<Text-field layout="Heading 1" style="Heading 1"><Font executable="false">Objective</Font></Text-field>

<Text-field layout="Heading 1" style="Heading 1">Maplet</Text-field>

bor := 'border'=true: s := 'inset'=0, 'spacing'=0: ck := 'background'="#DDFFFF": dc := 'background'="#CCFFFF": lc := 'background'="#EEFFFF": assignvalue:=()->Action( Evaluate('Plot'='Draw('aVar','bVar','cVar','VertView','HorView',axesType(RB1,RB2,RB3,RB4), scaleType(RB1c,RB2c), projType(RB1p,RB2p,RB3p), shadeType(RB1s,RB2s,RB3s,RB4s,RB5s,RB6s), lightType(RB1l,RB2l,RB3l,RB4l,RB5l), styleType(RB1t,RB2t,RB3t,RB4t,RB5t,RB6t,RB7t,RB8t), ShowTracex('ChB1','xT','aVar','bVar','cVar','VertView','HorView',axesType(RB1,RB2,RB3,RB4), scaleType(RB1c,RB2c), projType(RB1p,RB2p,RB3p), shadeType(RB1s,RB2s,RB3s,RB4s,RB5s,RB6s), lightType(RB1l,RB2l,RB3l,RB4l,RB5l), styleType(RB1t,RB2t,RB3t,RB4t,RB5t,RB6t,RB7t,RB8t)), ShowTracey('ChB2','yT','aVar','bVar','cVar','VertView','HorView',axesType(RB1,RB2,RB3,RB4), scaleType(RB1c,RB2c), projType(RB1p,RB2p,RB3p), shadeType(RB1s,RB2s,RB3s,RB4s,RB5s,RB6s), lightType(RB1l,RB2l,RB3l,RB4l,RB5l), styleType(RB1t,RB2t,RB3t,RB4t,RB5t,RB6t,RB7t,RB8t)), ShowTracez('ChB3','zT','aVar','bVar','cVar','VertView','HorView',axesType(RB1,RB2,RB3,RB4), scaleType(RB1c,RB2c), projType(RB1p,RB2p,RB3p), shadeType(RB1s,RB2s,RB3s,RB4s,RB5s,RB6s), lightType(RB1l,RB2l,RB3l,RB4l,RB5l), styleType(RB1t,RB2t,RB3t,RB4t,RB5t,RB6t,RB7t,RB8t)), ShowPlanex('ChB4','xT','aVar','bVar','cVar','VertView','HorView',axesType(RB1,RB2,RB3,RB4), scaleType(RB1c,RB2c), projType(RB1p,RB2p,RB3p), shadeType(RB1s,RB2s,RB3s,RB4s,RB5s,RB6s), lightType(RB1l,RB2l,RB3l,RB4l,RB5l), styleType(RB1t,RB2t,RB3t,RB4t,RB5t,RB6t,RB7t,RB8t)), ShowPlaney('ChB5','yT','aVar','bVar','cVar','VertView','HorView',axesType(RB1,RB2,RB3,RB4), scaleType(RB1c,RB2c), projType(RB1p,RB2p,RB3p), shadeType(RB1s,RB2s,RB3s,RB4s,RB5s,RB6s), lightType(RB1l,RB2l,RB3l,RB4l,RB5l), styleType(RB1t,RB2t,RB3t,RB4t,RB5t,RB6t,RB7t,RB8t)), ShowPlanez('ChB6','zT','aVar','bVar','cVar','VertView','HorView',axesType(RB1,RB2,RB3,RB4), scaleType(RB1c,RB2c), projType(RB1p,RB2p,RB3p), shadeType(RB1s,RB2s,RB3s,RB4s,RB5s,RB6s), lightType(RB1l,RB2l,RB3l,RB4l,RB5l), styleType(RB1t,RB2t,RB3t,RB4t,RB5t,RB6t,RB7t,RB8t)))'), Evaluate('xTrace'='display(conextrace('xT','aVar','bVar','cVar',0,90,axesType(RB1,RB2,RB3,RB4), scaleType(RB1c,RB2c), projType(RB1p,RB2p,RB3p), shadeType(RB1s,RB2s,RB3s,RB4s,RB5s,RB6s), lightType(RB1l,RB2l,RB3l,RB4l,RB5l), styleType(RB1t,RB2t,RB3t,RB4t,RB5t,RB6t,RB7t,RB8t)))'), Evaluate('yTrace'='display(coneytrace('yT','aVar','bVar','cVar',90,90,axesType(RB1,RB2,RB3,RB4), scaleType(RB1c,RB2c), projType(RB1p,RB2p,RB3p), shadeType(RB1s,RB2s,RB3s,RB4s,RB5s,RB6s), lightType(RB1l,RB2l,RB3l,RB4l,RB5l), styleType(RB1t,RB2t,RB3t,RB4t,RB5t,RB6t,RB7t,RB8t)))'), Evaluate('zTrace'='display(coneztrace('zT','aVar','bVar','cVar',90,0,axesType(RB1,RB2,RB3,RB4), scaleType(RB1c,RB2c), projType(RB1p,RB2p,RB3p), shadeType(RB1s,RB2s,RB3s,RB4s,RB5s,RB6s), lightType(RB1l,RB2l,RB3l,RB4l,RB5l), styleType(RB1t,RB2t,RB3t,RB4t,RB5t,RB6t,RB7t,RB8t)))')): ConeMaplet := Maplet( ButtonGroup['RG1'](),

