(*^ ::[ 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 = "NeXT Mathematica Notebook Front End Version 2.2"; NeXTStandardFontEncoding; fontset = title, inactive, noPageBreakBelow, noPageBreakInGroup, nohscroll, preserveAspect, groupLikeTitle, center, M7, bold, L1, e8, 24, "Times"; ; fontset = subtitle, inactive, noPageBreakBelow, noPageBreakInGroup, nohscroll, preserveAspect, groupLikeTitle, center, M7, bold, L1, e6, 18, "Times"; ; fontset = subsubtitle, inactive, noPageBreakBelow, noPageBreakInGroup, nohscroll, preserveAspect, groupLikeTitle, center, M7, italic, L1, e6, 14, "Times"; ; fontset = section, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, grayBox, M22, bold, L1, a20, 18, "Times"; ; fontset = subsection, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, blackBox, M19, bold, L1, a15, 14, "Times"; ; fontset = subsubsection, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, whiteBox, M18, bold, L1, a12, 12, "Times"; ; fontset = text, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 12; fontset = smalltext, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 10, "Times"; ; fontset = input, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeInput, M42, N23, bold, L1, 12, "Courier"; ; fontset = output, output, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, L-5, 12, "Courier"; ; fontset = message, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, L1, 12, "Courier"; ; fontset = print, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, L1, 12, "Courier"; ; fontset = info, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, L1, 12, "Courier"; ; fontset = postscript, PostScript, formatAsPostScript, output, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeGraphics, M7, l34, w282, h287, L1, 12, "Courier"; ; fontset = name, inactive, noPageBreakInGroup, nohscroll, preserveAspect, M7, italic, B65535, L1, 10, "Times"; ; fontset = header, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, italic, L1, 12, "Times"; ; fontset = leftheader, 12; fontset = footer, inactive, nohscroll, noKeepOnOnePage, preserveAspect, center, M7, italic, L1, 12, "Times"; ; fontset = leftfooter, 12; fontset = help, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 12; fontset = clipboard, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 12; fontset = completions, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 12, "Courier"; ; fontset = special1, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 12; fontset = special2, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 12; fontset = special3, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 12; fontset = special4, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 12; fontset = special5, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, L1, 12; paletteColors = 128; automaticGrouping; currentKernel; ] :[font = title; inactive; preserveAspect; startGroup] Why Is Pi the Same in C = 2 Pi r and A = Pi r^2? :[font = text; inactive; preserveAspect] We slice up a circle like a pie and rearrange the sectors to form a figure that is roughly a rectangle. As the sectors become thinner, the rectangle's left and right sides become more vertical and the top and bottom become flatter and more horizontal. We can imagine that in the limit we get an actual rectangle. The height of the rectangle equals the radius of the circle, r, and its length C/2. This is because the top and bottom of the rectangle are made up of all the small arcs that add up to the circumference of the circle. Since the rectangle has the same area as the circle, the length times the height is C/2 r = Pi r^2. Canceling r on both sides and multiplying by 2 gives the formula C = 2 Pi r. :[font = input; preserveAspect; startGroup] PiRectangle[4]; :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 282; pictureHeight = 96; endGroup] %! %%Creator: Mathematica %%AspectRatio: .34315 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.514018 0.163403 0.171573 0.163403 [ [ 0 0 0 0 ] [ 1 .34315 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p P 0 0 m 1 0 L 1 .34315 L 0 .34315 L closepath clip newpath p 1 0 0 r p .004 w .18721 .17157 m .18721 .17157 .1634 0 90 arc F .18721 .17157 m .18721 .17157 .1634 180 270 arc F .18721 .17157 m .18721 .17157 .1634 360 450 arc F .18721 .17157 m .18721 .17157 .1634 540 630 arc F P 0 1 0 r p .004 w .18721 .17157 m .18721 .17157 .1634 90 180 arc F .18721 .17157 m .18721 .17157 .1634 270 360 arc F .18721 .17157 m .18721 .17157 .1634 450 540 arc F .18721 .17157 m .18721 .17157 .1634 630 720 arc F P 1 0 0 r p .004 w .51402 .17157 m .51402 .17157 .1634 -135 -45 arc F .7451 .17157 m .7451 .17157 .1634 -135 -45 arc F P 0 1 0 r p .004 w .62956 .05603 m .62956 .05603 .1634 45 135 arc F .86065 .05603 m .86065 .05603 .1634 45 135 arc F P P % End of Graphics MathPictureEnd :[font = input; preserveAspect; startGroup] PiRectangle[6]; :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 282; pictureHeight = 93; endGroup] %! %%Creator: Mathematica %%AspectRatio: .33333 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.15873 0.166667 0.15873 [ [ 0 0 0 0 ] [ 1 .33333 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p P 0 0 m 1 0 L 1 .33333 L 0 .33333 L closepath clip newpath p 1 0 0 r p .004 w .18254 .16667 m .18254 .16667 .15873 0 60 arc F .18254 .16667 m .18254 .16667 .15873 120 180 arc F .18254 .16667 m .18254 .16667 .15873 240 300 arc F .18254 .16667 m .18254 .16667 .15873 360 420 arc F .18254 .16667 m .18254 .16667 .15873 480 540 arc F .18254 .16667 m .18254 .16667 .15873 600 660 arc F P 0 1 0 r p .004 w .18254 .16667 m .18254 .16667 .15873 60 120 arc F .18254 .16667 m .18254 .16667 .15873 180 240 arc F .18254 .16667 m .18254 .16667 .15873 300 360 arc F .18254 .16667 m .18254 .16667 .15873 420 480 arc F .18254 .16667 m .18254 .16667 .15873 540 600 arc F .18254 .16667 m .18254 .16667 .15873 660 720 arc F P 1 0 0 r p .004 w .5 .16667 m .5 .16667 .15873 -120 -60 arc F .65873 .16667 m .65873 .16667 .15873 -120 -60 arc F .81746 .16667 m .81746 .16667 .15873 -120 -60 arc F P 0 1 0 r p .004 w .57937 .0292 m .57937 .0292 .15873 60 120 arc F .7381 .0292 m .7381 .0292 .15873 60 120 arc F .89683 .0292 m .89683 .0292 .15873 60 120 arc F P P % End of Graphics MathPictureEnd :[font = input; preserveAspect; startGroup] PiRectangle[8]; :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 282; pictureHeight = 93; endGroup] %! %%Creator: Mathematica %%AspectRatio: .32995 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.495171 0.157121 0.164977 0.157121 [ [ 0 0 0 0 ] [ 1 .32995 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p P 0 0 m 1 0 L 1 .32995 L 0 .32995 L closepath clip newpath p 1 0 0 r p .004 w .18093 .16498 m .18093 .16498 .15712 0 45 arc F .18093 .16498 m .18093 .16498 .15712 90 135 arc F .18093 .16498 m .18093 .16498 .15712 180 225 arc F .18093 .16498 m .18093 .16498 .15712 270 315 arc F .18093 .16498 m .18093 .16498 .15712 360 405 arc F .18093 .16498 m .18093 .16498 .15712 450 495 arc F .18093 .16498 m .18093 .16498 .15712 540 585 arc F .18093 .16498 m .18093 .16498 .15712 630 675 arc F P 0 1 0 r p .004 w .18093 .16498 m .18093 .16498 .15712 45 90 arc F .18093 .16498 m .18093 .16498 .15712 135 180 arc F .18093 .16498 m .18093 .16498 .15712 225 270 arc F .18093 .16498 m .18093 .16498 .15712 315 360 arc F .18093 .16498 m .18093 .16498 .15712 405 450 arc F .18093 .16498 m .18093 .16498 .15712 495 540 arc F .18093 .16498 m .18093 .16498 .15712 585 630 arc F .18093 .16498 m .18093 .16498 .15712 675 720 arc F P 1 0 0 r p .004 w .49517 .16498 m .49517 .16498 .15712 -112.5 -67.5 arc F .61543 .16498 m .61543 .16498 .15712 -112.5 -67.5 arc F .73568 .16498 m .73568 .16498 .15712 -112.5 -67.5 arc F .85594 .16498 m .85594 .16498 .15712 -112.5 -67.5 arc F P 0 1 0 r p .004 w .5553 .01982 m .5553 .01982 .15712 67.5 112.5 arc F .67555 .01982 m .67555 .01982 .15712 67.5 112.5 arc F .79581 .01982 m .79581 .01982 .15712 67.5 112.5 arc F .91606 .01982 m .91606 .01982 .15712 67.5 112.5 arc F P P % End of Graphics MathPictureEnd :[font = input; preserveAspect; startGroup] PiRectangle[10]; :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 282; pictureHeight = 92; endGroup] %! %%Creator: Mathematica %%AspectRatio: .3284 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.49295 0.15638 0.164199 0.15638 [ [ 0 0 0 0 ] [ 1 .3284 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p P 0 0 m 1 0 L 1 .3284 L 0 .3284 L closepath clip newpath p 1 0 0 r p .004 w .18019 .1642 m .18019 .1642 .15638 0 36 arc F .18019 .1642 m .18019 .1642 .15638 72 108 arc F .18019 .1642 m .18019 .1642 .15638 144 180 arc F .18019 .1642 m .18019 .1642 .15638 216 252 arc F .18019 .1642 m .18019 .1642 .15638 288 324 arc F .18019 .1642 m .18019 .1642 .15638 360 396 arc F .18019 .1642 m .18019 .1642 .15638 432 468 arc F .18019 .1642 m .18019 .1642 .15638 504 540 arc F .18019 .1642 m .18019 .1642 .15638 576 612 arc F .18019 .1642 m .18019 .1642 .15638 648 684 arc F P 0 1 0 r p .004 w .18019 .1642 m .18019 .1642 .15638 36 72 arc F .18019 .1642 m .18019 .1642 .15638 108 144 arc F .18019 .1642 m .18019 .1642 .15638 180 216 arc F .18019 .1642 m .18019 .1642 .15638 252 288 arc F .18019 .1642 m .18019 .1642 .15638 324 360 arc F .18019 .1642 m .18019 .1642 .15638 396 432 arc F .18019 .1642 m .18019 .1642 .15638 468 504 arc F .18019 .1642 m .18019 .1642 .15638 540 576 arc F .18019 .1642 m .18019 .1642 .15638 612 648 arc F .18019 .1642 m .18019 .1642 .15638 684 720 arc F P 1 0 0 r p .004 w .49295 .1642 m .49295 .1642 .15638 -108 -72 arc F .5896 .1642 m .5896 .1642 .15638 -108 -72 arc F .68625 .1642 m .68625 .1642 .15638 -108 -72 arc F .78289 .1642 m .78289 .1642 .15638 -108 -72 arc F .87954 .1642 m .87954 .1642 .15638 -108 -72 arc F P 0 1 0 r p .004 w .54127 .01547 m .54127 .01547 .15638 72 108 arc F .63792 .01547 m .63792 .01547 .15638 72 108 arc F .73457 .01547 m .73457 .01547 .15638 72 108 arc F .83122 .01547 m .83122 .01547 .15638 72 108 arc F .92787 .01547 m .92787 .01547 .15638 72 108 arc F P P % End of Graphics MathPictureEnd :[font = input; preserveAspect; startGroup] PiRectangle[12]; :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 282; pictureHeight = 92; endGroup] %! %%Creator: Mathematica %%AspectRatio: .32756 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.491746 0.155979 0.163778 0.155979 [ [ 0 0 0 0 ] [ 1 .32756 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p P 0 0 m 1 0 L 1 .32756 L 0 .32756 L closepath clip newpath p 1 0 0 r p .004 w .17979 .16378 m .17979 .16378 .15598 0 30 arc F .17979 .16378 m .17979 .16378 .15598 60 90 arc F .17979 .16378 m .17979 .16378 .15598 120 150 arc F .17979 .16378 m .17979 .16378 .15598 180 210 arc F .17979 .16378 m .17979 .16378 .15598 240 270 arc F .17979 .16378 m .17979 .16378 .15598 300 330 arc F .17979 .16378 m .17979 .16378 .15598 360 390 arc F .17979 .16378 m .17979 .16378 .15598 420 450 arc F .17979 .16378 m .17979 .16378 .15598 480 510 arc F .17979 .16378 m .17979 .16378 .15598 540 570 arc F .17979 .16378 m .17979 .16378 .15598 600 630 arc F .17979 .16378 m .17979 .16378 .15598 660 690 arc F P 0 1 0 r p .004 w .17979 .16378 m .17979 .16378 .15598 30 60 arc F .17979 .16378 m .17979 .16378 .15598 90 120 arc F .17979 .16378 m .17979 .16378 .15598 150 180 arc F .17979 .16378 m .17979 .16378 .15598 210 240 arc F .17979 .16378 m .17979 .16378 .15598 270 300 arc F .17979 .16378 m .17979 .16378 .15598 330 360 arc F .17979 .16378 m .17979 .16378 .15598 390 420 arc F .17979 .16378 m .17979 .16378 .15598 450 480 arc F .17979 .16378 m .17979 .16378 .15598 510 540 arc F .17979 .16378 m .17979 .16378 .15598 570 600 arc F .17979 .16378 m .17979 .16378 .15598 630 660 arc F .17979 .16378 m .17979 .16378 .15598 690 720 arc F P 1 0 0 r p .004 w .49175 .16378 m .49175 .16378 .15598 -105 -75 arc F .57249 .16378 m .57249 .16378 .15598 -105 -75 arc F .65323 .16378 m .65323 .16378 .15598 -105 -75 arc F .73397 .16378 m .73397 .16378 .15598 -105 -75 arc F .81471 .16378 m .81471 .16378 .15598 -105 -75 arc F .89545 .16378 m .89545 .16378 .15598 -105 -75 arc F P 0 1 0 r p .004 w .53212 .01311 m .53212 .01311 .15598 75 105 arc F .61286 .01311 m .61286 .01311 .15598 75 105 arc F .6936 .01311 m .6936 .01311 .15598 75 105 arc F .77434 .01311 m .77434 .01311 .15598 75 105 arc F .85508 .01311 m .85508 .01311 .15598 75 105 arc F .93582 .01311 m .93582 .01311 .15598 75 105 arc F P P % End of Graphics MathPictureEnd :[font = input; preserveAspect; startGroup] PiRectangle[20]; :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 282; pictureHeight = 92; endGroup] %! %%Creator: Mathematica %%AspectRatio: .32633 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.490001 0.155397 0.163167 0.155397 [ [ 0 0 0 0 ] [ 1 .32633 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p P 0 0 m 1 0 L 1 .32633 L 0 .32633 L closepath clip newpath p 1 0 0 r p .004 w .17921 .16317 m .17921 .16317 .1554 0 18 arc F .17921 .16317 m .17921 .16317 .1554 36 54 arc F .17921 .16317 m .17921 .16317 .1554 72 90 arc F .17921 .16317 m .17921 .16317 .1554 108 126 arc F .17921 .16317 m .17921 .16317 .1554 144 162 arc F .17921 .16317 m .17921 .16317 .1554 180 198 arc F .17921 .16317 m .17921 .16317 .1554 216 234 arc F .17921 .16317 m .17921 .16317 .1554 252 270 arc F .17921 .16317 m .17921 .16317 .1554 288 306 arc F .17921 .16317 m .17921 .16317 .1554 324 342 arc F .17921 .16317 m .17921 .16317 .1554 360 378 arc F .17921 .16317 m .17921 .16317 .1554 396 414 arc F .17921 .16317 m .17921 .16317 .1554 432 450 arc F .17921 .16317 m .17921 .16317 .1554 468 486 arc F .17921 .16317 m .17921 .16317 .1554 504 522 arc F .17921 .16317 m .17921 .16317 .1554 540 558 arc F .17921 .16317 m .17921 .16317 .1554 576 594 arc F .17921 .16317 m .17921 .16317 .1554 612 630 arc F .17921 .16317 m .17921 .16317 .1554 648 666 arc F .17921 .16317 m .17921 .16317 .1554 684 702 arc F P 0 1 0 r p .004 w .17921 .16317 m .17921 .16317 .1554 18 36 arc F .17921 .16317 m .17921 .16317 .1554 54 72 arc F .17921 .16317 m .17921 .16317 .1554 90 108 arc F .17921 .16317 m .17921 .16317 .1554 126 144 arc F .17921 .16317 m .17921 .16317 .1554 162 180 arc F .17921 .16317 m .17921 .16317 .1554 198 216 arc F .17921 .16317 m .17921 .16317 .1554 234 252 arc F .17921 .16317 m .17921 .16317 .1554 270 288 arc F .17921 .16317 m .17921 .16317 .1554 306 324 arc F .17921 .16317 m .17921 .16317 .1554 342 360 arc F .17921 .16317 m .17921 .16317 .1554 378 396 arc F .17921 .16317 m .17921 .16317 .1554 414 432 arc F .17921 .16317 m .17921 .16317 .1554 450 468 arc F .17921 .16317 m .17921 .16317 .1554 486 504 arc F .17921 .16317 m .17921 .16317 .1554 522 540 arc F .17921 .16317 m .17921 .16317 .1554 558 576 arc F .17921 .16317 m .17921 .16317 .1554 594 612 arc F .17921 .16317 m .17921 .16317 .1554 630 648 arc F .17921 .16317 m .17921 .16317 .1554 666 684 arc F .17921 .16317 m .17921 .16317 .1554 702 720 arc F P 1 0 0 r p .004 w .49 .16317 m .49 .16317 .1554 -99 -81 arc F .53862 .16317 m .53862 .16317 .1554 -99 -81 arc F .58724 .16317 m .58724 .16317 .1554 -99 -81 arc F .63586 .16317 m .63586 .16317 .1554 -99 -81 arc F .68448 .16317 m .68448 .16317 .1554 -99 -81 arc F .7331 .16317 m .7331 .16317 .1554 -99 -81 arc F .78171 .16317 m .78171 .16317 .1554 -99 -81 arc F .83033 .16317 m .83033 .16317 .1554 -99 -81 arc F .87895 .16317 m .87895 .16317 .1554 -99 -81 arc F .92757 .16317 m .92757 .16317 .1554 -99 -81 arc F P 0 1 0 r p .004 w .51431 .00968 m .51431 .00968 .1554 81 99 arc