(*^ ::[ Information = "This is a Mathematica Notebook file. It contains ASCII text, and can be transferred by email, ftp, or other text-file transfer utility. It should be read or edited using a copy of Mathematica or MathReader. If you received this as email, use your mail application or copy/paste to save everything from the line containing (*^ down to the line containing ^*) into a plain text file. On some systems you may have to give the file a name ending with ".ma" to allow Mathematica to recognize it as a Notebook. The line below identifies what version of Mathematica created this file, but it can be opened using any other version as well."; FrontEndVersion = "Macintosh Mathematica Notebook Front End Version 2.2"; MacintoshStandardFontEncoding; fontset = title, inactive, noPageBreakBelow, nohscroll, preserveAspect, cellOutline, groupLikeTitle, center, M18, O486, R65535, e8, 24, "Calculus"; fontset = subtitle, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M18, O486, bold, R21845, G21845, B21845, e6, 12, "Calculus"; fontset = subsubtitle, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M18, O486, R21845, G21845, B21845, e6, 12, "Calculus"; fontset = section, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, grayBox, M18, O486, bold, R21845, G21845, B21845, a10, 12, "Calculus"; fontset = subsection, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, blackBox, M18, O486, bold, R21845, G21845, B21845, a10, 12, "Calculus"; fontset = subsubsection, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, whiteBox, M18, O486, bold, R21845, G21845, B21845, a10, 12, "Calculus"; fontset = text, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M18, O486, 12, "Calculus"; fontset = smalltext, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M18, O486, B65535, 12, "Calculus"; fontset = input, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeInput, M36, N23, O486, bold, L-5, 12, "Courier"; fontset = output, output, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M36, N23, O486, L-5, 12, "Courier"; fontset = message, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M18, N23, O486, R65535, L-5, 12, "Courier"; fontset = print, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M18, N23, O486, L-5, 12, "Courier"; fontset = info, inactive, noPageBreakInGroup, nowordwrap, 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noKeepOnOnePage, preserveAspect, whiteBox, M18, O486, bold, R21845, G21845, B21845, 12, "Calculus"; fontset = special2, inactive, nohscroll, noKeepOnOnePage, preserveAspect, center, M18, O486, R21845, G21845, B21845, 12, "Calculus"; fontset = special3, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M18, O486, 12, "Times"; fontset = special4, inactive, nohscroll, noKeepOnOnePage, preserveAspect, center, M18, O486, 10, "Courier"; fontset = special5, inactive, nohscroll, noKeepOnOnePage, preserveAspect, center, M18, O486, 10, "Courier"; automaticGrouping; currentKernel; ] :[font = title; inactive; preserveAspect; startGroup] Demonstration of the Area formula for Parallelograms :[font = input; preserveAspect; startGroup] Clear[tall,wide,grid] poly=Graphics[{RGBColor[0,1,0],Thickness[.02], Line[{{2,3},{6,3},{4,0},{0,0},{2,3}}]}]; grid[tall_,wide_]:= Table[ Graphics[{RGBColor[0,1,1],{Line[{{a,tall},{a,0}}]}, Line[{{0,b},{wide,b}}]}],{a,0,wide},{b,0,tall}]; cut=Graphics[{RGBColor[1,0,0],Line[{{2,3},{2,0}}]}]; Show[grid[5,6],poly,cut, Graphics[Text["base = 4 units",{2.1,0.3},{-1,0}]], Graphics[{RGBColor[1,0,0],Text["height = 3 units",{2.1,2},{-1,0}]}], Axes->True]; :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 19; pictureTop = 2; pictureWidth = 346; pictureHeight = 214; endGroup] %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.15873 0.0147151 0.117721 [ [(1)] .18254 .01472 0 2 Msboxa [(2)] .34127 .01472 0 2 Msboxa [(3)] .5 .01472 0 2 Msboxa [(4)] .65873 .01472 0 2 Msboxa [(5)] .81746 .01472 0 2 Msboxa [(6)] .97619 .01472 0 2 Msboxa [(1)] .01131 .13244 1 0 Msboxa [(2)] .01131 .25016 1 0 Msboxa [(3)] .01131 .36788 1 0 Msboxa [(4)] .01131 .4856 1 0 Msboxa [(5)] .01131 .60332 1 0 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 .61903 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin 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.01847 L s P p .001 w .53175 .01472 m .53175 .01847 L s P p .001 w .56349 .01472 m .56349 .01847 L s P p .001 w .59524 .01472 m .59524 .01847 L s P p .001 w .62698 .01472 m .62698 .01847 L s P p .001 w .69048 .01472 m .69048 .01847 L s P p .001 w .72222 .01472 m .72222 .01847 L s P p .001 w .75397 .01472 m .75397 .01847 L s P p .001 w .78571 .01472 m .78571 .01847 L s P p .001 w .84921 .01472 m .84921 .01847 L s P p .001 w .88095 .01472 m .88095 .01847 L s P p .001 w .9127 .01472 m .9127 .01847 L s P p .001 w .94444 .01472 m .94444 .01847 L s