ButtonGroup['RG2'](),

ButtonGroup['RG3'](),

ButtonGroup['RG4'](),

ButtonGroup['RG5'](),

ButtonGroup['RG6'](),

'onstartup' = RunWindow('MainWin'), Font['F1']('family'="Comic Sans MS", 'bold'='false', 'italic'='false', size=12), Font['F2']('family'="Comic Sans MS", 'bold'='true', 'italic'='false', size=14), Window['MainWin']('title' = "Cone with Traces", 'menubar'='Menu', 'layout' = 'Body'), Window['DescriptionWin']('title' = "Description", 'layout' = 'DescriptionBody', width=400, height=250),

Window['SyntaxWin']('title' = "Maple Syntax", 'layout' = 'SyntaxBody', width=400, height=430),

Window['NotesWin']('title' = "Notes", 'layout' = 'NotesBody', width=400, height=300),

Window['PrintingWin']('title' = "Printing", 'layout' = 'PrintingBody', width=400, height=250),

Window['AboutWin']('title' = "About", 'layout' = 'AboutBody', width=400, height=300),

Window['ExploreWin']('title' = "Cone with Traces", 'layout' = 'ExploreBody', width=400, height=300),

BoxLayout['DescriptionBody'](

BoxColumn(bor, 'inset'=0, 'spacing'=4,

BoxRow(s,

TextBox('wrapped'=true, 'width'=80, 'height'=15, ck, 'font'='F1',

'editable'='false', 'value'=

############################ DESCRIPTION TEXT (BELOW) ##################

"This Maplet plots a cone with parameters a, b, and c, together with traces and planes through the traces. Plots of the individual traces appear to the right of the cone plot. The parameters a, b, and c are chosen using the sliders. Moving the sliders re-draws the plots. Sliders may be moved with the mouse or changed incrementally by selecting with the mouse and then using the arrow keys. Trace values must be entered in the textboxes below the individual plots, and the plot button clicked to redraw the plots. The trace values must each be strictly less than the corresponding parameter values or an error is generated. Slider bars on the plot window adjust the viewing angle. Checkboxes below the cone plot toggle the traces and planes on and off. Various buttons on the menu bar change the appearance of the plot."

############################ DESCRIPTION TEXT (ABOVE) ##################

)

BoxRow(s,

Button("Close", 'font'='F1', CloseWindow('DescriptionWin') )

)

BoxLayout['SyntaxBody'](

BoxColumn(bor, 'inset'=0, 'spacing'=4,

BoxRow(s,

TextBox('wrapped'=true, 'width'=80, 'height'=15, ck, 'font'='F1',

'editable'='false', 'value'=

############################ SYNTAX TEXT (BELOW) ##################

"Maple Syntax: Entries in textboxes must use Maple Syntax. For example: \n Addition: a+b \n Subtraction: a-b \n Multiplication: a*b \n Division: a/b \n Powers: a^b \n Exponents of e: exp(a), use exp(1) for e = 2.718... \n Square root: sqrt(a) \n Log base 10: log10(a) \n Natural log: ln(a) \n Trigonometric functions: sin(a) \n Pi (3.14...): Pi \n Lists: [a,b,c] \n \n Use parentheses to clearly indicate order of operation."

