(*^ ::[ 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] Nesting Regular Polygons and Circles :[font = subsubtitle; inactive; preserveAspect] by George Beck :[font = text; inactive; preserveAspect] Circumscribe and Inscribe are functions that let you draw nested sequences of circles and regular polygons. :[font = section; inactive; preserveAspect; startGroup] Circumscribe :[font = input; preserveAspect; startGroup] Show @ Graphics @ Circumscribe[{3}, 1]; :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 189; pictureHeight = 189; endGroup] %! %%Creator: Mathematica %%AspectRatio: 1 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.238095 0.5 0.238095 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p P p p .004 w .97619 .5 m .2619 .91239 L .2619 .08761 L .97619 .5 L s newpath .5 .5 .47619 0 365.72958 arc s P P 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath % End of Graphics MathPictureEnd :[font = input; preserveAspect; startGroup] Show @ Graphics @ Circumscribe[{3,4,5}, 1]; :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 205; pictureHeight = 205; endGroup] %! %%Creator: Mathematica %%AspectRatio: 1 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.136205 0.5 0.136205 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p P p p .004 w .97619 .5 m .64715 .95288 L .11475 .7799 L .11475 .2201 L .64715 .04712 L .97619 .5 L s newpath .5 .5 .47619 0 365.72958 arc s P p .004 w .88525 .5 m .5 .88525 L .11475 .5 L .5 .11475 L .88525 .5 L s newpath .5 .5 .38525 0 365.72958 arc s P p .004 w .77241 .5 m .36379 .73591 L .36379 .26409 L .77241 .5 L s newpath .5 .5 .27241 0 365.72958 arc s P P 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath % End of Graphics MathPictureEnd :[font = input; preserveAspect; startGroup] Show @ Graphics @ Circumscribe[Table[7, {24}], 1]; :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 205; pictureHeight = 205; endGroup] %! 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%%Creator: Mathematica %%AspectRatio: 1 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.06965 0.5 0.06965 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p P p p .004 w .97619 .5 m .95288 .64715 L .88525 .7799 L .7799 .88525 L .64715 .95288 L .5 .97619 L .35285 .95288 L .2201 .88525 L .11475 .7799 L .04712 .64715 L .02381 .5 L .04712 .35285 L .11475 .2201 L .2201 .11475 L .35285 .04712 L .5 .02381 L .64715 .04712 L .7799 .11475 L .88525 .2201 L .95288 .35285 L .97619 .5 L s newpath .5 .5 .47619 0 365.72958 arc s P p .004 w .97033 .5 m .94484 .65272 L .87115 .78888 L .75724 .89374 L .61546 .95594 L .46116 .96872 L .31107 .93071 L .18146 .84603 L .08636 .72385 L .03609 .57741 L .03609 .42259 L .08636 .27615 L .18146 .15397 L .31107 .06929 L .46116 .03128 L .61546 .04406 L .75724 .10626 L .87115 .21112 L .94484 .34728 L .97033 .5 L s newpath .5 .5 .47033 0 365.72958 arc s P p .004 w .96391 .5 m .93594 .65867 L .85538 .7982 L .73196 .90176 L .58056 .95687 L .41944 .95687 L .26804 .90176 L .14462 .7982 L .06406 .65867 L .03609 .5 L .06406 .34133 L .14462 .2018 L .26804 .09824 L .41944 .04313 L .58056 .04313 L .73196 .09824 L .85538 .2018 L .93594 .34133 L .96391 .5 L s newpath .5 .5 .46391 0 365.72958 arc s P p .004 w .95687 .5 m .92601 .66504 L .83763 .80779 L .70364 .90897 L .54215 .95492 L .37497 .93942 L .22468 .86459 L .11157 .74051 L .05091 .58395 L .05091 .41605 L .11157 .25949 L .22468 .13541 L .37497 .06058 L .54215 .04508 L .70364 .09103 L .83763 .19221 L .92601 .33496 L .95687 .5 L s newpath .5 .5 .45687 0 365.72958 arc s P p .004 w .94909 .5 m .9149 .67186 L .81755 .81755 L .67186 .9149 L .5 .94909 L .32814 .9149 L .18245 .81755 L .0851 .67186 L .05091 .5 L .0851 .32814 L .18245 .18245 L .32814 .0851 L .5 .05091 L .67186 .0851 L .81755 .18245 L .9149 .32814 L .94909 .5 L s newpath .5 .5 .44909 0 365.72958 arc s P p .004 w .94046 .5 m .90238 .67915 L .79472 .82732 L .63611 .9189 L .45396 .93804 L .27977 .88145 L .14366 .75889 L .06917 .59158 L .06917 .40842 L .14366 .24111 L .27977 .11855 L .45396 .06196 L .63611 .0811 L .79472 .17268 L .90238 .32085 L .94046 .5 L s newpath .5 .5 .44046 0 365.72958 arc s P p .004 w .93083 .5 m .88817 .68693 L .76862 .83684 L .59587 .92003 L .40413 .92003 L .23138 .83684 L .11183 .68693 L .06917 .5 L .11183 .31307 L .23138 .16316 L .40413 .07997 L .59587 .07997 L .76862 .16316 L .88817 .31307 L .93083 .5 L s newpath .5 .5 .43083 0 365.72958 arc s P p .004 w .92003 .5 m .87192 .6952 L .7386 .84568 L .55063 .91697 L .35106 .89274 L .1856 .77853 L .09218 .60052 L .09218 .39948 L .1856 .22147 L .35106 .10726 L .55063 .08303 L .7386 .15432 L .87192 .3048 L .92003 .5 L s newpath .5 .5 .42003 0 365.72958 arc s P p .004 w .90782 .5 m .85319 .70391 L .70391 .85319 L .5 .90782 L .29609 .85319 L .14681 .70391 L .09218 .5 L .14681 .29609 L .29609 .14681 L .5 .09218 L .70391 .14681 L .85319 .29609 L .90782 .5 L s newpath .5 .5 .40782 0 365.72958 arc s P p .004 w .89393 .5 m .83139 .71297 L .66364 .85833 L .44394 .88992 L .24203 .79771 L .12203 .61098 L .12203 .38902 L .24203 .20229 L .44394 .11008 L .66364 .14167 L .83139 .28703 L .89393 .5 L s newpath .5 .5 .39393 0 365.72958 arc s P p .004 w .87797 .5 m .80579 .72217 L .6168 .85947 L .3832 .85947 L .19421 .72217 L .12203 .5 L .19421 .27783 L .3832 .14053 L .6168 .14053 L .80579 .27783 L .87797 .5 L s newpath .5 .5 .37797 0 365.72958 arc s P p .004 w .85947 .5 m .77537 .73106 L .56242 .85401 L .32026 .81131 L .16221 .62295 L .16221 .37705 L .32026 .18869 L .56242 .14599 L .77537 .26894 L .85947 .5 L s newpath .5 .5 .35947 0 365.72958 arc s P p .004 w .83779 .5 m .73886 .73886 L .5 .83779 L .26114 .73886 L .16221 .5 L .26114 .26114 L .5 .16221 L .73886 .26114 L .83779 .5 L s newpath .5 .5 .33779 0 365.72958 arc s P p .004 w .81208 .5 m .69458 .74399 L .43056 .80426 L .21883 .63541 L .21883 .36459 L .43056 .19574 L .69458 .25601 L .81208 .5 L s newpath .5 .5 .31208 0 365.72958 arc s P p .004 w .78117 .5 m .64059 .7435 L .35941 .7435 L .21883 .5 L .35941 .2565 L .64059 .2565 L .78117 .5 L s newpath .5 .5 .28117 0 365.72958 arc s P p .004 w .7435 .5 m .57525 .73159 L .303 .64313 L .303 .35687 L .57525 .26841 L .7435 .5 L s newpath .5 .5 .2435 0 365.72958 arc s P p .004 w .697 .5 m .5 .697 L .303 .5 L .5 .303 L .697 .5 L s newpath .5 .5 .197 0 365.72958 arc s P p .004 w .6393 .5 m .43035 .62064 L .43035 .37936 L .6393 .5 L s newpath .5 .5 .1393 0 365.72958 arc s P P 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath % End of Graphics MathPictureEnd :[font = section; inactive; preserveAspect; startGroup] Inscribe :[font = input; preserveAspect; startGroup] Show @ Graphics @ Inscribe[{3}, 1]; :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 35; pictureTop = 2; pictureWidth = 214; pictureHeight = 247; endGroup] %! %%Creator: Mathematica %%AspectRatio: 1.1547 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.34127 0.634921 0.57735 0.634921 [ [ 0 0 0 0 ] [ 1 1.1547 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p P p p .004 w .97619 .57735 m .02381 