/2) (10 - 2 $CellContext`b); $CellContext`leftsideRightTri = Graphics[ Style[ Line[{{0, 0}, { 0, 10 (($CellContext`b$$ - 5)/($CellContext`b$$ - 10))}}], Thick, Blue]]; $CellContext`topRightTri = Plot[10 (($CellContext`b$$ - 5)/($CellContext`b$$ - 10)) - 10 (($CellContext`b$$ - 5)/($CellContext`b$$^2 - 10 $CellContext`b$$)) $CellContext`x, {$CellContext`x, 0, 2 $CellContext`r}, PlotStyle -> {Thick, Blue}, Filling -> 0, FillingStyle -> RGBColor[0.25, 0.75, 0.25], AxesOrigin -> {0, 0}, AxesLabel -> {"x", None}]; $CellContext`rightTriArea[ Pattern[$CellContext`b, Blank[]]] := 5 $CellContext`b (($CellContext`b - 5)/($CellContext`b - 10)); $CellContext`leftsideIsosc = Plot[(Sqrt[( 5 - $CellContext`r)^2 - $CellContext`r^2]/$CellContext`r) \ $CellContext`x, {$CellContext`x, 0, $CellContext`r}, PlotStyle -> {Thick, Blue}, Filling -> 0, FillingStyle -> RGBColor[0.25, 0.75, 0.25], AxesOrigin -> {0, 0}, AxesLabel -> {"x", None}]; $CellContext`rightsideIsosc = Plot[2 Sqrt[(5 - $CellContext`r)^2 - $CellContext`r^2] - ( Sqrt[(5 - $CellContext`r)^2 - $CellContext`r^2]/$CellContext`r) \ $CellContext`x, {$CellContext`x, $CellContext`r, 2 $CellContext`r}, PlotStyle -> {Thick, Blue}, Filling -> 0, FillingStyle -> RGBColor[0.25, 0.75, 0.25], AxesOrigin -> {0, 0}, AxesLabel -> {"x", None}]; $CellContext`isoscArea[ Pattern[$CellContext`b, Blank[]]] := ($CellContext`b/2) Sqrt[(5 - $CellContext`b/2)^2 - ($CellContext`b/ 2)^2]; $CellContext`leftsideNorman = Graphics[ Style[ Line[{{0, 0}, {0, (10 - (2 + Pi) $CellContext`r)/2}}], Thick, Blue]]; $CellContext`rightsideNorman = Graphics[ Style[ Line[{{2 $CellContext`r, 0}, { 2 $CellContext`r, (10 - (2 + Pi) $CellContext`r)/2}}], Thick, Blue]]; $CellContext`topNorman = Plot[(10 - (2 + Pi) $CellContext`r)/2 + Sqrt[$CellContext`r^2 - ($CellContext`x - $CellContext`r)^2], \ {$CellContext`x, 0, 2 $CellContext`r}, PlotStyle -> {Thick, Blue}, Filling -> 0, FillingStyle -> RGBColor[0.25, 0.75, 0.25], AxesOrigin -> {0, 0}, AxesLabel -> {"x", None}]; $CellContext`normanArea[ Pattern[$CellContext`b, Blank[]]] := 5 $CellContext`b - ((2 + Pi/2)/ 4) $CellContext`b^2; $CellContext`leftsideHouse = Graphics[ Style[ Line[{{0, 0}, {0, 5 - 3 $CellContext`r}}], Thick, Blue]]; $CellContext`rightsideHouse = Graphics[ Style[ Line[{{2 $CellContext`r, 0}, { 2 $CellContext`r, 5 - 3 $CellContext`r}}], Thick, Blue]]; $CellContext`lefttopHouse = Plot[5 - 3 $CellContext`r + Sqrt[3] $CellContext`x, {$CellContext`x, 0, $CellContext`r}, PlotStyle -> {Thick, Blue}, Filling -> 0, FillingStyle -> RGBColor[0.25, 0.75, 0.25], AxesOrigin -> {0, 0}, AxesLabel -> {"x", None}]; $CellContext`righttopHouse = Plot[5 + (2 Sqrt[3] - 3) $CellContext`r - Sqrt[3] $CellContext`x, {$CellContext`x, $CellContext`r, 2 $CellContext`r}, PlotStyle -> {Thick, Blue}, Filling -> 0, FillingStyle -> RGBColor[0.25, 0.75, 0.25], AxesOrigin -> {0, 0}, AxesLabel -> {"x", None}]; $CellContext`houseArea[ Pattern[$CellContext`b, Blank[]]] := $CellContext`b (5 - (3/2) $CellContext`b) + Sqrt[3] $CellContext`b; Switch[$CellContext`fig$$, $CellContext`rect, $CellContext`figure = \ {$CellContext`topRect, $CellContext`leftsideRect, $CellContext`rightsideRect, \ $CellContext`base}; $CellContext`maxb = 5; $CellContext`areaFunc = $CellContext`rectArea; \ $CellContext`areaPlot = Plot[ $CellContext`areaFunc[$CellContext`x], {$CellContext`x, 0, $CellContext`maxb}, PlotRange -> {{0, 5}, Automatic}, PlotLabel -> Style[ Row[{"area of rectangle"}], 18], ImageSize -> 250], $CellContext`rightTri, $CellContext`figure = \ {$CellContext`topRightTri, $CellContext`leftsideRightTri, $CellContext`base}; \ $CellContext`maxb = 5; $CellContext`areaFunc = $CellContext`rightTriArea; \ $CellContext`areaPlot = ($CellContext`areaPlot = Plot[ $CellContext`areaFunc[$CellContext`x], {$CellContext`x, 0, $CellContext`maxb}, PlotRange -> {{0, 5}, Automatic}, PlotLabel -> Style[ Row[{"area of right triangle"}], 18], ImageSize -> 250]), $CellContext`isosc, $CellContext`figure = \ {$CellContext`leftsideIsosc, $CellContext`rightsideIsosc, $CellContext`base}; \ $CellContext`maxb = 5; $CellContext`areaFunc = $CellContext`isoscArea; \ $CellContext`areaPlot = Plot[ $CellContext`areaFunc[$CellContext`x], {$CellContext`x, 0, $CellContext`maxb}, PlotRange -> {{0, 5}, Automatic}, PlotLabel -> Style[ Row[{"area of isosceles triangle"}], 18], ImageSize -> 