F .56293 .00968 m .56293 .00968 .1554 81 99 arc F .61155 .00968 m .61155 .00968 .1554 81 99 arc F .66017 .00968 m .66017 .00968 .1554 81 99 arc F .70879 .00968 m .70879 .00968 .1554 81 99 arc F .75741 .00968 m .75741 .00968 .1554 81 99 arc F .80602 .00968 m .80602 .00968 .1554 81 99 arc F .85464 .00968 m .85464 .00968 .1554 81 99 arc F .90326 .00968 m .90326 .00968 .1554 81 99 arc F .95188 .00968 m .95188 .00968 .1554 81 99 arc F P P % End of Graphics MathPictureEnd :[font = input; preserveAspect; startGroup] PiRectangle[30]; :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 282; pictureHeight = 91; endGroup] %! %%Creator: Mathematica %%AspectRatio: .32595 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.489457 0.155216 0.162977 0.155216 [ [ 0 0 0 0 ] [ 1 .32595 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p P 0 0 m 1 0 L 1 .32595 L 0 .32595 L closepath clip newpath p 1 0 0 r p .004 w .17903 .16298 m .17903 .16298 .15522 0 12 arc F .17903 .16298 m .17903 .16298 .15522 24 36 arc F .17903 .16298 m .17903 .16298 .15522 48 60 arc F .17903 .16298 m .17903 .16298 .15522 72 84 arc F .17903 .16298 m .17903 .16298 .15522 96 108 arc F .17903 .16298 m .17903 .16298 .15522 120 132 arc F .17903 .16298 m .17903 .16298 .15522 144 156 arc F .17903 .16298 m .17903 .16298 .15522 168 180 arc F .17903 .16298 m .17903 .16298 .15522 192 204 arc F .17903 .16298 m .17903 .16298 .15522 216 228 arc F .17903 .16298 m .17903 .16298 .15522 240 252 arc F .17903 .16298 m .17903 .16298 .15522 264 276 arc F .17903 .16298 m .17903 .16298 .15522 288 300 arc F .17903 .16298 m .17903 .16298 .15522 312 324 arc F .17903 .16298 m .17903 .16298 .15522 336 348 arc F .17903 .16298 m .17903 .16298 .15522 360 372 arc F .17903 .16298 m .17903 .16298 .15522 384 396 arc F .17903 .16298 m .17903 .16298 .15522 408 420 arc F .17903 .16298 m .17903 .16298 .15522 432 444 arc F .17903 .16298 m .17903 .16298 .15522 456 468 arc F .17903 .16298 m .17903 .16298 .15522 480 492 arc F .17903 .16298 m .17903 .16298 .15522 504 516 arc F .17903 .16298 m .17903 .16298 .15522 528 540 arc F .17903 .16298 m .17903 .16298 .15522 552 564 arc F .17903 .16298 m .17903 .16298 .15522 576 588 arc F .17903 .16298 m .17903 .16298 .15522 600 612 arc F .17903 .16298 m .17903 .16298 .15522 624 636 arc F .17903 .16298 m .17903 .16298 .15522 648 660 arc F .17903 .16298 m .17903 .16298 .15522 672 684 arc F .17903 .16298 m .17903 .16298 .15522 696 708 arc F P 0 1 0 r p .004 w .17903 .16298 m .17903 .16298 .15522 12 24 arc F .17903 .16298 m .17903 .16298 .15522 36 48 arc F .17903 .16298 m .17903 .16298 .15522 60 72 arc F .17903 .16298 m .17903 .16298 .15522 84 96 arc F .17903 .16298 m .17903 .16298 .15522 108 120 arc F .17903 .16298 m .17903 .16298 .15522 132 144 arc F .17903 .16298 m .17903 .16298 .15522 156 168 arc F .17903 .16298 m .17903 .16298 .15522 180 192 arc F .17903 .16298 m .17903 .16298 .15522 204 216 arc F .17903 .16298 m .17903 .16298 .15522 228 240 arc F .17903 .16298 m .17903 .16298 .15522 252 264 arc F .17903 .16298 m .17903 .16298 .15522 276 288 arc F .17903 .16298 m .17903 .16298 .15522 300 312 arc F .17903 .16298 m .17903 .16298 .15522 324 336 arc F .17903 .16298 m .17903 .16298 .15522 348 360 arc F .17903 .16298 m .17903 .16298 .15522 372 384 arc F .17903 .16298 m .17903 .16298 .15522 396 408 arc F .17903 .16298 m .17903 .16298 .15522 420 432 arc F .17903 .16298 m .17903 .16298 .15522 444 456 arc F .17903 .16298 m .17903 .16298 .15522 468 480 arc F .17903 .16298 m .17903 .16298 .15522 492 504 arc F .17903 .16298 m .17903 .16298 .15522 516 528 arc F .17903 .16298 m .17903 .16298 .15522 540 552 arc F .17903 .16298 m .17903 .16298 .15522 564 576 arc F .17903 .16298 m .17903 .16298 .15522 588 600 arc F .17903 .16298 m .17903 .16298 .15522 612 624 arc F .17903 .16298 m .17903 .16298 .15522 636 648 arc F .17903 .16298 m .17903 .16298 .15522 