P p .002 w 0 .01472 m 1 .01472 L s P p .002 w .02381 .13244 m .03006 .13244 L s P [(1)] .01131 .13244 1 0 Mshowa p .002 w .02381 .25016 m .03006 .25016 L s P [(2)] .01131 .25016 1 0 Mshowa p .002 w .02381 .36788 m .03006 .36788 L s P [(3)] .01131 .36788 1 0 Mshowa p .002 w .02381 .4856 m .03006 .4856 L s P [(4)] .01131 .4856 1 0 Mshowa p .002 w .02381 .60332 m .03006 .60332 L s P [(5)] .01131 .60332 1 0 Mshowa p .001 w .02381 .03826 m .02756 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.02381 .01472 L s P .004 w .02381 .01472 m .97619 .01472 L s P p 0 1 1 r p .004 w .02381 .60332 m .02381 .01472 L s P .004 w .02381 .13244 m .97619 .13244 L s P p 0 1 1 r p .004 w .02381 .60332 m .02381 .01472 L s P .004 w .02381 .25016 m .97619 .25016 L s P p 0 1 1 r p .004 w .02381 .60332 m .02381 .01472 L s P .004 w .02381 .36788 m .97619 .36788 L s P p 0 1 1 r p .004 w .02381 .60332 m .02381 .01472 L s P .004 w .02381 .4856 m .97619 .4856 L s P p 0 1 1 r p .004 w .02381 .60332 m .02381 .01472 L s P .004 w .02381 .60332 m .97619 .60332 L s P p 0 1 1 r p .004 w .18254 .60332 m .18254 .01472 L s P .004 w .02381 .01472 m .97619 .01472 L s P p 0 1 1 r p .004 w .18254 .60332 m .18254 .01472 L s P .004 w .02381 .13244 m .97619 .13244 L s P p 0 1 1 r p .004 w .18254 .60332 m .18254 .01472 L s P .004 w .02381 .25016 m .97619 .25016 L s P p 0 1 1 r p .004 w .18254 .60332 m .18254 .01472 L s P .004 w .02381 .36788 m .97619 .36788 L s P p 0 1 1 r p .004 w .18254 .60332 m .18254 .01472 L s P 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1 r p .004 w .5 .60332 m .5 .01472 L s P .004 w .02381 .36788 m .97619 .36788 L s P p 0 1 1 r p .004 w .5 .60332 m .5 .01472 L s P .004 w .02381 .4856 m .97619 .4856 L s P p 0 1 1 r p .004 w .5 .60332 m .5 .01472 L s P .004 w .02381 .60332 m .97619 .60332 L s P p 0 1 1 r p .004 w .65873 .60332 m .65873 .01472 L s P .004 w .02381 .01472 m .97619 .01472 L s P p 0 1 1 r p .004 w .65873 .60332 m .65873 .01472 L s P .004 w .02381 .13244 m .97619 .13244 L s P p 0 1 1 r p .004 w .65873 .60332 m .65873 .01472 L s P .004 w .02381 .25016 m .97619 .25016 L s P p 0 1 1 r p .004 w .65873 .60332 m .65873 .01472 L s P .004 w .02381 .36788 m .97619 .36788 L s P p 0 1 1 r p .004 w .65873 .60332 m .65873 .01472 L s P .004 w .02381 .4856 m .97619 .4856 L s P p 0 1 1 r p .004 w .65873 .60332 m .65873 .01472 L s P .004 w .02381 .60332 m .97619 .60332 L s P p 0 1 1 r p .004 w .81746 .60332 m .81746 .01472 L s P .004 w .02381 .01472 m .97619 .01472 L s P p 0 1 1 r p .004 w .81746 .60332 m .81746 .01472 L s P .004 w .02381 .13244 m .97619 .13244 L s P p 0 1 1 r p .004 w .81746 .60332 m .81746 .01472 L s P .004 w .02381 .25016 m .97619 .25016 L s P p 0 1 1 r p .004 w .81746 .60332 m .81746 .01472 L s P .004 w .02381 .36788 m .97619 .36788 L s P p 0 1 1 r p .004 w .81746 .60332 m .81746 .01472 L s P .004 w .02381 .4856 m .97619 .4856 L s P p 0 1 1 r p .004 w .81746 .60332 m .81746 .01472 L s P .004 w .02381 .60332 m .97619 .60332 L s P p 0 1 1 r p .004 w .97619 .60332 m .97619 .01472 L s P .004 w .02381 .01472 m .97619 .01472 L s P p 0 1 1 r p .004 w .97619 .60332 m .97619 .01472 L s P .004 w .02381 .13244 m .97619 .13244 L s P p 0 1 1 r p .004 w .97619 .60332 m .97619 .01472 L s P .004 w .02381 .25016 m .97619 .25016 L s P p 0 1 1 r p .004 w .97619 .60332 m .97619 .01472 L s P .004 w .02381 .36788 m .97619 .36788 L s P p 0 1 1 r p .004 w .97619 .60332 m .97619 .01472 L s P .004 w .02381 .4856 m .97619 .4856 L s P p 0 1 1 r p .004 w .97619 .60332 m .97619 .01472 L s P .004 w .02381 .60332 m .97619 .60332 L s P p 0 1 0 r .02 w .34127 .36788 m .97619 .36788 L .65873 .01472 L .02381 .01472 L .34127 .36788 L s P p 1 0 0 r .004 w .34127 .36788 m .34127 .01472 L s P [(base = 4 units)] .35714 .05003 -1 0 Mshowa p 1 0 0 r [(height = 3 units)] .35714 .25016 -1 0 Mshowa P P % End of Graphics MathPictureEnd :[font = section; inactive; noPageBreak; preserveAspect; fontColorRed = 21844; fontColorGreen = 21844; fontColorBlue = 21844; fontSize = 14; startGroup] Consider the above parallelogram. Watch what happens as we cut off the triangle shape off of the left of the parallelogram and move it right. :[font = input; preserveAspect; startGroup] tri[d_]:=Polygon[{{0+d,0},{2+d,3},{2+d,0}}]; trap=Graphics[{RGBColor[0,1,0],Thickness[0.01], Line[{{2,0},{4,0},{6,3},{2,3},{2,0}}]}]; Do[Show[grid[3,6],trap,Graphics[{RGBColor[1,0,0],tri[d],Thickness[.1]}],grid[4,6], Axes->True,AspectRatio->Automatic],{d,0,4}] :[font = postscript; PostScript; formatAsPostScript; output; inactive; Cclosed; preserveAspect; pictureLeft = 19; pictureTop = 2; pictureWidth = 320; pictureHeight = 214; startGroup; animationSpeed = 30] %! %%Creator: Mathematica %%AspectRatio: .66667 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.15873 0.015873 0.15873 [ [(1)] .18254 .01587 0 2 Msboxa [(2)] .34127 .01587 0 2 Msboxa [(3)] .5 .01587 0 2 Msboxa [(4)] .65873 .01587 0 2 Msboxa [(5)] .81746 .01587 0 2 Msboxa [(6)] .97619 .01587 0 2 Msboxa [(1)] .01131 .1746 1 0 Msboxa [(2)] .01131 .33333 1 0 Msboxa [(3)] .01131 .49206 1 0 Msboxa [(4)] .01131 .65079 1 0 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 .66767 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p p .002 w .18254 .01587 m .18254 .02212 L s P [(1)] .18254 .01587 0 2 Mshowa p .002 w .34127 .01587 m .34127 .02212 L s P [(2)] .34127 .01587 0 2 Mshowa p .002 w .5 .01587 m .5 .02212 L s P [(3)] .5 .01587 0 2 Mshowa p .002 w .65873 .01587 m .65873 .02212 L s P [(4)] .65873 .01587 0 2 Mshowa p .002 w .81746 .01587 m .81746 .02212 L s P [(5)] .81746 .01587 0 2 Mshowa p .002 w .97619 .01587 m .97619 .02212 L s P [(6)] .97619 .01587 0 2 Mshowa p .001 w .05556 .01587 m .05556 .01962 L s P p .001 w .0873 .01587 m .0873 .01962 L s P p .001 w .11905 .01587 m .11905 .01962 L s P p .001 w .15079 .01587 m .15079 .01962 L s P p .001 w .21429 .01587 m .21429 .01962 L s P p .001 w .24603 .01587 m .24603 .01962 L s P p .001 w .27778 .01587 m .27778 .01962 L s P p .001 w 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.11905 .00714 L s P .004 w .02381 .19762 m .97619 .19762 L s P p 0 1 1 r p .004 w .11905 .29286 m .11905 .00714 L s P .004 w .02381 .29286 m .97619 .29286 L s P p 0 1 1 r p .004 w .21429 .29286 m .21429 .00714 L s P .004 w .02381 .00714 m .97619 .00714 L s P p 0 1 1 r p .004 w .21429 .29286 m .21429 .00714 L s P .004 w .02381 .10238 m .97619 .10238 L s P p 0 1 1 r p .004 w .21429 .29286 m .21429 .00714 L s P .004 w .02381 .19762 m .97619 .19762 L s P p 0 1 1 r p .004 w .21429 .29286 m .21429 .00714 L s P .004 w .02381 .29286 m .97619 .29286 L s P p 0 1 1 r p .004 w .30952 .29286 m .30952 .00714 L s P .004 w .02381 .00714 m .97619 .00714 L s P p 0 1 1 r p .004 w .30952 .29286 m .30952 .00714 L s P .004 w .02381 .10238 m .97619 .10238 L s P p 0 1 1 r p .004 w .30952 .29286 m .30952 .00714 L s P .004 w .02381 .19762 m .97619 .19762 L s P p 0 1 1 r p .004 w .30952 .29286 m .30952 .00714 L s P .004 w .02381 .29286 m .97619 .29286 L s P p 0 1 1 r p .004 w .40476 .29286 m .40476 .00714 L s P .004 w .02381 .00714 m .97619 .00714 L s P p 0 1 1 r p .004 w .40476 .29286 m .40476 .00714 L s P .004 w .02381 .10238 m .97619 .10238 L s P p 0 1 1 r p .004 w .40476 .29286 m .40476 .00714 L s P .004 w .02381 .19762 m .97619 .19762 L s P p 0 1 1 r p .004 w .40476 .29286 m .40476 .00714 L s P .004 w .02381 .29286 m .97619 .29286 L s P p 0 1 1 r p .004 w .5 .29286 m .5 .00714 L s P .004 w .02381 .00714 m .97619 .00714 L s P p 0 1 1 r p .004 w .5 .29286 m .5 .00714 L s P .004 w .02381 .10238 m .97619 .10238 L s P p 0 1 1 r p .004 w .5 .29286 m .5 .00714 L s P .004 w .02381 .19762 m .97619 .19762 L s P p 0 1 1 r p .004 w .5 .29286 m .5 .00714 L s P .004 w .02381 .29286 m .97619 .29286 L s P p 0 1 1 r p .004 w .59524 .29286 m .59524 .00714 L s P .004 w .02381 .00714 m .97619 .00714 L s P p 0 1 1 r p .004 w .59524 .29286 m .59524 .00714 L s P .004 w .02381 .10238 m .97619 .10238 L s P p 0 1 1 r p .004 w .59524 .29286 m .59524 .00714 L s P .004 w .02381 .19762 m .97619 .19762 L s P p 0 1 1 r p .004 w .59524 .29286 m .59524 .00714 L s P .004 w .02381 .29286 m .97619 .29286 L s P p 0 1 1 r p .004 w .69048 .29286 m .69048 .00714 L s P .004 w .02381 .00714 m .97619 .00714 L s P p 0 1 1 r p .004 w .69048 .29286 m .69048 .00714 L s P .004 w .02381 .10238 m .97619 .10238 L s P p 0 1 1 r p .004 w .69048 .29286 m .69048 .00714 L s P .004 w .02381 .19762 m .97619 .19762 L s P p 0 1 1 r p .004 w .69048 .29286 m .69048 .00714 L s P .004 w .02381 .29286 m .97619 .29286 L s P p 0 1 1 r p .004 w .78571 .29286 m .78571 .00714 L s P .004 w .02381 .00714 m .97619 .00714 L s P p 0 1 1 r p .004 w .78571 .29286 m .78571 .00714 L s P .004 w .02381 .10238 m .97619 .10238 L s P p 0 1 1 r p .004 w .78571 .29286 m .78571 .00714 L s P .004 w .02381 .19762 m .97619 .19762 L s P p 0 1 1 r p .004 w .78571 .29286 m .78571 .00714 L s P .004 w .02381 .29286 m .97619 .29286 L s P p 0 1 1 r p .004 w .88095 .29286 m .88095 .00714 L s P .004 w .02381 .00714 m .97619 .00714 L s P p 0 1 1 r p .004 w .88095 .29286 m .88095 .00714 L s P .004 w .02381 .10238 m .97619 .10238 L s P p 0 1 1 r p .004 w .88095 .29286 m .88095 .00714 L s P .004 w .02381 .19762 m .97619 .19762 L s P p 0 1 1 r p .004 w .88095 .29286 m .88095 .00714 L s P .004 w .02381 .29286 m .97619 .29286 L s P p 0 1 1 r p .004 w .97619 .29286 m .97619 .00714 L s P .004 w .02381 .00714 m .97619 .00714 L s P p 0 1 1 r p .004 w .97619 .29286 m .97619 .00714 L s P .004 w .02381 .10238 m .97619 .10238 L s P p 0 1 1 r p .004 w .97619 .29286 m .97619 .00714 L s P .004 w .02381 .19762 m .97619 .19762 L s P p 0 1 1 r p .004 w .97619 .29286 m .97619 .00714 L s P .004 w .02381 .29286 m .97619 .29286 L s P p 1 0 0 r .004 w .21429 .19762 m .21429 .00714 L s P [(base = 7 units, height = 2 units)] .21429 .29286 -1 0 Mshowa P % End of Graphics MathPictureEnd :[font = section; inactive; preserveAspect; fontColorRed = 21844; fontColorGreen = 21844; fontColorBlue = 21844; fontSize = 14; startGroup] Consider the above parallelogram. Area = 14 units (count the squares inside!) What happens when we cut the triangle shape off of the left of the parallelogram and move it right? :[font = input; preserveAspect; startGroup] tri[d_]:=Polygon[{{0+d,0},{2+d,2},{2+d,0}}] trap=Graphics[{RGBColor[0,1,0],Thickness[.01], Line[{{2,2},{9,2},{7,0},{2,0},{2,2}}]}]; Do[Show[trap,Graphics[{tri[d],Thickness[.1]}],grid[3,10], Axes->True,AspectRatio->Automatic, PlotRange->{{0.2,10},{-0.2,2.2}}], {d,0,7}] :[font = postscript; PostScript; formatAsPostScript; output; inactive; Cclosed; preserveAspect; pictureLeft = 19; pictureTop = 2; pictureWidth = 378; pictureHeight = 92; startGroup; animationSpeed = 30] %! %%Creator: Mathematica %%AspectRatio: .2449 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations -0.0204082 0.102041 0.0204082 0.102041 [ [(4)] .38776 .02041 0 2 Msboxa [(6)] .59184 .02041 0 2 Msboxa [(8)] .79592 .02041 0 2 Msboxa [(10)] 1 .02041 0 2 Msboxa [(0.5)] .17117 .07143 1 0 Msboxa [(1)] .17117 .12245 1 0 Msboxa [(1.5)] .17117 .17347 1 0 Msboxa [(2)] .17117 .22449 1 0 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 .2459 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p p .002 w .38776 .02041 m .38776 .02666 L s P [(4)] .38776 .02041 0 2 Mshowa p .002 w .59184 .02041 m .59184 .02666 L s P [(6)] .59184 .02041 0 2 Mshowa p .002 w .79592 .02041 m .79592 .02666 L s P [(8)] .79592 .02041 0 2 Mshowa p .002 w 1 .02041 m 1 .02666 L s P [(10)] 1 .02041 0 2 Mshowa p .001 w .22449 .02041 m .22449 .02416 L s P p .001 w .26531 .02041 m .26531 .02416 L s P p .001 w .30612 .02041 m .30612 .02416 L s P p .001 w .34694 .02041 m .34694 .02416 L s P p .001 w .42857 .02041 m .42857 .02416 L s P p .001 w .46939 .02041 m .46939 .02416 L s P p .001 w .5102 .02041 m .5102 .02416 L s P p .001 w .55102 .02041 m .55102 .02416 L s P p .001 w .63265 .02041 m .63265 .02416 L s P p .001 w .67347 .02041 m .67347 .02416 L s P p .001 w .71429 .02041 m .71429 .02416 L s P p .001 w .7551 .02041 m .7551 .02416 L s P p .001 w .83673 .02041 m .83673 .02416 L s P p .001 w .87755 .02041 m .87755 .02416 L s P p .001 w .91837 .02041 m .91837 .02416 L s P p .001 w .95918 .02041 m .95918 .02416 L s P p .001 w .14286 .02041 m .14286 .02416 L s P p .001 w .10204 .02041 m .10204 .02416 L s P p .001 w .06122 .02041 m .06122 .02416 L s P p .001 w .02041 .02041 m .02041 .02416 L s P p .002 w 0 .02041 m 1 .02041 L s P p .002 w .18367 .07143 m .18992 .07143 L s P [(0.5)] .17117 .07143 1 0 Mshowa p .002 w .18367 .12245 m .18992 .12245 L s P [(1)] .17117 .12245 1 0 Mshowa p .002 w .18367 .17347 m .18992 .17347 L s P [(1.5)] .17117 .17347 1 0 Mshowa p .002 w .18367 .22449 m .18992 .22449 L s P [(2)] .17117 .22449 1 0 Mshowa p .001 w .18367 .03061 m .18742 .03061 L s P p .001 w .18367 .04082 m .18742 .04082 L s P p .001 w .18367 .05102 m .18742 .05102 L s P p .001 w .18367 .06122 m .18742 .06122 L s P p .001 w .18367 .08163 m .18742 .08163 L s P p .001 w .18367 .09184 m .18742 .09184 L s P p .001 w .18367 .10204 m .18742 .10204 L s P p .001 w .18367 .11224 m .18742 .11224 L s P p .001 w .18367 .13265 m .18742 .13265 L s P p .001 w .18367 .14286 m .18742 .14286 L s P p .001 w .18367 .15306 m .18742 .15306 L s P p .001 w .18367 .16327 m .18742 .16327 L s P p .001 w .18367 .18367 m .18742 .18367 L s P p .001 w .18367 .19388 m .18742 .19388 L s P p .001 w .18367 .20408 m .18742 .20408 L s P p .001 w .18367 .21429 m .18742 .21429 L s P p .001 w .18367 .0102 m .18742 .0102 L s P p .001 w .18367 .23469 m .18742 .23469 L s P p .001 w .18367 .2449 m .18742 .2449 L s P p .002 w .18367 0 m .18367 .2449 L s P P 0 0 m 1 0 L 1 .2449 L 0 .2449 L closepath clip newpath p p 0 1 0 r .01 w .18367 .22449 m .89796 .22449 L .69388 .02041 L .18367 .02041 L .18367 .22449 L s P p -0.02041 .02041 m .18367 .22449 L .18367 .02041 L F P p 0 1 1 r p .004 w s s P .004 w s 0 .02041 m 1 .02041 L s 1 .02041 m 0 0 rlineto P p 0 1 1 r p .004 w s s P .004 w s 0 .12245 m 1 .12245 L s 1 .12245 m 0 0 rlineto P p 0 1 1 r p .004 w s s P .004 w s 0 .22449 m 1 .22449 L s 1 .22449 m 0 0 rlineto P p 0 1 1 r p .004 w s s P .004 w s s P p 0 1 1 r p .004 w s .08163 .2449 m .08163 .02041 L s .08163 .02041 m 0 0 rlineto P .004 w s 0 .02041 m 1 .02041 L s 1 .02041 m 0 0 rlineto P p 0 1 1 r p .004 w s .08163 .2449 m .08163 .02041 L s .08163 .02041 m 0 0 rlineto P .004 w s 0 .12245 m 1 .12245 L s 1 .12245 m 0 0 rlineto P p 0 1 1 r p .004 w s .08163 .2449 m .08163 .02041 L s .08163 .02041 m 0 0 rlineto P .004 w s 0 .22449 m 1 .22449 L s 1 .22449 m 0 0 rlineto P p 0 1 1 r p .004 w s .08163 .2449 m .08163 .02041 L s .08163 .02041 m 0 0 rlineto P .004 w s s P p 0 1 1 r p .004 w s .18367 .2449 m .18367 .02041 L s .18367 .02041 m 0 0 rlineto P .004 w s 0 .02041 m 1 .02041 L s 1 .02041 m 0 0 rlineto P p 0 1 1 r p .004 w s .18367 .2449 m .18367 .02041 L s .18367 .02041 m 0 0 rlineto P .004 w s 0 .12245 m 1 .12245 L s 1 .12245 m 0 0 rlineto P p 0 1 1 r p .004 w s .18367 .2449 m .18367 .02041 L s .18367 .02041 m 0 0 rlineto P .004 w s 0 .22449 m 1 .22449 L s 1 .22449 m 0 0 rlineto P p 0 1 1 r p .004 w s .18367 .2449 m .18367 .02041 L s .18367 .02041 m 0 0 rlineto P .004 w s s P p 0 1 1 r p .004 w s .28571 .2449 m .28571 .02041 L s .28571 .02041 m 0 0 rlineto P .004 w s 0 .02041 m 1 .02041 L s 1 .02041 m 0 0 rlineto P p 0 1 1 r p .004 w s .28571 .2449 m .28571 .02041 L s .28571 .02041 m 0 0 rlineto P .004 w s 0 .12245 m 1 .12245 L s 1 .12245 m 0 0 rlineto P p 0 1 1 r p .004 w s .28571 .2449 m .28571 .02041 L s .28571 .02041 m 0 0 rlineto P .004 w s 0 .22449 m 1 .22449 L s 1 .22449 m 0 0 rlineto P p 0 1 1 r p .004 w s .28571 .2449 m .28571 .02041 L s .28571 .02041 m 0 0 rlineto P .004 w s s P p 0 1 1 r p .004 w s .38776 .2449 m .38776 .02041 L s .38776 .02041 m 0 0 rlineto P .004 w s 0 .02041 m 1 .02041 L s 1 .02041 m 0 0 rlineto P p 0 1 1 r p .004 w s .38776 .2449 m .38776 .02041 L s .38776 .02041 m 0 0 rlineto P .004 w s 0 .12245 m 1 .12245 L s 1 .12245 m 0 0 rlineto P p 0 1 1 r p .004 w s .38776 .2449 m .38776 .02041 L s .38776 .02041 m 0 0 rlineto P .004 w s 0 .22449 m 1 .22449 L s 1 .22449 m 0 0 rlineto P p 0 1 1 r p .004 w s .38776 .2449 m .38776 .02041 L s .38776 .02041 m 0 0 rlineto P .004 w s s P p 0 1 1 r p .004 w s .4898 .2449 m .4898 .02041 L s .4898 .02041 m 0 0 rlineto P .004 w s 0 .02041 m 1 .02041 L s 1 .02041 m 0 0 rlineto P p 0 1 1 r p .004 w s .4898 .2449 m .4898 .02041 L s .4898 .02041 m 0 0 rlineto P .004 w s 0 .12245 m 1 .12245 L s 1 .12245 m 0 0 rlineto P p 0 1 1 r p .004 w s .4898 .2449 m .4898 .02041 L s .4898 .02041 m 0 0 rlineto P .004 w s 0 .22449 m 1 .22449 L s 1 .22449 m 0 0 rlineto P p 0 1 1 r p .004 w s .4898 .2449 m .4898 .02041 L s .4898 .02041 m 0 0 rlineto P .004 w s s P p 0 1 1 r p .004 w s .59184 .2449 m .59184 .02041 L s .59184 .02041 m 0 0 rlineto P .004 w s 0 .02041 m 1 .02041 L s 1 .02041 m 0 0 rlineto P p 0 1 1 r p .004 w s .59184 .2449 m .59184 .02041 L s .59184 .02041 m 0 0 rlineto P .004 w s 0 .12245 m 1 .12245 L s 1 .12245 m 0 0 rlineto P p 0 1 1 r p .004 w s .59184 .2449 m .59184 .02041 L s .59184 .02041 m 0 0 rlineto P .004 w s 0 .22449 m 1 .22449 L s 1 .22449 m 0 0 rlineto P p 0 1 1 r p .004 w s .59184 .2449 m .59184 .02041 L s .59184 .02041 m 0 0 rlineto P .004 w s s P p 0 1 1 r p .004 w s .69388 .2449 m .69388 .02041 L s .69388 .02041 m 0 0 rlineto P .004 w s 0 .02041 m 1 .02041 L s 1 .02041 m 0 0 rlineto P p 0 1 1 r p .004 w s .69388 .2449 m .69388 .02041 L s .69388 .02041 m 0 0 rlineto P .004 w s 0 .12245 m 1 .12245 L s 1 .12245 m 0 0 rlineto P p 0 1 1 r p .004 w s .69388 .2449 m .69388 .02041 L s .69388 .02041 m 0 0 rlineto P .004 w s 0 .22449 m 1 .22449 L s 1 .22449 m 0 0 rlineto P p 0 1 1 r p .004 w s .69388 .2449 m .69388 .02041 L s .69388 .02041 m 0 0 rlineto P .004 w s s P p 0 1 1 r p .004 w s .79592 .2449 m .79592 .02041 L s .79592 .02041 m 0 0 rlineto P .004 w s 0 .02041 m 1 .02041 L s 1 .02041 m 0 0 rlineto P p 0 1 1 r p .004 w s .79592 .2449 m .79592 .02041 L s .79592 .02041 m 0 0 rlineto P .004 w s 0 .12245 m 1 .12245 L s 1 .12245 m 0 0 rlineto P p 0 1 1 r p .004 w s .79592 .2449 m .79592 .02041 L s .79592 .02041 m 0 0 rlineto P .004 w s 0 .22449 m 1 .22449 L s 1 .22449 m 0 0 rlineto P p 0 1 1 r p .004 w s .79592 .2449 m .79592 .02041 L s .79592 .02041 m 0 0 rlineto P .004 w s s P p 0 1 1 r p .004 w s .89796 .2449 m .89796 .02041 L s .89796 .02041 m 0 0 rlineto P .004 w s 0 .02041 m 1 .02041 L s 1 .02041 m 0 0 rlineto P p 0 1 1 r p .004 w s .89796 .2449 m .89796 .02041 L s .89796 .02041 m 0 0 rlineto P .004 w s 0 .12245 m 1 .12245 L s 1 .12245 m 0 0 rlineto P p 0 1 1 r p .004 w s .89796 .2449 m .89796 .02041 L s .89796 .02041 m 0 0 rlineto P .004 w s 0 .22449 m 1 .22449 L s 1 .22449 m 0 0 rlineto P p 0 1 1 r p .004 w s .89796 .2449 m .89796 .02041 L s .89796 .02041 m 0 0 rlineto P .004 w s s P p 0 1 1 r p .004 w s 1 .2449 m 1 .02041 L s 1 .02041 m 0 0 rlineto P .004 w s 0 .02041 m 1 .02041 L s 1 .02041 m 0 0 rlineto P p 0 1 1 r p .004 w s 1 .2449 m 1 .02041 L s 1 .02041 m 0 0 rlineto P .004 w s 0 .12245 m 1 .12245 L s 1 .12245 m 0 0 rlineto P p 0 1 1 r p .004 w s 1 .2449 m 1 .02041 L s 1 .02041 m 0 0 rlineto P .004 w s 0 .22449 m 1 .22449 L s 1 .22449 m 0 0 rlineto P p 0 1 1 r p .004 w s 1 .2449 m 1 .02041 L s 1 .02041 m 0 0 rlineto P .004 w s s P P % End of Graphics MathPictureEnd :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 19; pictureTop = 2; pictureWidth = 378; pictureHeight = 92; animationSpeed = 30] %! %%Creator: Mathematica %%AspectRatio: .2449 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations -0.0204082 0.102041 0.0204082 0.102041 [ [(4)] .38776 .02041 0 2 Msboxa [(6)] .59184 .02041 0 2 Msboxa [(8)] .79592 .02041 0 2 Msboxa [(10)] 1 .02041 0 2 Msboxa [(0.5)] .17117 .07143 1 0 Msboxa [(1)] .17117 .12245 1 0 Msboxa [(1.5)] .17117 .17347 1 0 Msboxa [(2)] .17117 .22449 1 0 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 .2459 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin 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s P p 0 1 1 r p .004 w .8 1 m .8 0 L s P .004 w 0 .375 m .93333 .375 L s P p 0 1 1 r p .004 w .8 1 m .8 0 L s P .004 w 0 .5 m .93333 .5 L s P p 0 1 1 r p .004 w .8 1 m .8 0 L s P .004 w 0 .625 m .93333 .625 L s P p 0 1 1 r p .004 w .8 1 m .8 0 L s P .004 w 0 .75 m .93333 .75 L s P p 0 1 1 r p .004 w .8 1 m .8 0 L s P .004 w 0 .875 m .93333 .875 L s P p 0 1 1 r p .004 w .8 1 m .8 0 L s P .004 w 0 1 m .93333 1 L s P p 0 1 1 r p .004 w .86667 1 m .86667 0 L s P .004 w 0 0 m .93333 0 L s P p 0 1 1 r p .004 w .86667 1 m .86667 0 L s P .004 w 0 .125 m .93333 .125 L s P p 0 1 1 r p .004 w .86667 1 m .86667 0 L s P .004 w 0 .25 m .93333 .25 L s P p 0 1 1 r p .004 w .86667 1 m .86667 0 L s P .004 w 0 .375 m .93333 .375 L s P p 0 1 1 r p .004 w .86667 1 m .86667 0 L s P .004 w 0 .5 m .93333 .5 L s P p 0 1 1 r p .004 w .86667 1 m .86667 0 L s P .004 w 0 .625 m .93333 .625 L s P p 0 1 1 r p .004 w .86667 1 m .86667 0 L s P .004 w 0 .75 m .93333 .75 L s P p 0 1 1 r p .004 w .86667 1 m .86667 0 L s P .004 w 0 .875 m .93333 .875 L s P p 0 1 1 r p .004 w .86667 1 m .86667 0 L s P .004 w 0 1 m .93333 1 L s P p 0 1 1 r p .004 w .93333 1 m .93333 0 L s P .004 w 0 0 m .93333 0 L s P p 0 1 1 r p .004 w .93333 1 m .93333 0 L s P .004 w 0 .125 m .93333 .125 L s P p 0 1 1 r p .004 w .93333 1 m .93333 0 L s P .004 w 0 .25 m .93333 .25 L s P p 0 1 1 r p .004 w .93333 1 m .93333 0 L s P .004 w 0 .375 m .93333 .375 L s P p 0 1 1 r p .004 w .93333 1 m .93333 0 L s P .004 w 0 .5 m .93333 .5 L s P p 0 1 1 r p .004 w .93333 1 m .93333 0 L s P .004 w 0 .625 m .93333 .625 L s P p 0 1 1 r p .004 w .93333 1 m .93333 0 L s P .004 w 0 .75 m .93333 .75 L s P p 0 1 1 r p .004 w .93333 1 m .93333 0 L s P .004 w 0 .875 m .93333 .875 L s P p 0 1 1 r p .004 w .93333 1 m .93333 0 L s P .004 w 0 1 m .93333 1 L s P p 1 0 0 r .004 w .6 .875 m .6 0 L s P [(base = 4)] .36667 .0375 -1 0 Mshowa p 1 0 0 r [(height = 7)] .33333 .5 1 0 Mshowa P P % End of Graphics MathPictureEnd :[font = subsection; inactive; preserveAspect; fontSize = 14; startGroup] Now let's cut this parallelogram into shapes. :[font = input; preserveAspect; startGroup] cut2=Graphics[{RGBColor[1,0,0],Line[{{5,3.5},{5,0}}]}]; Show[poly3,cut,cut2,Graphics[{Text["SHAPE 1",{5.2,3},{-1,0}], Text["SHAPE 2",{2.2,1}, {-1,0}]}], Axes->True,AspectRatio->1,PlotRange->{{0,15},{0,8}}]; :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 19; pictureTop = 2; pictureWidth = 214; pictureHeight = 214; endGroup; endGroup] %! %%Creator: Mathematica %%AspectRatio: 1 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0 0.0666667 0 0.125 [ [(2)] .13333 0 0 2 Msboxa [(4)] .26667 0 0 2 Msboxa [(6)] .4 0 0 2 Msboxa [(8)] .53333 0 0 2 Msboxa [(10)] .66667 0 0 2 Msboxa [(12)] .8 0 0 2 Msboxa [(14)] .93333 0 0 2 Msboxa [(0)] -0.0125 0 1 0 Msboxa [(1)] -0.0125 .125 1 0 Msboxa [(2)] -0.0125 .25 1 0 Msboxa [(3)] -0.0125 .375 1 0 Msboxa [(4)] -0.0125 .5 1 0 Msboxa [(5)] -0.0125 .625 1 0 Msboxa [(6)] -0.0125 .75 1 0 Msboxa [(7)] -0.0125 .875 1 0 Msboxa [(8)] -0.0125 1 1 0 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 1.001 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p p .002 w .13333 0 m .13333 .00625 L s P [(2)] .13333 0 0 2 Mshowa p .002 w .26667 0 m .26667 .00625 L s P [(4)] .26667 0 0 2 Mshowa p .002 w .4 0 m .4 .00625 L s P [(6)] .4 0 0 2 Mshowa p .002 w .53333 0 m .53333 .00625 L s P [(8)] .53333 0 0 2 Mshowa p .002 w .66667 0 m .66667 .00625 L s P [(10)] .66667 0 0 2 Mshowa p .002 w .8 0 m .8 .00625 L s P [(12)] .8 0 0 2 Mshowa p .002 w .93333 0 m .93333 .00625 L s P [(14)] .93333 0 0 2 Mshowa p .001 w .02667 0 m .02667 .00375 L s P p .001 w .05333 0 m .05333 .00375 L s P p .001 w .08 0 m .08 .00375 L s P p .001 w .10667 0 m .10667 .00375 L s P p .001 w .16 0 m .16 .00375 L s P p .001 w .18667 0 m .18667 .00375 L s P p .001 w .21333 0 m .21333 .00375 L s P p .001 w .24 0 m .24 .00375 L s P p .001 w .29333 0 m .29333 .00375 L s P p .001 w .32 0 m .32 .00375 L s P p .001 w .34667 0 m .34667 .00375 L s P p .001 w .37333 0 m .37333 .00375 L s P p .001 w .42667 0 m .42667 .00375 L s P p .001 w .45333 0 m .45333 .00375 L s P p .001 w .48 0 m .48 .00375 L s P p .001 w .50667 0 m .50667 .00375 L s P p .001 w .56 0 m .56 .00375 L s P p .001 w .58667 0 m .58667 .00375 L s P p .001 w .61333 0 m .61333 .00375 L s P p .001 w .64 0 m .64 .00375 L s P p .001 w .69333 0 m .69333 .00375 L s P p .001 w .72 0 m .72 .00375 L s P p .001 w .74667 0 m .74667 .00375 L s P p .001 w .77333 0 m .77333 .00375 L s P p .001 w .82667 0 m .82667 .00375 L s P p .001 w .85333 0 m .85333 .00375 L s P p .001 w .88 0 m .88 .00375 L s P p .001 w .90667 0 m .90667 .00375 L s P p .001 w .96 0 m .96 .00375 L s P p .001 w .98667 0 m .98667 .00375 L s P p .002 w 0 0 m 1 0 L s P p .002 w 0 0 m .00625 0 L s P [(0)] -0.0125 0 1 0 Mshowa p .002 w 0 .125 m .00625 .125 L s P [(1)] -0.0125 .125 1 0 Mshowa p .002 w 0 .25 m .00625 .25 L s P [(2)] -0.0125 .25 1 0 Mshowa p .002 w 0 .375 m .00625 .375 L s P [(3)] -0.0125 .375 1 0 Mshowa p .002 w 0 .5 m .00625 .5 L s P [(4)] -0.0125 .5 1 0 Mshowa p .002 w 0 .625 m .00625 .625 L s P [(5)] -0.0125 .625 1 0 Mshowa p .002 w 0 .75 m .00625 .75 L s P [(6)] -0.0125 .75 1 0 Mshowa p .002 w 0 .875 m .00625 .875 L s P [(7)] -0.0125 .875 1 0 Mshowa p .002 w 0 1 m .00625 1 L s P [(8)] -0.0125 1 1 0 Mshowa p .001 w 0 .025 m .00375 .025 L s P p .001 w 0 .05 m .00375 .05 L s P p .001 w 0 .075 m .00375 .075 L s P p .001 w 0 .1 m .00375 .1 L s P p .001 w 0 .15 m .00375 .15 L s P p .001 w 0 .175 m .00375 .175 L s P p .001 w 0 .2 m .00375 .2 L s P p .001 w 0 .225 m .00375 .225 L s P p .001 w 0 .275 m .00375 .275 L s P p .001 w 0 .3 m .00375 .3 L s P p .001 w 0 .325 m .00375 .325 L s P p .001 w 0 .35 m .00375 .35 L s P p .001 w 0 .4 m .00375 .4 L s P p .001 w 0 .425 m .00375 .425 L s P p .001 w 0 .45 m .00375 .45 L s P p .001 w 0 .475 m .00375 .475 L s P p .001 w 0 .525 m .00375 .525 L s P p .001 w 0 .55 m .00375 .55 L s P p .001 w 0 .575 m .00375 .575 L s P p .001 w 0 .6 m .00375 .6 L s P p .001 w 0 .65 m .00375 .65 L s P p .001 w 0 .675 m .00375 .675 L s P p .001 w 0 .7 m .00375 .7 L s P p .001 w 0 .725 m .00375 .725 L s P p .001 w 0 .775 m .00375 .775 L s P p .001 w 0 .8 m .00375 .8 L s P p .001 w 0 .825 m .00375 .825 L s P p .001 w 0 .85 m .00375 .85 L s P p .001 w 0 .9 m .00375 .9 L s P p .001 w 0 .925 m .00375 .925 L s P p .001 w 0 .95 m .00375 .95 L s P p .001 w 0 .975 m .00375 .975 L s P p .002 w 0 0 m 0 1 L s P P 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath p p 0 0 1 r .06667 0 m .6 .875 L .86667 .875 L .33333 0 L F P p 1 0 0 r .004 w .6 .875 m .6 0 L s P p 1 0 0 r .004 w .33333 .4375 m .33333 0 L s P p [(SHAPE 1)] .34667 .375 -1 0 Mshowa [(SHAPE 2)] .14667 .125 -1 0 Mshowa P P % End of Graphics MathPictureEnd :[font = subsection; inactive; preserveAspect; fontSize = 14; startGroup] Let's move the parallelogram( SHAPE 1 ). :[font = input; preserveAspect; startGroup] Clear[tri] shape1=Graphics[{RGBColor[1,0,0], Polygon[{{9,3.5},{9,7},{13,7}}]}]; parr[d_]:=Polygon[{{5+d,0},{9+d,3.5},{9+d,7},{5+d,3.5}}]; tri[c_]:=Polygon[{{1+c,0},{5+c,0},{5+c,3.5}}]; Do[Show[shape1,Graphics[{RGBColor[0,0,1],parr[d]}], Axes->True,AspectRatio->Automatic, PlotRange->{{0,14},{0,8}}], {d,0,4}]; :[font = postscript; PostScript; formatAsPostScript; output; inactive; Cclosed; preserveAspect; pictureLeft = 19; pictureTop = 2; pictureWidth = 374; pictureHeight = 214; startGroup; animationSpeed = 30] %! %%Creator: Mathematica %%AspectRatio: .57143 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0 0.0714286 0 0.0714286 [ [(2)] .14286 0 0 2 Msboxa [(4)] .28571 0 0 2 Msboxa [(6)] .42857 0 0 2 Msboxa [(8)] .57143 0 0 2 Msboxa [(10)] .71429 0 0 2 Msboxa [(12)] .85714 0 0 2 Msboxa [(14)] 1 0 0 2 Msboxa [(0)] -0.0125 0 1 0 Msboxa [(1)] -0.0125 .07143 1 0 Msboxa [(2)] -0.0125 .14286 1 0 Msboxa [(3)] -0.0125 .21429 1 0 Msboxa [(4)] -0.0125 .28571 1 0 Msboxa [(5)] -0.0125 .35714 1 0 Msboxa [(6)] -0.0125 .42857 1 0 Msboxa [(7)] -0.0125 .5 1 0 Msboxa [(8)] -0.0125 .57143 1 0 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 .57243 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p p .002 w .14286 0 m .14286 .00625 L s P [(2)] .14286 0 0 2 Mshowa p .002 w .28571 0 m .28571 .00625 L s P [(4)] .28571 0 0 2 Mshowa p .002 w .42857 0 m .42857 .00625 L s P [(6)] .42857 0 0 2 Mshowa p .002 w .57143 0 m .57143 .00625 L s P [(8)] .57143 0 0 2 Mshowa p .002 w .71429 0 m .71429 .00625 L s P [(10)] .71429 0 0 2 Mshowa p .002 w .85714 0 m .85714 .00625 L s P [(12)] .85714 0 0 2 Mshowa p .002 w 1 0 m 1 .00625 L s P [(14)] 1 0 0 2 Mshowa p .001 w .02857 0 m .02857 .00375 L s P p .001 w .05714 0 m .05714 .00375 L s P p .001 w .08571 0 m .08571 .00375 L s P p .001 w .11429 0 m .11429 .00375 L s P p .001 w .17143 0 m .17143 .00375 L s P p .001 w .2 0 m .2 .00375 L s P p .001 w .22857 0 m .22857 .00375 L s P p .001 w .25714 0 m .25714 .00375 L s P p .001 w .31429 0 m .31429 .00375 L s P p .001 w .34286 0 m .34286 .00375 L s P p .001 w .37143 0 m .37143 .00375 L s P p .001 w .4 0 m .4 .00375 L s P p .001 w .45714 0 m .45714 .00375 L s P p .001 w .48571 0 m .48571 .00375 L s P p .001 w .51429 0 m .51429 .00375 L s P p .001 w .54286 0 m .54286 .00375 L s P p .001 w .6 0 m .6 .00375 L s P p .001 w .62857 0 m .62857 .00375 L s P p .001 w .65714 0 m .65714 .00375 L s P p .001 w .68571 0 m .68571 .00375 L s P p .001 w .74286 0 m .74286 .00375 L s P p .001 w .77143 0 m .77143 .00375 L s P p .001 w .8 0 m .8 .00375 L s P p .001 w .82857 0 m .82857 .00375 L s P p .001 w .88571 0 m .88571 .00375 L s P p .001 w .91429 0 m .91429 .00375 L s P p .001 w .94286 0 m .94286 .00375 L s P p .001 w .97143 0 m .97143 .00375 L s P p .002 w 0 0 m 1 0 L s P p .002 w 0 0 m .00625 0 L s P [(0)] -0.0125 0 1 0 Mshowa p .002 w 0 .07143 m .00625 .07143 L s P [(1)] -0.0125 .07143 1 0 Mshowa p .002 w 0 .14286 m .00625 .14286 L s P [(2)] -0.0125 .14286 1 0 Mshowa p .002 w 0 .21429 m .00625 .21429 L s P [(3)] -0.0125 .21429 1 0 Mshowa p .002 w 0 .28571 m .00625 .28571 L s P [(4)] -0.0125 .28571 1 0 Mshowa p .002 w 0 .35714 m .00625 .35714 L s P [(5)] -0.0125 .35714 1 0 Mshowa p .002 w 0 .42857 m .00625 .42857 L s P [(6)] -0.0125 .42857 1 0 Mshowa p .002 w 0 .5 m .00625 .5 L s P [(7)] -0.0125 .5 1 0 Mshowa p .002 w 0 .57143 m .00625 .57143 L s P [(8)] -0.0125 .57143 1 0 Mshowa p .001 w 0 .01429 m .00375 .01429 L s P p .001 w 0 .02857 m .00375 .02857 L s P p .001 w 0 .04286 m .00375 .04286 L s P p .001 w 0 .05714 m .00375 .05714 L s P p .001 w 0 .08571 m .00375 .08571 L s P p .001 w 0 .1 m .00375 .1 L s P p .001 w 0 .11429 m .00375 .11429 L s P p .001 w 0 .12857 m .00375 .12857 L s P p .001 w 0 .15714 m .00375 .15714 L s P p .001 w 0 .17143 m .00375 .17143 L s P p .001 w 0 .18571 m .00375 .18571 L s P p .001 w 0 .2 m .00375 .2 L s P p .001 w 0 .22857 m .00375 .22857 L s P p .001 w 0 .24286 m .00375 .24286 L s P p .001 w 0 .25714 m .00375 .25714 L s P p .001 w 0 .27143 m .00375 .27143 L s P p .001 w 0 .3 m .00375 .3 L s P p .001 w 0 .31429 m .00375 .31429 L s P p .001 w 0 .32857 m .00375 .32857 L s P p .001 w 0 .34286 m .00375 .34286 L s P p .001 w 0 .37143 m .00375 .37143 L s P p .001 w 0 .38571 m .00375 .38571 L s P p .001 w 0 .4 m .00375 .4 L s P p .001 w 0 .41429 m .00375 .41429 L s P p .001 w 0 .44286 m .00375 .44286 L s P p .001 w 0 .45714 m .00375 .45714 L s P p .001 w 0 .47143 m .00375 .47143 L s P p .001 w 0 .48571 m .00375 .48571 L s P p .001 w 0 .51429 m .00375 .51429 L s P p .001 w 0 .52857 m .00375 .52857 L s P p .001 w 0 .54286 m .00375 .54286 L s P p .001 w 0 .55714 m .00375 .55714 L s P p .002 w 0 0 m 0 .57143 L s P P 0 0 m 1 0 L 1 .57143 L 0 .57143 L closepath clip newpath p p 1 0 0 r .64286 .25 m .64286 .5 L .92857 .5 L F P p 0 0 1 r .35714 0 m .64286 .25 L .64286 .5 L .35714 .25 L F P P % End of Graphics MathPictureEnd :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 19; pictureTop = 2; pictureWidth = 374; pictureHeight = 214; animationSpeed = 30] %! %%Creator: Mathematica %%AspectRatio: .57143 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0 0.0714286 0 0.0714286 [ [(2)] .14286 0 0 2 Msboxa [(4)] .28571 0 0 2 Msboxa [(6)] .42857 0 0 2 Msboxa [(8)] .57143 0 0 2 Msboxa [(10)] .71429 0 0 2 Msboxa [(12)] .85714 0 0 2 Msboxa [(14)] 1 0 0 2 Msboxa [(0)] -0.0125 0 1 0 Msboxa [(1)] -0.0125 .07143 1 0 Msboxa [(2)] -0.0125 .14286 1 0 Msboxa [(3)] -0.0125 .21429 1 0 Msboxa [(4)] -0.0125 .28571 1 0 Msboxa [(5)] -0.0125 .35714 1 0 Msboxa [(6)] -0.0125 .42857 1 0 Msboxa [(7)] -0.0125 .5 1 0 Msboxa [(8)] -0.0125 .57143 1 0 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 .57243 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p p .002 w .14286 0 m .14286 .00625 L s P [(2)] .14286 0 0 2 Mshowa p .002 w .28571 0 m .28571 .00625 L s P [(4)] .28571 0 0 2 Mshowa p .002 w .42857 0 m .42857 .00625 L s P [(6)] .42857 0 0 2 Mshowa p .002 w .57143 0 m .57143 .00625 L s P [(8)] .57143 0 0 2 Mshowa p .002 w .71429 0 m .71429 .00625 L s P [(10)] .71429 0 0 2 Mshowa p .002 w .85714 0 m .85714 .00625 L s P [(12)] .85714 0 0 2 Mshowa p .002 w 1 0 m 1 .00625 L s P [(14)] 1 0 0 2 Mshowa p .001 w .02857 0 m .02857 .00375 L s P p .001 w .05714 0 m .05714 .00375 L s P p .001 w .08571 0 m .08571 .00375 L s P p .001 w .11429 0 m .11429 .00375 L s P p .001 w .17143 0 m .17143 .00375 L s P p .001 w .2 0 m .2 .00375 L s P p .001 w .22857 0 m .22857 .00375 L s P p .001 w .25714 0 m .25714 .00375 L s P p .001 w .31429 0 m .31429 .00375 L s P p .001 w .34286 0 m .34286 .00375 L s P p .001 w .37143 0 m .37143 .00375 L s P p .001 w .4 0 m .4 .00375 L s P p .001 w .45714 0 m .45714 .00375 L s P p .001 w .48571 0 m .48571 .00375 L s P p .001 w .51429 0 m .51429 .00375 L s P p .001 w .54286 0 m .54286 .00375 L s P p .001 w .6 0 m .6 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