250], $CellContext`norm, $CellContext`figure = \ {$CellContext`topNorman, $CellContext`base, $CellContext`leftsideNorman, \ $CellContext`rightsideNorman}; $CellContext`maxb = 20/(2 + Pi); If[$CellContext`b$$ > $CellContext`maxb, $CellContext`b$$ = 2]; $CellContext`areaFunc = $CellContext`normanArea; \ $CellContext`areaPlot = Plot[ $CellContext`areaFunc[$CellContext`x], {$CellContext`x, 0, $CellContext`maxb}, PlotRange -> {{0, 5}, Automatic}, PlotLabel -> Style[ Row[{"area of Norman window"}], 18], ImageSize -> 250], $CellContext`house, $CellContext`figure = \ {$CellContext`lefttopHouse, $CellContext`righttopHouse, \ $CellContext`leftsideHouse, $CellContext`rightsideHouse, $CellContext`base}; \ $CellContext`maxb = 10/3; If[$CellContext`b$$ > $CellContext`maxb, $CellContext`b$$ = 2]; $CellContext`areaFunc = $CellContext`houseArea; \ $CellContext`areaPlot = Plot[ $CellContext`areaFunc[$CellContext`x], {$CellContext`x, 0, $CellContext`maxb}, PlotRange -> {{0, 5}, Automatic}, PlotLabel -> Style[ Row[{"area of side of house"}], 18], ImageSize -> 250]]; $CellContext`pointOnCurve = Graphics[{ PointSize[Large], RGBColor[0.25, 0.75, 0.25], Point[{$CellContext`b$$, $CellContext`areaFunc[$CellContext`b$$]}]}]; Text[ Pane[ Row[{ Show[$CellContext`figure, Axes -> True, PlotRange -> {{0, 5}, {0, 5}}, AspectRatio -> 1, ImageSize -> 300], "", Column[{ Show[$CellContext`areaPlot, $CellContext`pointOnCurve], "", Style[ Row[{ Style["x", Italic], " = ", If[ MachineNumberQ[$CellContext`b$$], NumberForm[$CellContext`b$$, {6, 4}], $CellContext`b$$]}], 24], Style[ Row[{"area = ", If[ MachineNumberQ[ $CellContext`areaFunc[$CellContext`b$$]], NumberForm[ $CellContext`areaFunc[$CellContext`b$$], {6, 4}], $CellContext`areaFunc[$CellContext`b$$]]}], 24]}]}], ImageSize -> {560, 320}]]), "Specifications" :> {{{$CellContext`fig$$, $CellContext`rect, "figure"}, {$CellContext`rect -> "rectangle", $CellContext`rightTri -> "right triangle", $CellContext`isosc -> "isosceles triangle", $CellContext`norm -> "Norman window", $CellContext`house -> "side of house"}, ControlType -> PopupMenu}, {{$CellContext`b$$, 3, "length of base, x"}, 0.0001, Dynamic[$CellContext`maxb]}}, "Options" :> {TrackedSymbols -> True}, "DefaultOptions" :> {ControllerLinking -> True}], ImageSizeCache->{603., {217.34375, 222.65625}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellID->1197865573], Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`b$$ = 3.3333333333333335`, $CellContext`fig$$ = $CellContext`rightTri, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{{ Hold[$CellContext`fig$$], $CellContext`rightTri, "figure"}, {$CellContext`rect -> "rectangle", $CellContext`rightTri -> "right triangle", $CellContext`isosc -> "isosceles triangle", $CellContext`norm -> "Norman window", $CellContext`house -> "side of house"}}, {{ Hold[$CellContext`b$$], 3.3333333333333335`, "length of base, x"}, 0.0001, Dynamic[$CellContext`maxb]}}, Typeset`size$$ = {560., {159., 164.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = True, $CellContext`fig$455894$$ = False, $CellContext`b$455895$$ = 0}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`b$$ = 3.3333333333333335`, $CellContext`fig$$ = $CellContext`rightTri}, "ControllerVariables" :> { Hold[$CellContext`fig$$, $CellContext`fig$455894$$, False], Hold[$CellContext`b$$, $CellContext`b$455895$$, 0]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> ($CellContext`base = Graphics[ Style[ Line[{{0, 0}, {$CellContext`b$$, 0}}], Thick, Blue]]; $CellContext`r = $CellContext`b$$/ 2; $CellContext`leftsideRect = Graphics[ Style[ Line[{{0, 0}, {0, 5 - 2 $CellContext`r}}], Thick, Blue]]; $CellContext`rightsideRect = Graphics[ Style[ Line[{{2 $CellContext`r, 0}, { 2 $CellContext`r, 5 - 2 $CellContext`r}}], Thick, Blue]]; $CellContext`topRect = Plot[5 - 2 $CellContext`r, {$CellContext`x, 0, 2 $CellContext`r}, PlotStyle -> {Thick, Blue}, Filling -> 0, FillingStyle -> RGBColor[0.25, 0.75, 0.25], AxesOrigin -> {0, 0}, AxesLabel -> {"x", None}]; $CellContext`rectArea[ Pattern[$CellContext`b, Blank[]]] := ($CellContext`b/2) (10 - 2 $CellContext`b); $CellContext`leftsideRightTri = Graphics[ Style[ Line[{{0, 0}, { 0, 10 (($CellContext`b$$ - 5)/($CellContext`b$$ - 10))}}], Thick, Blue]]; $CellContext`topRightTri = Plot[10 (($CellContext`b$$ - 5)/($CellContext`b$$ - 10)) - 10 (($CellContext`b$$ - 5)/($CellContext`b$$^2 - 10 $CellContext`b$$)) $CellContext`x, {$CellContext`x, 0, 2 $CellContext`r}, PlotStyle -> {Thick, Blue}, Filling -> 0, FillingStyle -> RGBColor[0.25, 0.75, 0.25], AxesOrigin -> {0, 0}, AxesLabel -> {"x", None}]; $CellContext`rightTriArea[ Pattern[$CellContext`b, Blank[]]] := 5 $CellContext`b (($CellContext`b - 5)/($CellContext`b - 10)); $CellContext`leftsideIsosc = Plot[(Sqrt[( 5 - $CellContext`r)^2 - $CellContext`r^2]/$CellContext`r) \ $CellContext`x, {$CellContext`x, 0, $CellContext`r}, PlotStyle -> {Thick, Blue}, Filling -> 0, FillingStyle -> RGBColor[0.25, 0.75, 0.25], AxesOrigin -> {0, 0}, AxesLabel -> {"x", None}]; $CellContext`rightsideIsosc = Plot[2 Sqrt[(5 - $CellContext`r)^2 - $CellContext`r^2] - ( Sqrt[(5 - $CellContext`r)^2 - $CellContext`r^2]/$CellContext`r) \ $CellContext`x, {$CellContext`x, $CellContext`r, 2 $CellContext`r}, PlotStyle -> {Thick, Blue}, Filling -> 0, FillingStyle -> RGBColor[0.25, 0.75, 0.25], AxesOrigin -> {0, 0}, AxesLabel -> {"x", None}]; $CellContext`isoscArea[ Pattern[$CellContext`b, Blank[]]] := ($CellContext`b/2) Sqrt[(5 - $CellContext`b/2)^2 - ($CellContext`b/ 2)^2]; $CellContext`leftsideNorman = Graphics[ Style[ Line[{{0, 0}, {0, (10 - (2 + Pi) $CellContext`r)/2}}], Thick, Blue]]; $CellContext`rightsideNorman = Graphics[ Style[ Line[{{2 $CellContext`r, 0}, { 2 $CellContext`r, (10 - (2 + Pi) $CellContext`r)/2}}], Thick, Blue]]; $CellContext`topNorman = Plot[(10 - (2 + Pi) $CellContext`r)/2 + Sqrt[$CellContext`r^2 - ($CellContext`x - $CellContext`r)^2], \ {$CellContext`x, 0, 2 $CellContext`r}, PlotStyle -> {Thick, Blue}, Filling -> 0, FillingStyle -> RGBColor[0.25, 0.75, 0.25], AxesOrigin -> {0, 0}, AxesLabel -> {"x", None}]; $CellContext`normanArea[ Pattern[$CellContext`b, Blank[]]] := 5 $CellContext`b - ((2 + Pi/2)/ 4) $CellContext`b^2; $CellContext`leftsideHouse = Graphics[ Style[ Line[{{0, 0}, {0, 5 - 3 $CellContext`r}}], Thick, Blue]]; $CellContext`rightsideHouse = Graphics[ Style[ Line[{{2 $CellContext`r, 0}, { 2 $CellContext`r, 5 - 3 $CellContext`r}}], Thick, Blue]]; $CellContext`lefttopHouse = Plot[5 - 3 $CellContext`r + Sqrt[3] $CellContext`x, {$CellContext`x, 0, $CellContext`r}, PlotStyle -> {Thick, Blue}, Filling -> 0, FillingStyle -> RGBColor[0.25, 0.75, 0.25], AxesOrigin -> {0, 0}, AxesLabel -> {"x", None}]; $CellContext`righttopHouse = Plot[5 + (2 Sqrt[3] - 3) $CellContext`r - Sqrt[3] $CellContext`x, {$CellContext`x, $CellContext`r, 2 $CellContext`r}, PlotStyle -> {Thick, Blue}, Filling -> 0, FillingStyle -> RGBColor[0.25, 0.75, 0.25], AxesOrigin -> {0, 0}, AxesLabel -> {"x", None}]; $CellContext`houseArea[ Pattern[$CellContext`b, Blank[]]] := $CellContext`b (5 - (3/2) $CellContext`b) + Sqrt[3] $CellContext`b; Switch[$CellContext`fig$$, $CellContext`rect, $CellContext`figure = \ {$CellContext`topRect, $CellContext`leftsideRect, $CellContext`rightsideRect, \ $CellContext`base}; $CellContext`maxb = 5; $CellContext`areaFunc = $CellContext`rectArea; \ $CellContext`areaPlot = Plot[ $CellContext`areaFunc[$CellContext`x], {$CellContext`x, 0, $CellContext`maxb}, PlotRange -> {{0, 5}, Automatic}, PlotLabel -> Style[ Row[{"area of rectangle"}], 18], ImageSize -> 250], $CellContext`rightTri, $CellContext`figure = \ {$CellContext`topRightTri, $CellContext`leftsideRightTri, $CellContext`base}; \ $CellContext`maxb = 5; $CellContext`areaFunc = $CellContext`rightTriArea; \ $CellContext`areaPlot = ($CellContext`areaPlot = Plot[ $CellContext`areaFunc[$CellContext`x], {$CellContext`x, 0, $CellContext`maxb}, PlotRange -> {{0, 5}, Automatic}, PlotLabel -> Style[ Row[{"area of right triangle"}], 18], ImageSize -> 250]), $CellContext`isosc, $CellContext`figure = \ {$CellContext`leftsideIsosc, $CellContext`rightsideIsosc, $CellContext`base}; \ $CellContext`maxb = 5; $CellContext`areaFunc = $CellContext`isoscArea; \ $CellContext`areaPlot = Plot[ $CellContext`areaFunc[$CellContext`x], {$CellContext`x, 0, $CellContext`maxb}, PlotRange -> {{0, 5}, Automatic}, PlotLabel -> Style[ Row[{"area of isosceles triangle"}], 18], ImageSize -> 250], $CellContext`norm, $CellContext`figure = \ {$CellContext`topNorman, $CellContext`base, $CellContext`leftsideNorman, \ $CellContext`rightsideNorman}; $CellContext`maxb = 20/(2 + Pi); If[$CellContext`b$$ > $CellContext`maxb, $CellContext`b$$ = 2]; $CellContext`areaFunc = $CellContext`normanArea; \ $CellContext`areaPlot = Plot[ $CellContext`areaFunc[$CellContext`x], {$CellContext`x, 0, $CellContext`maxb}, PlotRange -> {{0, 5}, Automatic}, PlotLabel -> Style[ Row[{"area of Norman window"}], 18], ImageSize -> 250], $CellContext`house, $CellContext`figure = \ {$CellContext`lefttopHouse, $CellContext`righttopHouse, \ $CellContext`leftsideHouse, $CellContext`rightsideHouse, $CellContext`base}; \ $CellContext`maxb = 10/3; If[$CellContext`b$$ > $CellContext`maxb, $CellContext`b$$ = 2]; $CellContext`areaFunc = $CellContext`houseArea; \ $CellContext`areaPlot = Plot[ $CellContext`areaFunc[$CellContext`x], {$CellContext`x, 0, $CellContext`maxb}, PlotRange -> {{0, 5}, Automatic}, PlotLabel -> Style[ Row[{"area of side of house"}], 18], ImageSize -> 250]]; $CellContext`pointOnCurve = Graphics[{ PointSize[Large], RGBColor[0.25, 0.75, 0.25], Point[{$CellContext`b$$, $CellContext`areaFunc[$CellContext`b$$]}]}]; Text[ Pane[ Row[{ Show[$CellContext`figure, Axes -> True, PlotRange -> {{0, 5}, {0, 5}}, AspectRatio -> 1, ImageSize -> 300], "", Column[{ Show[$CellContext`areaPlot, $CellContext`pointOnCurve], "", Style[ Row[{ Style["x", Italic], " = ", If[ MachineNumberQ[$CellContext`b$$], NumberForm[$CellContext`b$$, {6, 4}], $CellContext`b$$]}], 24], Style[ Row[{"area = ", If[ MachineNumberQ[ $CellContext`areaFunc[$CellContext`b$$]], NumberForm[ $CellContext`areaFunc[$CellContext`b$$], {6, 4}], $CellContext`areaFunc[$CellContext`b$$]]}], 24]}]}], ImageSize -> {560, 320}]]), "Specifications" :> {{{$CellContext`fig$$, $CellContext`rightTri, "figure"}, {$CellContext`rect -> "rectangle", $CellContext`rightTri -> "right triangle", $CellContext`isosc -> "isosceles triangle", $CellContext`norm -> "Norman window", $CellContext`house -> "side of house"}, ControlType -> PopupMenu}, {{$CellContext`b$$, 3.3333333333333335`, "length of base, x"}, 0.0001, Dynamic[$CellContext`maxb]}}, "Options" :> {TrackedSymbols -> True}, "DefaultOptions" :> {ControllerLinking -> True}], ImageSizeCache->{603., {217.34375, 222.65625}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellID->2014978433], Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`b$$ = 2.400052, $CellContext`fig$$ = $CellContext`isosc, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{{ Hold[$CellContext`fig$$], $CellContext`isosc, "figure"}, {$CellContext`rect -> "rectangle", $CellContext`rightTri -> "right triangle", $CellContext`isosc -> "isosceles triangle", $CellContext`norm -> "Norman window", $CellContext`house -> "side of house"}}, {{ Hold[$CellContext`b$$], 2.400052, "length of base, x"}, 0.0001, Dynamic[$CellContext`maxb]}}, Typeset`size$$ = {560., {159., 164.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = True, $CellContext`fig$455949$$ = False, $CellContext`b$455950$$ = 0}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`b$$ = 2.400052, $CellContext`fig$$ = $CellContext`isosc}, "ControllerVariables" :> { Hold[$CellContext`fig$$, $CellContext`fig$455949$$, False], Hold[$CellContext`b$$, $CellContext`b$455950$$, 0]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> ($CellContext`base = Graphics[ Style[ Line[{{0, 0}, {$CellContext`b$$, 0}}], Thick, Blue]]; $CellContext`r = $CellContext`b$$/ 2; $CellContext`leftsideRect = Graphics[ Style[ Line[{{0, 0}, {0, 5 - 2 $CellContext`r}}], Thick, Blue]]; $CellContext`rightsideRect = Graphics[ Style[ Line[{{2 $CellContext`r, 0}, { 2 $CellContext`r, 5 - 2 $CellContext`r}}], Thick, Blue]]; $CellContext`topRect = Plot[ 5 - 2 $CellContext`r, {$CellContext`x, 0, 2 $CellContext`r}, PlotStyle -> {Thick, Blue}, Filling -> 0, FillingStyle -> RGBColor[0.25, 0.75, 0.25], AxesOrigin -> {0, 0}, AxesLabel -> {"x", None}]; $CellContext`rectArea[ Pattern[$CellContext`b, Blank[]]] := ($CellContext`b/2) (10 - 2 $CellContext`b); $CellContext`leftsideRightTri = Graphics[ Style[ Line[{{0, 0}, { 0, 10 (($CellContext`b$$ - 5)/($CellContext`b$$ - 10))}}], Thick, Blue]]; $CellContext`topRightTri = Plot[10 (($CellContext`b$$ - 5)/($CellContext`b$$ - 10)) - 10 (($CellContext`b$$ - 5)/($CellContext`b$$^2 - 10 $CellContext`b$$)) $CellContext`x, {$CellContext`x, 0, 2 $CellContext`r}, PlotStyle -> {Thick, Blue}, Filling -> 0, FillingStyle -> RGBColor[0.25, 0.75, 0.25], AxesOrigin -> {0, 0}, AxesLabel -> {"x", None}]; $CellContext`rightTriArea[ Pattern[$CellContext`b, Blank[]]] := 5 $CellContext`b (($CellContext`b - 5)/($CellContext`b - 10)); $CellContext`leftsideIsosc = Plot[(Sqrt[( 5 - $CellContext`r)^2 - $CellContext`r^2]/$CellContext`r) \ $CellContext`x, {$CellContext`x, 0, $CellContext`r}, PlotStyle -> {Thick, Blue}, Filling -> 0, FillingStyle -> RGBColor[0.25, 0.75, 0.25], AxesOrigin -> {0, 0}, AxesLabel -> {"x", None}]; $CellContext`rightsideIsosc = Plot[2 Sqrt[(5 - $CellContext`r)^2 - $CellContext`r^2] - ( Sqrt[(5 - $CellContext`r)^2 - $CellContext`r^2]/$CellContext`r) \ $CellContext`x, {$CellContext`x, $CellContext`r, 2 $CellContext`r}, PlotStyle -> {Thick, Blue}, Filling -> 0, FillingStyle -> RGBColor[0.25, 0.75, 0.25], AxesOrigin -> {0, 0}, AxesLabel -> {"x", None}]; $CellContext`isoscArea[ Pattern[$CellContext`b, Blank[]]] := ($CellContext`b/2) Sqrt[(5 - $CellContext`b/2)^2 - ($CellContext`b/ 2)^2]; $CellContext`leftsideNorman = Graphics[ Style[ Line[{{0, 0}, {0, (10 - (2 + Pi) $CellContext`r)/2}}], Thick, Blue]]; $CellContext`rightsideNorman = Graphics[ Style[ Line[{{2 $CellContext`r, 0}, { 2 $CellContext`r, (10 - (2 + Pi) $CellContext`r)/2}}], Thick, Blue]]; $CellContext`topNorman = Plot[(10 - (2 + Pi) $CellContext`r)/2 + Sqrt[$CellContext`r^2 - ($CellContext`x - $CellContext`r)^2], \ {$CellContext`x, 0, 2 $CellContext`r}, PlotStyle -> {Thick, Blue}, Filling -> 0, FillingStyle -> RGBColor[0.25, 0.75, 0.25], AxesOrigin -> {0, 0}, AxesLabel -> {"x", None}]; $CellContext`normanArea[ Pattern[$CellContext`b, Blank[]]] := 5 $CellContext`b - ((2 + Pi/2)/ 4) $CellContext`b^2; $CellContext`leftsideHouse = Graphics[ Style[ Line[{{0, 0}, {0, 5 - 3 $CellContext`r}}], Thick, Blue]]; $CellContext`rightsideHouse = Graphics[ Style[ Line[{{2 $CellContext`r, 0}, { 2 $CellContext`r, 5 - 3 $CellContext`r}}], Thick, Blue]]; $CellContext`lefttopHouse = Plot[5 - 3 $CellContext`r + Sqrt[3] $CellContext`x, {$CellContext`x, 0, $CellContext`r}, PlotStyle -> {Thick, Blue}, Filling -> 0, FillingStyle -> RGBColor[0.25, 0.75, 0.25], AxesOrigin -> {0, 0}, AxesLabel -> {"x", None}]; $CellContext`righttopHouse = Plot[5 + (2 Sqrt[3] - 3) $CellContext`r - Sqrt[3] $CellContext`x, {$CellContext`x, $CellContext`r, 2 $CellContext`r}, PlotStyle -> {Thick, Blue}, Filling -> 0, FillingStyle -> RGBColor[0.25, 0.75, 0.25], AxesOrigin -> {0, 0}, AxesLabel -> {"x", None}]; $CellContext`houseArea[ Pattern[$CellContext`b, Blank[]]] := $CellContext`b (5 - (3/2) $CellContext`b) + Sqrt[3] $CellContext`b; Switch[$CellContext`fig$$, $CellContext`rect, $CellContext`figure = \ {$CellContext`topRect, $CellContext`leftsideRect, $CellContext`rightsideRect, \ $CellContext`base}; $CellContext`maxb = 5; $CellContext`areaFunc = $CellContext`rectArea; \ $CellContext`areaPlot = Plot[ $CellContext`areaFunc[$CellContext`x], {$CellContext`x, 0, $CellContext`maxb}, PlotRange -> {{0, 5}, Automatic}, PlotLabel -> Style[ Row[{"area of rectangle"}], 18], ImageSize -> 250], $CellContext`rightTri, $CellContext`figure = \ {$CellContext`topRightTri, $CellContext`leftsideRightTri, $CellContext`base}; \ $CellContext`maxb = 5; $CellContext`areaFunc = $CellContext`rightTriArea; \ $CellContext`areaPlot = ($CellContext`areaPlot = Plot[ $CellContext`areaFunc[$CellContext`x], {$CellContext`x, 0, $CellContext`maxb}, PlotRange -> {{0, 5}, Automatic}, PlotLabel -> Style[ Row[{"area of right triangle"}], 18], ImageSize -> 250]), $CellContext`isosc, $CellContext`figure = \ {$CellContext`leftsideIsosc, $CellContext`rightsideIsosc, $CellContext`base}; \ $CellContext`maxb = 5; $CellContext`areaFunc = $CellContext`isoscArea; \ $CellContext`areaPlot = Plot[ $CellContext`areaFunc[$CellContext`x], {$CellContext`x, 0, $CellContext`maxb}, PlotRange -> {{0, 5}, Automatic}, PlotLabel -> Style[ Row[{"area of isosceles triangle"}], 18], ImageSize -> 250], $CellContext`norm, $CellContext`figure = \ {$CellContext`topNorman, $CellContext`base, $CellContext`leftsideNorman, \ $CellContext`rightsideNorman}; $CellContext`maxb = 20/(2 + Pi); If[$CellContext`b$$ > $CellContext`maxb, $CellContext`b$$ = 2]; $CellContext`areaFunc = $CellContext`normanArea; \ $CellContext`areaPlot = Plot[ $CellContext`areaFunc[$CellContext`x], {$CellContext`x, 0, $CellContext`maxb}, PlotRange -> {{0, 5}, Automatic}, PlotLabel -> Style[ Row[{"area of Norman window"}], 18], ImageSize -> 250], $CellContext`house, $CellContext`figure = \ {$CellContext`lefttopHouse, $CellContext`righttopHouse, \ $CellContext`leftsideHouse, $CellContext`rightsideHouse, $CellContext`base}; \ $CellContext`maxb = 10/3; If[$CellContext`b$$ > $CellContext`maxb, $CellContext`b$$ = 2]; $CellContext`areaFunc = $CellContext`houseArea; \ $CellContext`areaPlot = Plot[ $CellContext`areaFunc[$CellContext`x], {$CellContext`x, 0, $CellContext`maxb}, PlotRange -> {{0, 5}, Automatic}, PlotLabel -> Style[ Row[{"area of side of house"}], 18], ImageSize -> 250]]; $CellContext`pointOnCurve = Graphics[{ PointSize[Large], RGBColor[0.25, 0.75, 0.25], Point[{$CellContext`b$$, $CellContext`areaFunc[$CellContext`b$$]}]}]; Text[ Pane[ Row[{ Show[$CellContext`figure, Axes -> True, PlotRange -> {{0, 5}, {0, 5}}, AspectRatio -> 1, ImageSize -> 300], "", Column[{ Show[$CellContext`areaPlot, $CellContext`pointOnCurve], "", Style[ Row[{ Style["x", Italic], " = ", If[ MachineNumberQ[$CellContext`b$$], NumberForm[$CellContext`b$$, {6, 4}], $CellContext`b$$]}], 24], Style[ Row[{"area = ", If[ MachineNumberQ[ $CellContext`areaFunc[$CellContext`b$$]], NumberForm[ $CellContext`areaFunc[$CellContext`b$$], {6, 4}], $CellContext`areaFunc[$CellContext`b$$]]}], 24]}]}], ImageSize -> {560, 320}]]), "Specifications" :> {{{$CellContext`fig$$, $CellContext`isosc, "figure"}, {$CellContext`rect -> "rectangle", $CellContext`rightTri -> "right triangle", $CellContext`isosc -> "isosceles triangle", $CellContext`norm -> "Norman window", $CellContext`house -> "side of house"}, ControlType -> PopupMenu}, {{$CellContext`b$$, 2.400052, "length of base, x"}, 0.0001, Dynamic[$CellContext`maxb]}}, "Options" :> {TrackedSymbols -> True}, "DefaultOptions" :> {ControllerLinking -> True}], ImageSizeCache->{603., {217.34375, 222.65625}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellID->2072893888], Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`b$$ = 2.2400328000000003`, $CellContext`fig$$ = $CellContext`house, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{{ Hold[$CellContext`fig$$], $CellContext`house, "figure"}, {$CellContext`rect -> "rectangle", $CellContext`rightTri -> "right triangle", $CellContext`isosc -> "isosceles triangle", $CellContext`norm -> "Norman window", $CellContext`house -> "side of house"}}, {{ Hold[$CellContext`b$$], 2.2400328000000003`, "length of base, x"}, 0.0001, Dynamic[$CellContext`maxb]}}, Typeset`size$$ = {560., {159., 164.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = True, $CellContext`fig$456004$$ = False, $CellContext`b$456005$$ = 0}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`b$$ = 2.2400328000000003`, $CellContext`fig$$ = $CellContext`house}, "ControllerVariables" :> { Hold[$CellContext`fig$$, $CellContext`fig$456004$$, False], Hold[$CellContext`b$$, $CellContext`b$456005$$, 0]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> ($CellContext`base = Graphics[ Style[ Line[{{0, 0}, {$CellContext`b$$, 0}}], Thick, Blue]]; $CellContext`r = $CellContext`b$$/ 2; $CellContext`leftsideRect = Graphics[ Style[ Line[{{0, 0}, {0, 5 - 2 $CellContext`r}}], Thick, Blue]]; $CellContext`rightsideRect = Graphics[ Style[ Line[{{2 $CellContext`r, 0}, { 2 $CellContext`r, 5 - 2 $CellContext`r}}], Thick, Blue]]; $CellContext`topRect = Plot[5 - 2 $CellContext`r, {$CellContext`x, 0, 2 $CellContext`r}, PlotStyle -> {Thick, Blue}, Filling -> 0, FillingStyle -> RGBColor[0.25, 0.75, 0.25], AxesOrigin -> {0, 0}, AxesLabel -> {"x", None}]; $CellContext`rectArea[ Pattern[$CellContext`b, Blank[]]] := ($CellContext`b/2) (10 - 2 $CellContext`b); $CellContext`leftsideRightTri = Graphics[ Style[ Line[{{0, 0}, { 0, 10 (($CellContext`b$$ - 5)/($CellContext`b$$ - 10))}}], Thick, Blue]]; $CellContext`topRightTri = Plot[10 (($CellContext`b$$ - 5)/($CellContext`b$$ - 10)) - 10 (($CellContext`b$$ - 5)/($CellContext`b$$^2 - 10 $CellContext`b$$)) $CellContext`x, {$CellContext`x, 0, 2 $CellContext`r}, PlotStyle -> {Thick, Blue}, Filling -> 0, FillingStyle -> RGBColor[0.25, 0.75, 0.25], AxesOrigin -> {0, 0}, AxesLabel -> {"x", None}]; $CellContext`rightTriArea[ Pattern[$CellContext`b, Blank[]]] := 5 $CellContext`b (($CellContext`b - 5)/($CellContext`b - 10)); $CellContext`leftsideIsosc = Plot[(Sqrt[( 5 - $CellContext`r)^2 - $CellContext`r^2]/$CellContext`r) \ $CellContext`x, {$CellContext`x, 0, $CellContext`r}, PlotStyle -> {Thick, Blue}, Filling -> 0, FillingStyle -> RGBColor[0.25, 0.75, 0.25], AxesOrigin -> {0, 0}, AxesLabel -> {"x", None}]; $CellContext`rightsideIsosc = Plot[2 Sqrt[(5 - $CellContext`r)^2 - $CellContext`r^2] - ( Sqrt[(5 - $CellContext`r)^2 - $CellContext`r^2]/$CellContext`r) \ $CellContext`x, {$CellContext`x, $CellContext`r, 2 $CellContext`r}, PlotStyle -> {Thick, Blue}, Filling -> 0, FillingStyle -> RGBColor[0.25, 0.75, 0.25], AxesOrigin -> {0, 0}, AxesLabel -> {"x", None}]; $CellContext`isoscArea[ Pattern[$CellContext`b, Blank[]]] := ($CellContext`b/2) Sqrt[(5 - $CellContext`b/2)^2 - ($CellContext`b/ 2)^2]; $CellContext`leftsideNorman = Graphics[ Style[ Line[{{0, 0}, {0, (10 - (2 + Pi) $CellContext`r)/2}}], Thick, Blue]]; $CellContext`rightsideNorman = Graphics[ Style[ Line[{{2 $CellContext`r, 0}, { 2 $CellContext`r, (10 - (2 + Pi) $CellContext`r)/2}}], Thick, Blue]]; $CellContext`topNorman = Plot[(10 - (2 + Pi) $CellContext`r)/2 + Sqrt[$CellContext`r^2 - ($CellContext`x - $CellContext`r)^2], \ {$CellContext`x, 0, 2 $CellContext`r}, PlotStyle -> {Thick, Blue}, Filling -> 0, FillingStyle -> RGBColor[0.25, 0.75, 0.25], AxesOrigin -> {0, 0}, AxesLabel -> {"x", None}]; $CellContext`normanArea[ Pattern[$CellContext`b, Blank[]]] := 5 $CellContext`b - ((2 + Pi/2)/ 4) $CellContext`b^2; $CellContext`leftsideHouse = Graphics[ Style[ Line[{{0, 0}, {0, 5 - 3 $CellContext`r}}], Thick, Blue]]; $CellContext`rightsideHouse = Graphics[ Style[ Line[{{2 $CellContext`r, 0}, { 2 $CellContext`r, 5 - 3 $CellContext`r}}], Thick, Blue]]; $CellContext`lefttopHouse = Plot[5 - 3 $CellContext`r + Sqrt[3] $CellContext`x, {$CellContext`x, 0, $CellContext`r}, PlotStyle -> {Thick, Blue}, Filling -> 0, FillingStyle -> RGBColor[0.25, 0.75, 0.25], AxesOrigin -> {0, 0}, AxesLabel -> {"x", None}]; $CellContext`righttopHouse = Plot[5 + (2 Sqrt[3] - 3) $CellContext`r - Sqrt[3] $CellContext`x, {$CellContext`x, $CellContext`r, 2 $CellContext`r}, PlotStyle -> {Thick, Blue}, Filling -> 0, FillingStyle -> RGBColor[0.25, 0.75, 0.25], AxesOrigin -> {0, 0}, AxesLabel -> {"x", None}]; $CellContext`houseArea[ Pattern[$CellContext`b, Blank[]]] := $CellContext`b (5 - (3/2) $CellContext`b) + Sqrt[3] $CellContext`b; Switch[$CellContext`fig$$, $CellContext`rect, $CellContext`figure = \ {$CellContext`topRect, $CellContext`leftsideRect, $CellContext`rightsideRect, \ $CellContext`base}; $CellContext`maxb = 5; $CellContext`areaFunc = $CellContext`rectArea; \ $CellContext`areaPlot = Plot[ $CellContext`areaFunc[$CellContext`x], {$CellContext`x, 0, $CellContext`maxb}, PlotRange -> {{0, 5}, Automatic}, PlotLabel -> Style[ Row[{"area of rectangle"}], 18], ImageSize -> 250], $CellContext`rightTri, $CellContext`figure = \ {$CellContext`topRightTri, $CellContext`leftsideRightTri, $CellContext`base}; \ $CellContext`maxb = 5; $CellContext`areaFunc = $CellContext`rightTriArea; \ $CellContext`areaPlot = ($CellContext`areaPlot = Plot[ $CellContext`areaFunc[$CellContext`x], {$CellContext`x, 0, $CellContext`maxb}, PlotRange -> {{0, 5}, Automatic}, PlotLabel -> Style[ Row[{"area of right triangle"}], 18], ImageSize -> 250]), $CellContext`isosc, $CellContext`figure = \ {$CellContext`leftsideIsosc, $CellContext`rightsideIsosc, $CellContext`base}; \ $CellContext`maxb = 5; $CellContext`areaFunc = $CellContext`isoscArea; \ $CellContext`areaPlot = Plot[ $CellContext`areaFunc[$CellContext`x], {$CellContext`x, 0, $CellContext`maxb}, PlotRange -> {{0, 5}, Automatic}, PlotLabel -> Style[ Row[{"area of isosceles triangle"}], 18], ImageSize -> 250], $CellContext`norm, $CellContext`figure = \ {$CellContext`topNorman, $CellContext`base, $CellContext`leftsideNorman, \ $CellContext`rightsideNorman}; $CellContext`maxb = 20/(2 + Pi); If[$CellContext`b$$ > $CellContext`maxb, $CellContext`b$$ = 2]; $CellContext`areaFunc = $CellContext`normanArea; \ $CellContext`areaPlot = Plot[ $CellContext`areaFunc[$CellContext`x], {$CellContext`x, 0, $CellContext`maxb}, PlotRange -> {{0, 5}, Automatic}, PlotLabel -> Style[ Row[{"area of Norman window"}], 18], ImageSize -> 250], $CellContext`house, $CellContext`figure = \ {$CellContext`lefttopHouse, $CellContext`righttopHouse, \ $CellContext`leftsideHouse, $CellContext`rightsideHouse, $CellContext`base}; \ $CellContext`maxb = 10/3; If[$CellContext`b$$ > $CellContext`maxb, $CellContext`b$$ = 2]; $CellContext`areaFunc = $CellContext`houseArea; \ $CellContext`areaPlot = Plot[ $CellContext`areaFunc[$CellContext`x], {$CellContext`x, 0, $CellContext`maxb}, PlotRange -> {{0, 5}, Automatic}, PlotLabel -> Style[ Row[{"area of side of house"}], 18], ImageSize -> 250]]; $CellContext`pointOnCurve = Graphics[{ PointSize[Large], RGBColor[0.25, 0.75, 0.25], Point[{$CellContext`b$$, $CellContext`areaFunc[$CellContext`b$$]}]}]; Text[ Pane[ Row[{ Show[$CellContext`figure, Axes -> True, PlotRange -> {{0, 5}, {0, 5}}, AspectRatio -> 1, ImageSize -> 300], "", Column[{ Show[$CellContext`areaPlot, $CellContext`pointOnCurve], "", Style[ Row[{ Style["x", Italic], " = ", If[ MachineNumberQ[$CellContext`b$$], NumberForm[$CellContext`b$$, {6, 4}], $CellContext`b$$]}], 24], Style[ Row[{"area = ", If[ MachineNumberQ[ $CellContext`areaFunc[$CellContext`b$$]], NumberForm[ $CellContext`areaFunc[$CellContext`b$$], {6, 4}], $CellContext`areaFunc[$CellContext`b$$]]}], 24]}]}], ImageSize -> {560, 320}]]), "Specifications" :> {{{$CellContext`fig$$, $CellContext`house, "figure"}, {$CellContext`rect -> "rectangle", $CellContext`rightTri -> "right triangle", $CellContext`isosc -> "isosceles triangle", $CellContext`norm -> "Norman window", $CellContext`house -> "side of house"}, ControlType -> PopupMenu}, {{$CellContext`b$$, 2.2400328000000003`, "length of base, x"}, 0.0001, Dynamic[$CellContext`maxb]}}, "Options" :> {TrackedSymbols -> True}, "DefaultOptions" :> {ControllerLinking -> True}], ImageSizeCache->{603., {217.34375, 222.65625}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellID->500370335] }, Open ]], Cell["", "DetailsSection"], Cell[CellGroupData[{ Cell["", "ControlSuggestionsSection"], Cell[BoxData[ TooltipBox[ RowBox[{ CheckboxBox[True], Cell[" Resize Images"]}], "\"Click inside an image to reveal its orange resize frame.\\nDrag any of \ the orange resize handles to resize the image.\"", TooltipDelay->0.35]], "ControlSuggestions", CellChangeTimes->{3.35696210375764*^9, 3.4604952684991164`*^9}, FontFamily->"Verdana", CellTags->"ResizeImages"], Cell[BoxData[ TooltipBox[ RowBox[{ CheckboxBox[False], Cell[" Rotate and Zoom in 3D"]}], RowBox[{ "\"Drag a 3D graphic to rotate it. Starting the drag near the center \ tumbles\\nthe graphic; starting near a corner turns it parallel to the plane \ of the screen.\\nHold down \"", FrameBox[ "Ctrl", Background -> GrayLevel[0.9], FrameMargins -> 2, FrameStyle -> GrayLevel[0.9]], "\" (or \"", FrameBox[ "Cmd", Background -> GrayLevel[0.9], FrameMargins -> 2, FrameStyle -> GrayLevel[0.9]], "\" on Mac) and drag up and down to zoom.\""}], TooltipDelay->0.35]], "ControlSuggestions", FontFamily->"Verdana", CellTags->"RotateAndZoomIn3D"], Cell[BoxData[ TooltipBox[ RowBox[{ CheckboxBox[False], Cell[" Drag Locators"]}], RowBox[{"\"Drag any locator (\"", GraphicsBox[ LocatorBox[ Scaled[{0.5, 0.5}]], ImageSize -> 20], "\", etc.) to move it around.\""}], TooltipDelay->0.35]], "ControlSuggestions", FontFamily->"Verdana", CellTags->"DragLocators"], Cell[BoxData[ TooltipBox[ RowBox[{ CheckboxBox[False], Cell[" Create and Delete Locators"]}], RowBox[{"\"Insert a new locator in the graphic by holding down the \"", FrameBox[ "Alt", Background -> GrayLevel[0.9], FrameMargins -> 2, FrameStyle -> GrayLevel[0.9]], "\" key\\nand clicking where you want it to be. Delete a locator by \ clicking it\\nwhile holding down the \"", FrameBox[ "Alt", Background -> GrayLevel[0.9], FrameMargins -> 2, FrameStyle -> GrayLevel[0.9]], "\" key.\""}], TooltipDelay->0.35]], "ControlSuggestions", FontFamily->"Verdana", CellTags->"CreateAndDeleteLocators"], Cell[BoxData[ TooltipBox[ RowBox[{ CheckboxBox[True], Cell[" Slider Zoom"]}], RowBox[{"\"Hold down the \"", FrameBox[ "Alt", Background -> GrayLevel[0.9], FrameMargins -> 2, FrameStyle -> GrayLevel[0.9]], "\" key while moving a slider to make fine adjustments in the slider \ value.\\nHold \"", FrameBox[ "Ctrl", Background -> GrayLevel[0.9], FrameMargins -> 2, FrameStyle -> GrayLevel[0.9]], "\" and/or \"", FrameBox[ "Shift", Background -> GrayLevel[0.9], FrameMargins -> 2, FrameStyle -> GrayLevel[0.9]], "\" at the same time as \"", FrameBox[ "Alt", Background -> GrayLevel[0.9], FrameMargins -> 2, FrameStyle -> GrayLevel[0.9]], "\" to make ever finer adjustments.\""}], TooltipDelay->0.35]], "ControlSuggestions", 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