1.12721 L .02381 .02749 L .97619 .57735 L s newpath .34127 .57735 .31746 0 365.72958 arc s P P 0 0 m 1 0 L 1 1.1547 L 0 1.1547 L closepath clip newpath % End of Graphics MathPictureEnd :[font = input; preserveAspect; startGroup] Show @ Graphics @ Inscribe[{3,5,3,5}, 1]; :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 35; pictureTop = 2; pictureWidth = 214; pictureHeight = 247; endGroup] %! %%Creator: Mathematica %%AspectRatio: 1.1547 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.34127 0.634921 0.57735 0.634921 [ [ 0 0 0 0 ] [ 1 1.1547 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p P p p .004 w .46969 .57735 m .38095 .69948 L .23738 .65283 L .23738 .50187 L .38095 .45522 L .46969 .57735 L s newpath .34127 .57735 .10389 0 365.72958 arc s P p .004 w .5981 .57735 m .21285 .79977 L .21285 .35493 L .5981 .57735 L s newpath .34127 .57735 .12842 0 365.72958 arc s P p .004 w .65873 .57735 m .43937 .87927 L .08444 .76395 L .08444 .39075 L .43937 .27543 L .65873 .57735 L s newpath .34127 .57735 .25683 0 365.72958 arc s P p .004 w .97619 .57735 m .02381 1.12721 L .02381 .02749 L .97619 .57735 L s newpath .34127 .57735 .31746 0 365.72958 arc s P P 0 0 m 1 0 L 1 1.1547 L 0 1.1547 L closepath clip newpath % End of Graphics MathPictureEnd :[font = input; preserveAspect; startGroup] Show @ Graphics @ Inscribe[Table[6, {24}], 1]; :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 35; pictureTop = 2; pictureWidth = 214; pictureHeight = 247; endGroup] %! %%Creator: Mathematica %%AspectRatio: .86603 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.47619 0.433013 0.47619 [ [ 0 0 0 0 ] [ 1 .86603 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p P p p .004 w .51742 .43301 m .50871 .4481 L .49129 .4481 L .48258 .43301 L .49129 .41793 L .50871 .41793 L .51742 .43301 L s newpath .5 .43301 .01508 0 365.72958 arc s P p .004 w .52011 .43301 m .51006 .45043 L .48994 .45043 L .47989 .43301 L .48994 .4156 L .51006 .4156 L .52011 .43301 L s newpath .5 .43301 .01742 0 365.72958 arc s P p .004 w .52322 .43301 m .51161 .45312 L .48839 .45312 L .47678 .43301 L .48839 .4129 L .51161 .4129 L .52322 .43301 L s newpath .5 .43301 .02011 0 365.72958 arc s P p .004 w .52682 .43301 m .51341 .45624 L .48659 .45624 L .47318 .43301 L .48659 .40979 L .51341 .40979 L .52682 .43301 L s newpath .5 .43301 .02322 0 365.72958 arc s P p .004 w .53096 .43301 m .51548 .45983 L .48452 .45983 L .46904 .43301 L .48452 .4062 L .51548 .4062 L .53096 .43301 L s newpath .5 .43301 .02682 0 365.72958 arc s P p .004 w .53575 .43301 m .51788 .46398 L .48212 .46398 L .46425 .43301 L .48212 .40205 L .51788 .40205 L .53575 .43301 L s newpath .5 .43301 .03096 0 365.72958 arc s P p .004 w .54129 .43301 m .52064 .46877 L .47936 .46877 L .45871 .43301 L .47936 .39726 L .52064 .39726 L .54129 .43301 L s newpath .5 .43301 .03575 0 365.72958 arc s P p .004 w .54767 .43301 m .52384 .4743 L .47616 .4743 L .45233 .43301 L .47616 .39173 L .52384 .39173 L .54767 .43301 L s newpath .5 .43301 .04129 0 365.72958 arc s P p .004 w .55505 .43301 m .52752 .48069 L .47248 .48069 L .44495 .43301 L .47248 .38534 L .52752 .38534 L .55505 .43301 L s newpath .5 .43301 .04767 0 365.72958 arc s P p .004 w .56356 .43301 m .53178 .48806 L .46822 .48806 L .43644 .43301 L .46822 .37796 L .53178 .37796 L .56356 .43301 L s newpath .5 .43301 .05505 0 365.72958 arc s P p .004 w .5734 .43301 m .5367 .49658 L .4633 .49658 L .4266 .43301 L .4633 .36945 L .5367 .36945 L .5734 .43301 L s newpath .5 .43301 .06356 0 365.72958 