660 672 arc F .17903 .16298 m .17903 .16298 .15522 684 696 arc F .17903 .16298 m .17903 .16298 .15522 708 720 arc F P 1 0 0 r p .004 w .48946 .16298 m .48946 .16298 .15522 -96 -84 arc F .52191 .16298 m .52191 .16298 .15522 -96 -84 arc F .55435 .16298 m .55435 .16298 .15522 -96 -84 arc F .5868 .16298 m .5868 .16298 .15522 -96 -84 arc F .61925 .16298 m .61925 .16298 .15522 -96 -84 arc F .6517 .16298 m .6517 .16298 .15522 -96 -84 arc F .68415 .16298 m .68415 .16298 .15522 -96 -84 arc F .7166 .16298 m .7166 .16298 .15522 -96 -84 arc F .74905 .16298 m .74905 .16298 .15522 -96 -84 arc F .7815 .16298 m .7815 .16298 .15522 -96 -84 arc F .81395 .16298 m .81395 .16298 .15522 -96 -84 arc F .84639 .16298 m .84639 .16298 .15522 -96 -84 arc F .87884 .16298 m .87884 .16298 .15522 -96 -84 arc F .91129 .16298 m .91129 .16298 .15522 -96 -84 arc F .94374 .16298 m .94374 .16298 .15522 -96 -84 arc F P 0 1 0 r p .004 w .50568 .00861 m .50568 .00861 .15522 84 96 arc F .53813 .00861 m .53813 .00861 .15522 84 96 arc F .57058 .00861 m .57058 .00861 .15522 84 96 arc F .60303 .00861 m .60303 .00861 .15522 84 96 arc F .63548 .00861 m .63548 .00861 .15522 84 96 arc F .66793 .00861 m .66793 .00861 .15522 84 96 arc F .70037 .00861 m .70037 .00861 .15522 84 96 arc F .73282 .00861 m .73282 .00861 .15522 84 96 arc F .76527 .00861 m .76527 .00861 .15522 84 96 arc F .79772 .00861 m .79772 .00861 .15522 84 96 arc F .83017 .00861 m .83017 .00861 .15522 84 96 arc F .86262 .00861 m .86262 .00861 .15522 84 96 arc F .89507 .00861 m .89507 .00861 .15522 84 96 arc F .92752 .00861 m .92752 .00861 .15522 84 96 arc F .95997 .00861 m .95997 .00861 .15522 84 96 arc F P P % End of Graphics MathPictureEnd :[font = input; preserveAspect; startGroup] PiRectangle[50]; :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 282; pictureHeight = 91; endGroup] %! %%Creator: Mathematica %%AspectRatio: .32576 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.489178 0.155123 0.162879 0.155123 [ [ 0 0 0 0 ] [ 1 .32576 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p P 0 0 m 1 0 L 1 .32576 L 0 .32576 L closepath clip newpath p 1 0 0 r p .004 w .17893 .16288 m .17893 .16288 .15512 0 7.2 arc F .17893 .16288 m .17893 .16288 .15512 14.4 21.6 arc F .17893 .16288 m .17893 .16288 .15512 28.8 36 arc F .17893 .16288 m .17893 .16288 .15512 43.2 50.4 arc F .17893 .16288 m .17893 .16288 .15512 57.6 64.8 arc F .17893 .16288 m .17893 .16288 .15512 72 79.2 arc F .17893 .16288 m .17893 .16288 .15512 86.4 93.6 arc F .17893 .16288 m .17893 .16288 .15512 100.8 108 arc F .17893 .16288 m .17893 .16288 .15512 115.2 122.4 arc F .17893 .16288 m .17893 .16288 .15512 129.6 136.8 arc F .17893 .16288 m .17893 .16288 .15512 144 151.2 arc F .17893 .16288 m .17893 .16288 .15512 158.4 165.6 arc F .17893 .16288 m .17893 .16288 .15512 172.8 180 arc F .17893 .16288 m .17893 .16288 .15512 187.2 194.4 arc F .17893 .16288 m .17893 .16288 .15512 201.6 208.8 arc F .17893 .16288 m .17893 .16288 .15512 216 223.2 arc F .17893 .16288 m .17893 .16288 .15512 230.4 237.6 arc F .17893 .16288 m .17893 .16288 .15512 244.8 252 arc F .17893 .16288 m .17893 .16288 .15512 259.2 266.4 arc F .17893 .16288 m .17893 .16288 .15512 273.6 280.8 arc F .17893 .16288 m .17893 .16288 .15512 288 295.2 arc F .17893 .16288 m .17893 .16288 .15512 302.4 309.6 arc F .17893 .16288 m .17893 .16288 .15512 316.8 324 arc F .17893 .16288 m .17893 .16288 .15512 331.2 338.4 arc F .17893 .16288 m .17893 .16288 .15512 345.6 352.8 arc F .17893 .16288 m .17893 .16288 .15512 360 367.2 arc F .17893 .16288 m .17893 .16288 .15512 374.4 381.6 arc F .17893 .16288 m .17893 .16288 .15512 388.8 396 arc F .17893 .16288 m .17893 .16288 .15512 403.2 410.4 arc F .17893 .16288 m .17893 .16288 .15512 417.6 424.8 arc F .17893 .16288 m .17893 .16288 .15512 432 439.2 arc F .17893 .16288 m .17893 .16288 .15512 446.4 453.6 arc F .17893 .16288 