############################ SYNTAX TEXT (ABOVE) ##################

)

BoxRow(s,

Button("Close", 'font'='F1', CloseWindow('SyntaxWin') )

)

BoxLayout['NotesBody'](

BoxColumn(bor, 'inset'=0, 'spacing'=4,

BoxRow(s,

TextBox('wrapped'=true, 'width'=80, 'height'=15, ck, 'font'='F1',

'editable'='false', 'value'=

############################ NOTES TEXT (BELOW) ##################

" \n\nWarnings! \n 1. The absolute values of the x and y traces must be strictly less than the corresponding parameter values (e.g. the absolute value of trace at x must be less than a) or an error box pops up. If this happens, just close the box, adjust the values, and replot. Trace at z larger than c won't generate an error, but the trace and plane float above (or below) the plot of the cone which ranges from -c to c in height. \n 2. This Maplet makes a lot of demand on memory. If it begins to slow down after repeated plotting, close it and restart to make it more responsive. \n 3. The graphs will be distorted (e.g. circles will appear as ellipses) unless 'constrained' is selected under the 'scale' option on the menu bar. Also, if 'constrained' is selected, and circles appear elliptical (set a=b=c=1 and trace at z =1/2--the z trace should be a circle), it may be necessary to resize the entire Maplet window itself (by clicking on a corner and dragging) until the z-trace looks like a circle."

############################ NOTES TEXT (ABOVE) ##################

)

BoxRow(s,

Button("Close", 'font'='F1', CloseWindow('NotesWin') )

)

BoxLayout['PrintingBody'](

BoxColumn(bor, 'inset'=0, 'spacing'=4,

BoxRow(s,

TextBox('wrapped'=true, 'width'=80, 'height'=15, ck, 'font'='F1',

'editable'='false', 'value'=

############################ PRINTING TEXT (BELOW) ##################

"Currently the best way to get a printout of this Maplet (on a PC at least) is to press Alt PrntScrn while the Maplet is the active window. This puts a copy of the window image on the clipboard. You can then paste this image into another application, such as Word, and then print it from there. Please check the Maple website at www.maplesoft.com for future developments!"

############################ PRINTING TEXT (ABOVE) ##################

)

BoxRow(s,

Button("Close", 'font'='F1', CloseWindow('PrintingWin') )

)

BoxLayout['AboutBody'](

BoxColumn(bor, 'inset'=0, 'spacing'=6, background="#990099",

BoxColumn(s, background="#990099",

Label(font=F2, "Saint Michael\'s College", foreground="#FFFF00", background="#990099"),

Label(font=F1, "Colchester, VT", foreground="#FFFF00", background="#990099"),

Label("blank space",background="#990099", foreground="#990099"),

Label(ck, font=F1, "Development Team:", foreground="#FFFF00", background="#990099"),

Label(ck, font=F1, "\t\tJoanna Ellis-Monaghan", foreground="#FFFFFF", background="#990099"),

Label(ck, font=F1, "\t\tColin Kriwox", foreground="#FFFFFF", background="#990099"),

Label(ck, font=F1, "\t\tLaura McLane", foreground="#FFFFFF", background="#990099"),

Label(ck, font=F1, "\t\twith George Ashline and Zsuzsanna Kadas", foreground="#FFFFFF", background="#990099"),

Label("blank space",background="#990099", foreground="#990099"),

Button("Close", 'font'='F1', CloseWindow('AboutWin'))

)