arc s P p .004 w .58475 .43301 m .54238 .50641 L .45762 .50641 L .41525 .43301 L .45762 .35962 L .54238 .35962 L .58475 .43301 L s newpath .5 .43301 .0734 0 365.72958 arc s P p .004 w .59786 .43301 m .54893 .51776 L .45107 .51776 L .40214 .43301 L .45107 .34826 L .54893 .34826 L .59786 .43301 L s newpath .5 .43301 .08475 0 365.72958 arc s P p .004 w .613 .43301 m .5565 .53088 L .4435 .53088 L .387 .43301 L .4435 .33515 L .5565 .33515 L .613 .43301 L s newpath .5 .43301 .09786 0 365.72958 arc s P p .004 w .63048 .43301 m .56524 .54601 L .43476 .54601 L .36952 .43301 L .43476 .32001 L .56524 .32001 L .63048 .43301 L s newpath .5 .43301 .113 0 365.72958 arc s P p .004 w .65067 .43301 m .57533 .5635 L .42467 .5635 L .34933 .43301 L .42467 .30253 L .57533 .30253 L .65067 .43301 L s newpath .5 .43301 .13048 0 365.72958 arc s P p .004 w .67398 .43301 m .58699 .58368 L .41301 .58368 L .32602 .43301 L .41301 .28234 L .58699 .28234 L .67398 .43301 L s newpath .5 .43301 .15067 0 365.72958 arc s P p .004 w .70089 .43301 m .60045 .60699 L .39955 .60699 L .29911 .43301 L .39955 .25903 L .60045 .25903 L .70089 .43301 L s newpath .5 .43301 .17398 0 365.72958 arc s P p .004 w .73197 .43301 m .61599 .63391 L .38401 .63391 L .26803 .43301 L .38401 .23212 L .61599 .23212 L .73197 .43301 L s newpath .5 .43301 .20089 0 365.72958 arc s P p .004 w .76786 .43301 m .63393 .66498 L .36607 .66498 L .23214 .43301 L .36607 .20104 L .63393 .20104 L .76786 .43301 L s newpath .5 .43301 .23197 0 365.72958 arc s P p .004 w .80929 .43301 m .65465 .70087 L .34535 .70087 L .19071 .43301 L .34535 .16516 L .65465 .16516 L .80929 .43301 L s newpath .5 .43301 .26786 0 365.72958 arc s P p .004 w .85714 .43301 m .67857 .74231 L .32143 .74231 L .14286 .43301 L .32143 .12372 L .67857 .12372 L .85714 .43301 L s newpath .5 .43301 .30929 0 365.72958 arc s P p .004 w .91239 .43301 m .7062 .79016 L .2938 .79016 L .08761 .43301 L .2938 .07587 L .7062 .07587 L .91239 .43301 L s newpath .5 .43301 .35714 0 365.72958 arc s P p .004 w .97619 .43301 m .7381 .84541 L .2619 .84541 L .02381 .43301 L .2619 .02062 L .7381 .02062 L .97619 .43301 L s newpath .5 .43301 .41239 0 365.72958 arc s P P 0 0 m 1 0 L 1 .86603 L 0 .86603 L closepath clip newpath % End of Graphics MathPictureEnd :[font = input; preserveAspect; startGroup] Show @ Graphics @ Inscribe[Range[3, 12], 1]; :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 35; pictureTop = 2; pictureWidth = 214; pictureHeight = 247; endGroup; endGroup] %! %%Creator: Mathematica %%AspectRatio: 1.1547 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations 0.34127 0.634921 0.57735 0.634921 [ [ 0 0 0 0 ] [ 1 1.1547 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath [ ] 0 setdash 0 g p P p p .004 w .45353 .57735 m .43849 .63348 L .3974 .67457 L .34127 .68961 L .28514 .67457 L .24405 .63348 L .22901 .57735 L .24405 .52122 L .28514 .48013 L .34127 .46509 L .3974 .48013 L .43849 .52122 L .45353 .57735 L s newpath .34127 .57735 .10843 0 365.72958 arc s P p .004 w .45827 .57735 m .4397 .6406 L .38987 .68378 L .32462 .69316 L .26465 .66577 L .22901 .61031 L .22901 .54439 L .26465 .48893 L .32462 .46154 L .38987 .47092 L .4397 .5141 L .45827 .57735 L s newpath .34127 .57735 .11226 0 365.72958 arc s P p .004 w .46429 .57735 m .44079 .64966 L .37928 .69435 L .30325 .69435 L .24175 .64966 L .21825 .57735 L .24175 .50504 L .30325 .46035 L .37928 .46035 L .44079 .50504 L .46429 .57735 L s newpath .34127 .57735 .117 0 365.72958 arc s P p .004 w .47218 .57735 m .44156 .6615 L .364 .70628 L .27581 .69073 L .21825 .62213 L .21825 .53257 L .27581 .46397 L .364 .44842 L .44156 .4932 L .47218 .57735 L s newpath .34127 .57735 .12302 0 365.72958 arc s P p .004 w .48297 .57735 m .44147 .67755 L .34127 .71905 L .24107 .67755 L .19957 .57735 L .24107 .47715 L .34127 .43565 L .44147 .47715 L .48297 .57735 L s newpath .34127 .57735 .13091 0 365.72958 arc s P p .004 w .49855 .57735 m .43933 .70031 L .30627 .73068 L .19957 .64559 L .19957 .50911 L .30627 .42402 L .43933 .45439 L .49855 .57735 L s newpath .34127 .57735 .1417 0 365.72958 arc s P p .004 w .52288 .57735 m .43207 .73463 L .25047 .73463 L .15966 .57735 L .25047 .42007 L .43207 .42007 L .52288 .57735 L s newpath .34127 .57735 .15728 0 365.72958 arc s P p .004 w .56575 .57735 m .41064 .79084 L .15966 .7093 L .15966 .44541 L .41064 .36386 L .56575 .57735 L s newpath .34127 .57735 .18161 0 365.72958 arc s P p .004 w .65873 .57735 m .34127 .89481 L .02381 .57735 L .34127 .25989 L .65873 .57735 L s newpath .34127 .57735 .22448 0 365.72958 arc s P p .004 w .97619 .57735 m .02381 1.12721 L .02381 .02749 L .97619 .57735 L s newpath .34127 .57735 .31746 0 365.72958 arc s P P 0 0 m 1 0 L 1 1.1547 L 0 1.1547 L closepath clip newpath % End of Graphics MathPictureEnd :[font = section; inactive; pageBreak; preserveAspect; startGroup] Implementation :[font = subsection; inactive; preserveAspect; startGroup] Usage messages :[font = input; initialization; preserveAspect] *) SetOptions[Graphics, AspectRatio -> Automatic, PlotRange -> All]; (* :[font = input; initialization; preserveAspect] *) Circumscribe::usage = "CircumscribeAux[l, r] draws a list of nested polygons and circles. Each polygon is circumscribed about the previous circle, and each circle passes through the vertices of the previous polygon. The number of sides of the polygons comes from the list l, and the first circle has radius r."; (* :[font = input; initialization; preserveAspect; endGroup] *) Inscribe::usage = "CircumscribeAux[l, r] draws a list of nested polygons and circles. Each polygon is inscribed in the previous circle, and each circle passes through the midpoints of the sides of the previous polygon. The number of sides of the polygons comes from the list l, and the first circle has radius r."; (* :[font = subsection; inactive; preserveAspect; startGroup] Function definitions :[font = input; initialization; preserveAspect] *) Circumscribe[n_?NumberQ, r_] := Module[ {a, vertices}, a = 2 N[Pi] / n; vertices = Table[ r Sec[a / 2] {Cos[i a], Sin[i a]}, {i, 0, n} ]; { RGBColor[0,0,1], Line[vertices], RGBColor[0,1,0], Circle[{0, 0}, r Sec[a / 2]] } ] (* :[font = input; initialization; preserveAspect] *) Circumscribe[{n_?NumberQ}, r_] := {Circumscribe[n, r]} (* :[font = input; initialization; preserveAspect] *) Circumscribe[l_List, r_] := Module[ {k, c}, {k, c} = Circumscribe[First @ l, r]; Append[ Circumscribe[Rest @ l, Last @ c], {k, c} ] ] (* :[font = input; initialization; preserveAspect] *) Inscribe[n_?NumberQ, r_] := Module[ {a, vertices}, a = 2 N[Pi] / n; vertices = Table[ r {Cos[i a], Sin[i a]}, {i, 0, n} ]; { RGBColor[1,0,0], Line[vertices], RGBColor[0,1,0], Circle[{0, 0}, r Cos[a / 2]] } ] (* :[font = input; initialization; preserveAspect] *) Inscribe[{n_?NumberQ}, r_] := {Inscribe[n, r]} (* :[font = input; initialization; preserveAspect; endGroup; endGroup; endGroup] *) Inscribe[l_List, r_] := Module[ {k, c}, {k, c} = Inscribe[First @ l, r]; Append[ Inscribe[Rest @ l, Last @ c], {k, c} ] ] (* ^*)