m .17893 .16288 .15512 460.8 468 arc F .17893 .16288 m .17893 .16288 .15512 475.2 482.4 arc F .17893 .16288 m .17893 .16288 .15512 489.6 496.8 arc F .17893 .16288 m .17893 .16288 .15512 504 511.2 arc F .17893 .16288 m .17893 .16288 .15512 518.4 525.6 arc F .17893 .16288 m .17893 .16288 .15512 532.8 540 arc F .17893 .16288 m .17893 .16288 .15512 547.2 554.4 arc F .17893 .16288 m .17893 .16288 .15512 561.6 568.8 arc F .17893 .16288 m .17893 .16288 .15512 576 583.2 arc F .17893 .16288 m .17893 .16288 .15512 590.4 597.6 arc F .17893 .16288 m .17893 .16288 .15512 604.8 612 arc F .17893 .16288 m .17893 .16288 .15512 619.2 626.4 arc F .17893 .16288 m .17893 .16288 .15512 633.6 640.8 arc F .17893 .16288 m .17893 .16288 .15512 648 655.2 arc F .17893 .16288 m .17893 .16288 .15512 662.4 669.6 arc F .17893 .16288 m .17893 .16288 .15512 676.8 684 arc F .17893 .16288 m .17893 .16288 .15512 691.2 698.4 arc F .17893 .16288 m .17893 .16288 .15512 705.6 712.8 arc F P 0 1 0 r p .004 w .17893 .16288 m .17893 .16288 .15512 7.2 14.4 arc F .17893 .16288 m .17893 .16288 .15512 21.6 28.8 arc F .17893 .16288 m .17893 .16288 .15512 36 43.2 arc F .17893 .16288 m .17893 .16288 .15512 50.4 57.6 arc F .17893 .16288 m .17893 .16288 .15512 64.8 72 arc F .17893 .16288 m .17893 .16288 .15512 79.2 86.4 arc F .17893 .16288 m .17893 .16288 .15512 93.6 100.8 arc F .17893 .16288 m .17893 .16288 .15512 108 115.2 arc F .17893 .16288 m .17893 .16288 .15512 122.4 129.6 arc F .17893 .16288 m .17893 .16288 .15512 136.8 144 arc F .17893 .16288 m .17893 .16288 .15512 151.2 158.4 arc F .17893 .16288 m .17893 .16288 .15512 165.6 172.8 arc F .17893 .16288 m .17893 .16288 .15512 180 187.2 arc F .17893 .16288 m .17893 .16288 .15512 194.4 201.6 arc F .17893 .16288 m .17893 .16288 .15512 208.8 216 arc F .17893 .16288 m .17893 .16288 .15512 223.2 230.4 arc F .17893 .16288 m .17893 .16288 .15512 237.6 244.8 arc F .17893 .16288 m .17893 .16288 .15512 252 259.2 arc F .17893 .16288 m .17893 .16288 .15512 266.4 273.6 arc F .17893 .16288 m .17893 .16288 .15512 280.8 288 arc F .17893 .16288 m .17893 .16288 .15512 295.2 302.4 arc F .17893 .16288 m .17893 .16288 .15512 309.6 316.8 arc F .17893 .16288 m .17893 .16288 .15512 324 331.2 arc F .17893 .16288 m .17893 .16288 .15512 338.4 345.6 arc F .17893 .16288 m .17893 .16288 .15512 352.8 360 arc F .17893 .16288 m .17893 .16288 .15512 367.2 374.4 arc F .17893 .16288 m .17893 .16288 .15512 381.6 388.8 arc F .17893 .16288 m .17893 .16288 .15512 396 403.2 arc F .17893 .16288 m .17893 .16288 .15512 410.4 417.6 arc F .17893 .16288 m .17893 .16288 .15512 424.8 432 arc F .17893 .16288 m .17893 .16288 .15512 439.2 446.4 arc F .17893 .16288 m .17893 .16288 .15512 453.6 460.8 arc F .17893 .16288 m .17893 .16288 .15512 468 475.2 arc F .17893 .16288 m .17893 .16288 .15512 482.4 489.6 arc F .17893 .16288 m .17893 .16288 .15512 496.8 504 arc F .17893 .16288 m .17893 .16288 .15512 511.2 518.4 arc F .17893 .16288 m .17893 .16288 .15512 525.6 532.8 arc F .17893 .16288 m .17893 .16288 .15512 540 547.2 arc F .17893 .16288 m .17893 .16288 .15512 554.4 561.6 arc F .17893 .16288 m .17893 .16288 .15512 568.8 576 arc F .17893 .16288 m .17893 .16288 .15512 583.2 590.4 arc F .17893 .16288 m .17893 .16288 .15512 597.6 604.8 arc F .17893 .16288 m .17893 .16288 .15512 612 619.2 arc F .17893 .16288 m .17893 .16288 .15512 626.4 633.6 arc F .17893 .16288 m .17893 .16288 .15512 640.8 648 arc F .17893 .16288 m .17893 .16288 .15512 655.2 662.4 arc F .17893 .16288 m .17893 .16288 .15512 669.6 676.8 arc F .17893 .16288 m .17893 .16288 .15512 684 691.2 arc F .17893 .16288 m .17893 .16288 .15512 698.4 705.6 arc F .17893 .16288 m .17893 .16288 .15512 712.8 720 arc F P 1 0 0 r p .004 w .48918 .16288 m .48918 .16288 .15512 -93.6 -86.4 arc F .50866 .16288 m .50866 .16288 .15512 -93.6 -86.4 arc F .52814 .16288 m .52814 .16288 .15512 -93.6 -86.4 arc