BoxLayout['ExploreBody'](

BoxColumn(bor, 'inset'=0, 'spacing'=4,

BoxRow(s,

TextBox('wrapped'=true, 'width'=80, 'height'=15, ck, 'font'='F1',

'editable'='false', 'value'=

############################ Explore TEXT (BELOW) ##################

"Here are a few suggested activities to begin exploring the concepts illustrated by this Maplet. \n\n To begin with, try various traces of the cones with the following parameters\n\na=10 b=10 c=10 a=3 b=4 c=1 a= 2 b=2 c=1 \n \na. What are the general shapes of the x, y, and z traces for the cone? \nb. For which parameter values (if any) are the traces only a single point? Why? \nc. For which parameter values (if any) are there no traces for your cone? \n\nd. Why do you suppose an error is generated if the absolute value of trace at x is larger than a? Hint: plot x traces closer and closer to the value of a and see what happens. \n\ne. What happens if the trace at z is greater than c? Explain why the plot of the cone ranges in height from -c to c. \n\nf. Is there any place where the general shapes of the traces change? If so, where, and how do they change? \n\ng. Choose distinct values for a, b, and c (eg a=4, b=2, c=1) and determine equations for the y trace at y = 0, y = 1/2, and y = 1. Do the equations agree with the graphs in the Maplet? Determine the equation for the z trace at z = 1/2. What curve is this? Does it agree with the graph in the Maplet?"

############################ Explore TEXT (ABOVE) ##################

)

BoxRow(s,

Button("Close", 'font'='F1', CloseWindow('ExploreWin') )

)

BoxLayout['Body']( BoxRow(s, ck, BoxColumn(s, ck, bor, 'caption'="Cone with Traces", BoxRow(s,ck, Plotter['Plot'](lc), Slider['VertView'](lower=0,background="#DDFFFF",filled=true,majorticks=30,minorticks=10,orientation=vertical,snapticks=false,upper=360,value=60,'onchange'=assignvalue()) ), Slider['HorView'](lower=0,background="#DDFFFF",filled=true,majorticks=30,minorticks=10,orientation=horizontal,snapticks=false,upper=360,value=45,'onchange'=assignvalue()), BoxRow(s,ck, [CheckBox['ChB1'](caption="Show Xtrace", 'onchange'=assignvalue())], [CheckBox['ChB2'](caption="Show Ytrace", 'onchange'=assignvalue())], [CheckBox['ChB3'](caption="Show Ztrace", 'onchange'=assignvalue())]), BoxRow(s,ck, [CheckBox['ChB4'](caption="Show Xplane", 'onchange'=assignvalue())], [CheckBox['ChB5'](caption="Show Yplane", 'onchange'=assignvalue())], [CheckBox['ChB6'](caption="Show Zplane", 'onchange'=assignvalue())] ) ), BoxColumn(s,ck, Plotter['xTrace'](lc, width=150, height=150), BoxRow(s, ck, bor, Label("Trace at x = ",'font'='F1',ck), TextField['xT'](5,lc,'value'=1/2) ), Plotter['yTrace'](lc, width=150, height=150), BoxRow(s, ck, bor, Label("Trace at y = ",'font'='F1',ck), TextField['yT'](5,lc,'value'=1/2) ), Plotter['zTrace'](lc, width=150, height=150), BoxRow(s, ck, bor, Label("Trace at z = ",'font'='F1',ck), TextField['zT'](5,lc,'value'=1/2) ) ), BoxColumn(s, ck, BoxRow(s, ck, bor, 'caption'="Equation of a Cone", MathMLViewer('value' = MathML[Export](x^2/a^2+y^2/b^2=z^2/c^2), height = 70, width = 140) ), BoxColumn(s, ck, 'caption'="Parameters:", BoxRow(s,ck, Label("a: ", 'font'='F1', ck), Slider['aVar'](lower=1,background="#DDFFFF",filled=true,majorticks=1,orientation=horizontal,snapticks=false,upper=10,value=1,'onchange'=assignvalue()) ), BoxRow(s,ck, Label("b: ", 'font'='F1', ck), Slider['bVar'](lower=1,background="#DDFFFF",filled=true,majorticks=1,orientation=horizontal,snapticks=false,upper=10,value=1,'onchange'=assignvalue()) ), BoxRow(s,ck, Label("c: ", 'font'='F1', ck), Slider['cVar'](lower=1,background="#DDFFFF",filled=true,majorticks=1,orientation=horizontal,snapticks=false,upper=10,value=1,'onchange'=assignvalue()) ) ), BoxRow('inset'=0, 'spacing'=0, ck, Button("Plot", dc, 'tooltip'="Plot", 'onclick'=assignvalue()), Button("Close", Shutdown(), dc) ) ) ) ), MenuBar['Menu']( Menu("Explore", MenuItem("Cone with Traces", 'onclick'=RunWindow('ExploreWin')) ), Menu("Axes",

RadioButtonMenuItem['RB1']("Normal",'value'=true,'group'='RG1','onclick'=assignvalue()), RadioButtonMenuItem['RB2']("Boxed",'group'='RG1','onclick'=assignvalue()),

RadioButtonMenuItem['RB3']("Framed",'group'='RG1','onclick'=assignvalue()),

RadioButtonMenuItem['RB4']("None",'group'='RG1','onclick'=assignvalue())

Menu("Scale",

RadioButtonMenuItem['RB1c']("Unconstrained",'group'='RG2','onclick'=assignvalue()), RadioButtonMenuItem['RB2c']("Constrained",'value'=true,'group'='RG2','onclick'=assignvalue())

Menu("Projection", RadioButtonMenuItem['RB1p']("Orthogonal",'group'='RG3','onclick'=assignvalue()), RadioButtonMenuItem['RB2p']("Fisheye",'group'='RG3','onclick'=assignvalue()), RadioButtonMenuItem['RB3p']("Normal",'value'=true,'group'='RG3','onclick'=assignvalue())

Menu("Shading",

RadioButtonMenuItem['RB1s']("XYZ",'value'=true,'group'='RG4','onclick'=assignvalue()), RadioButtonMenuItem['RB2s']("XY",'group'='RG4','onclick'=assignvalue()), RadioButtonMenuItem['RB3s']("Z",'group'='RG4','onclick'=assignvalue()), RadioButtonMenuItem['RB4s']("ZGRAYSCALE",'group'='RG4','onclick'=assignvalue()), RadioButtonMenuItem['RB5s']("ZHUE",'group'='RG4','onclick'=assignvalue()), RadioButtonMenuItem['RB6s']("None",'group'='RG4','onclick'=assignvalue())

Menu("Lightmodel",

RadioButtonMenuItem['RB1l']("Light1",'group'='RG5','onclick'=assignvalue()), RadioButtonMenuItem['RB2l']("Light2", 'group'='RG5','onclick'=assignvalue()), RadioButtonMenuItem['RB3l']("Light3",'group'='RG5','onclick'=assignvalue()), RadioButtonMenuItem['RB4l']("Light4",'group'='RG5','onclick'=assignvalue()), RadioButtonMenuItem['RB5l']("None",'value'=true,'group'='RG5','onclick'=assignvalue())

Menu("Style",

RadioButtonMenuItem['RB8t']("Patch",'group'='RG6','onclick'=assignvalue()), RadioButtonMenuItem['RB2t']("Hidden",'group'='RG6','onclick'=assignvalue()), RadioButtonMenuItem['RB3t']("WireFrame",'group'='RG6','onclick'=assignvalue()), RadioButtonMenuItem['RB4t']("Contour",'group'='RG6','onclick'=assignvalue()), RadioButtonMenuItem['RB5t']("PNG", value=true, 'group'='RG6','onclick'=assignvalue()), RadioButtonMenuItem['RB6t']("PatchContour",'group'='RG6','onclick'=assignvalue()), RadioButtonMenuItem['RB7t']("Line",'group'='RG6','onclick'=assignvalue()), RadioButtonMenuItem['RB1t']("Point",'group'='RG6','onclick'=assignvalue())

), Menu("Help",

MenuItem("Description", onclick=RunWindow('DescriptionWin')), MenuItem("Notes", onclick=RunWindow('NotesWin')),

MenuItem("Maple Syntax", onclick=RunWindow('SyntaxWin')), MenuItem("Printing", onclick=RunWindow('PrintingWin')),

MenuItem("About", onclick=RunWindow('AboutWin'))

)

) ):