F .54762 .16288 m .54762 .16288 .15512 -93.6 -86.4 arc F .5671 .16288 m .5671 .16288 .15512 -93.6 -86.4 arc F .58658 .16288 m .58658 .16288 .15512 -93.6 -86.4 arc F .60606 .16288 m .60606 .16288 .15512 -93.6 -86.4 arc F .62554 .16288 m .62554 .16288 .15512 -93.6 -86.4 arc F .64502 .16288 m .64502 .16288 .15512 -93.6 -86.4 arc F .6645 .16288 m .6645 .16288 .15512 -93.6 -86.4 arc F .68398 .16288 m .68398 .16288 .15512 -93.6 -86.4 arc F .70346 .16288 m .70346 .16288 .15512 -93.6 -86.4 arc F .72294 .16288 m .72294 .16288 .15512 -93.6 -86.4 arc F .74242 .16288 m .74242 .16288 .15512 -93.6 -86.4 arc F .76191 .16288 m .76191 .16288 .15512 -93.6 -86.4 arc F .78139 .16288 m .78139 .16288 .15512 -93.6 -86.4 arc F .80087 .16288 m .80087 .16288 .15512 -93.6 -86.4 arc F .82035 .16288 m .82035 .16288 .15512 -93.6 -86.4 arc F .83983 .16288 m .83983 .16288 .15512 -93.6 -86.4 arc F .85931 .16288 m .85931 .16288 .15512 -93.6 -86.4 arc F .87879 .16288 m .87879 .16288 .15512 -93.6 -86.4 arc F .89827 .16288 m .89827 .16288 .15512 -93.6 -86.4 arc F .91775 .16288 m .91775 .16288 .15512 -93.6 -86.4 arc F .93723 .16288 m .93723 .16288 .15512 -93.6 -86.4 arc F .95671 .16288 m .95671 .16288 .15512 -93.6 -86.4 arc F P 0 1 0 r p .004 w .49892 .00806 m .49892 .00806 .15512 86.4 93.6 arc F .5184 .00806 m .5184 .00806 .15512 86.4 93.6 arc F .53788 .00806 m .53788 .00806 .15512 86.4 93.6 arc F .55736 .00806 m .55736 .00806 .15512 86.4 93.6 arc F .57684 .00806 m .57684 .00806 .15512 86.4 93.6 arc F .59632 .00806 m .59632 .00806 .15512 86.4 93.6 arc F .6158 .00806 m .6158 .00806 .15512 86.4 93.6 arc F .63528 .00806 m .63528 .00806 .15512 86.4 93.6 arc F .65476 .00806 m .65476 .00806 .15512 86.4 93.6 arc F .67424 .00806 m .67424 .00806 .15512 86.4 93.6 arc F .69372 .00806 m .69372 .00806 .15512 86.4 93.6 arc F .7132 .00806 m .7132 .00806 .15512 86.4 93.6 arc F .73268 .00806 m .73268 .00806 .15512 86.4 93.6 arc F .75216 .00806 m .75216 .00806 .15512 86.4 93.6 arc F .77165 .00806 m .77165 .00806 .15512 86.4 93.6 arc F .79113 .00806 m .79113 .00806 .15512 86.4 93.6 arc F .81061 .00806 m .81061 .00806 .15512 86.4 93.6 arc F .83009 .00806 m .83009 .00806 .15512 86.4 93.6 arc F .84957 .00806 m .84957 .00806 .15512 86.4 93.6 arc F .86905 .00806 m .86905 .00806 .15512 86.4 93.6 arc F .88853 .00806 m .88853 .00806 .15512 86.4 93.6 arc F .90801 .00806 m .90801 .00806 .15512 86.4 93.6 arc F .92749 .00806 m .92749 .00806 .15512 86.4 93.6 arc F .94697 .00806 m .94697 .00806 .15512 86.4 93.6 arc F .96645 .00806 m .96645 .00806 .15512 86.4 93.6 arc F P P % End of Graphics MathPictureEnd :[font = section; inactive; preserveAspect; startGroup] Implementation :[font = input; initialization; preserveAspect] *) SetOptions[Graphics, AspectRatio -> Automatic]; (* :[font = input; initialization; preserveAspect] *) Needs["Graphics`Colors`"] (* :[font = subsection; inactive; preserveAspect; startGroup] Usage messages :[font = input; initialization; preserveAspect; endGroup] *) PiRectangle::usage = "PiRectangle[n] draws a circle cut into n equal sectors (n needs to be even) and rearranges them to form an approximate rectangle with dimensions 1 X Pi."; (* :[font = subsection; inactive; preserveAspect; startGroup] Function definitions :[font = input; initialization; preserveAspect] *) PiRectangle[n_?OddQ] := Print["PiRectangle needs an even argument."] (* :[font = input; initialization; preserveAspect; endGroup; endGroup; endGroup] *) PiRectangle[n_?EvenQ] := Module[ {a, x, y}, a = 2 N[Pi] / n; x = 2 Sin[a / 2]; y = - Cos[a / 2]; Show @ Graphics @ { Red, Table[ Disk[{-2, 0}, 1, {2 i, 2 i + 1} a], {i, 0, n - 1} ], Green, Table[ Disk[{-2, 0}, 1, {2 i + 1, 2 i + 2} a], {i, 0, n - 1} ], Red, Table[ Disk[{i x, 0}, 1, {-a/2, a/2}- N[Pi/2]], {i, 0, (n - 1) / 2} ], Green, Table[ Disk[{x/2 + i x, y}, 1, {-a/2, a/2} + N[Pi/2]], {i, 0, (n - 1) / 2} ] } ] (* ^*)