(************** Content-type: application/mathematica ************** Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). 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For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. *******************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 1730742, 37541]*) (*NotebookOutlinePosition[ 1731441, 37566]*) (* CellTagsIndexPosition[ 1731397, 37562]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell["Triangulation of surfaces", "Subtitle"], Cell["\<\ Ivan Cnop Vrije universiteit Brussel icnop@vub.ac.be\ \>", "Subsubtitle"], Cell[CellGroupData[{ Cell["Problem", "Section"], Cell[CellGroupData[{ Cell["\<\ If we plot three dimensional surfaces, we may get bad results near \ discontinuities\ \>", "Subsubsection"], Cell[BoxData[ \(TraditionalForm\`f(x_, y_) := \(-\(\(10\ x\)\/\@\(x\^2 + 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.69143 .53583 .6982 .55465 .68737 .5446 .68032 Metetra .769 .833 .902 r .5446 .68032 .55465 .68737 .57352 .67605 .5636 .66864 Metetra .775 .828 .893 r .5636 .66864 .57352 .67605 .59246 .66427 .58264 .65642 Metetra .779 .821 .885 r .58264 .65642 .59246 .66427 .61144 .65207 .60173 .6437 Metetra .782 .812 .877 r .60173 .6437 .61144 .65207 .63047 .63954 .62087 .63057 Metetra .782 .803 .869 r .62087 .63057 .63047 .63954 .64955 .62675 .64004 .61714 Metetra .781 .792 .862 r .64004 .61714 .64955 .62675 .66867 .61382 .65925 .60354 Metetra .778 .782 .856 r .65925 .60354 .66867 .61382 .68784 .60085 .67851 .58991 Metetra .773 .771 .851 r .67851 .58991 .68784 .60085 .70706 .58796 .69781 .57639 Metetra .767 .761 .848 r .69781 .57639 .70706 .58796 .72635 .57525 .71718 .5631 Metetra .76 .752 .845 r .71718 .5631 .72635 .57525 .74571 .56281 .73662 .55015 Metetra .753 .744 .844 r .73662 .55015 .74571 .56281 .76516 .5507 .75614 .53761 Metetra .746 .736 .843 r .75614 .53761 .76516 .5507 .7847 .53896 .77576 .52552 Metetra .738 .73 .844 r .77576 .52552 .7847 .53896 .80434 .52763 .79548 .51392 Metetra .731 .725 .845 r .79548 .51392 .80434 .52763 .8241 .51669 .81532 .50279 Metetra .725 .722 .847 r .81532 .50279 .8241 .51669 .84398 .50616 .83529 .49211 Metetra .719 .719 .849 r .83529 .49211 .84398 .50616 .86398 .49601 .85539 .48187 Metetra .713 .716 .852 r .85539 .48187 .86398 .49601 .88412 .4862 .87562 .47201 Metetra .708 .715 .854 r .87562 .47201 .88412 .4862 .9044 .47672 .896 .46251 Metetra .704 .714 .857 r .896 .46251 .9044 .47672 .92482 .46753 .91653 .45331 Metetra .699 .714 .86 r .91653 .45331 .92482 .46753 .94539 .4586 .9372 .44439 Metetra .696 .714 .862 r .9372 .44439 .94539 .4586 .96611 .4499 .95803 .4357 Metetra .695 .827 .946 r .36616 .75549 .37731 .76193 .3955 .75456 .38445 .7482 Metetra .701 .831 .945 r .38445 .7482 .3955 .75456 .41381 .74687 .40285 .74056 Metetra .708 .835 .942 r .40285 .74056 .41381 .74687 .43222 .73879 .42135 .73254 Metetra .716 .838 .94 r .42135 .73254 .43222 .73879 .45073 .73031 .43997 .72408 Metetra .725 .841 .936 r .43997 .72408 .45073 .73031 .46933 .72136 .45868 .71513 Metetra .735 .844 .931 r .45868 .71513 .46933 .72136 .48803 .71193 .47749 .70564 Metetra .745 .845 .926 r .47749 .70564 .48803 .71193 .50681 .70196 .49639 .69557 Metetra .755 .845 .919 r .49639 .69557 .50681 .70196 .52567 .69143 .51537 .68486 Metetra .765 .844 .911 r .51537 .68486 .52567 .69143 .5446 .68032 .53442 .67349 Metetra .774 .84 .902 r .53442 .67349 .5446 .68032 .5636 .66864 .55353 .66144 Metetra .781 .835 .893 r .55353 .66144 .5636 .66864 .58264 .65642 .57269 .64875 Metetra .787 .827 .884 r .57269 .64875 .58264 .65642 .60173 .6437 .5919 .63546 Metetra .79 .818 .874 r .5919 .63546 .60173 .6437 .62087 .63057 .61114 .62167 Metetra .79 .807 .865 r .61114 .62167 .62087 .63057 .64004 .61714 .63041 .60751 Metetra .789 .795 .858 r .63041 .60751 .64004 .61714 .65925 .60354 .64972 .59314 Metetra .785 .783 .851 r .64972 .59314 .65925 .60354 .67851 .58991 .66906 .57874 Metetra .779 .771 .846 r .66906 .57874 .67851 .58991 .69781 .57639 .68844 .5645 Metetra .772 .759 .842 r .68844 .5645 .69781 .57639 .71718 .5631 .70788 .55056 Metetra .764 .749 .84 r .70788 .55056 .71718 .5631 .73662 .55015 .7274 .53705 Metetra .755 .74 .839 r .7274 .53705 .73662 .55015 .75614 .53761 .74699 .52406 Metetra .747 .732 .839 r .74699 .52406 .75614 .53761 .77576 .52552 .76669 .51162 Metetra .739 .726 .84 r .76669 .51162 .77576 .52552 .79548 .51392 .78649 .49976 Metetra .731 .721 .841 r .78649 .49976 .79548 .51392 .81532 .50279 .80642 .48845 Metetra .724 .717 .844 r .80642 .48845 .81532 .50279 .83529 .49211 .82648 .47767 Metetra .717 .715 .847 r .82648 .47767 .83529 .49211 .85539 .48187 .84667 .46737 Metetra .711 .713 .85 r .84667 .46737 .85539 .48187 .87562 .47201 .86701 .45749 Metetra .706 .712 .853 r .86701 .45749 .87562 .47201 .896 .46251 .88749 .44799 Metetra .702 .711 .856 r .88749 .44799 .896 .46251 .91653 .45331 .90813 .43882 Metetra .697 .711 .859 r .90813 .43882 .91653 .45331 .9372 .44439 .92891 .42994 Metetra .694 .711 .862 r .92891 .42994 .9372 .44439 .95803 .4357 .94985 .42129 Metetra .691 .827 .949 r .35485 .74901 .36616 .75549 .38445 .7482 .37323 .74181 Metetra .697 .832 .947 r .37323 .74181 .38445 .7482 .40285 .74056 .39172 .73427 Metetra .705 .836 .945 r .39172 .73427 .40285 .74056 .42135 .73254 .41033 .72632 Metetra .713 .841 .943 r .41033 .72632 .42135 .73254 .43997 .72408 .42905 .71793 Metetra .723 .845 .939 r .42905 .71793 .43997 .72408 .45868 .71513 .44787 .70902 Metetra .733 .849 .935 r .44787 .70902 .45868 .71513 .47749 .70564 .4668 .69953 Metetra .745 .851 .929 r .4668 .69953 .47749 .70564 .49639 .69557 .48581 .68939 Metetra .756 .852 .922 r .48581 .68939 .49639 .69557 .51537 .68486 .50491 .67854 Metetra .768 .851 .913 r .50491 .67854 .51537 .68486 .53442 .67349 .52409 .66693 Metetra .778 .848 .904 r .52409 .66693 .53442 .67349 .55353 .66144 .54332 .65452 Metetra .788 .843 .893 r .54332 .65452 .55353 .66144 .57269 .64875 .56261 .64133 Metetra .795 .835 .882 r .56261 .64133 .57269 .64875 .5919 .63546 .58193 .62741 Metetra .799 .824 .871 r .58193 .62741 .5919 .63546 .61114 .62167 .60128 .61287 Metetra .8 .812 .861 r .60128 .61287 .61114 .62167 .63041 .60751 .62066 .59786 Metetra .797 .798 .852 r .62066 .59786 .63041 .60751 .64972 .59314 .64006 .5826 Metetra .793 .784 .845 r .64006 .5826 .64972 .59314 .66906 .57874 .65948 .56732 Metetra .785 .77 .839 r .65948 .56732 .66906 .57874 .68844 .5645 .67895 .55224 Metetra .777 .757 .835 r .67895 .55224 .68844 .5645 .70788 .55056 .69846 .53757 Metetra .767 .746 .833 r .69846 .53757 .70788 .55056 .7274 .53705 .71805 .52345 Metetra .757 .736 .833 r .71805 .52345 .7274 .53705 .74699 .52406 .73772 .50998 Metetra .748 .728 .833 r .73772 .50998 .74699 .52406 .76669 .51162 .75749 .4972 Metetra .738 .721 .835 r .75749 .4972 .76669 .51162 .78649 .49976 .77738 .48511 Metetra .73 .716 .838 r .77738 .48511 .78649 .49976 .80642 .48845 .7974 .47366 Metetra .722 .713 .841 r .7974 .47366 .80642 .48845 .82648 .47767 .81755 .46281 Metetra .715 .71 .844 r .81755 .46281 .82648 .47767 .84667 .46737 .83784 .45249 Metetra .709 .709 .848 r .83784 .45249 .84667 .46737 .86701 .45749 .85828 .44264 Metetra .704 .708 .852 r .85828 .44264 .86701 .45749 .88749 .44799 .87887 .43319 Metetra .699 .708 .855 r .87887 .43319 .88749 .44799 .90813 .43882 .89962 .42407 Metetra .695 .709 .859 r .89962 .42407 .90813 .43882 .92891 .42994 .92052 .41525 Metetra .691 .71 .862 r .92052 .41525 .92891 .42994 .94985 .42129 .94158 .40667 Metetra .686 .827 .951 r .34338 .74245 .35485 .74901 .37323 .74181 .36184 .73537 Metetra .692 .832 .95 r .36184 .73537 .37323 .74181 .39172 .73427 .38043 .72795 Metetra .7 .837 .949 r .38043 .72795 .39172 .73427 .41033 .72632 .39914 .72013 Metetra .709 .843 .946 r .39914 .72013 .41033 .72632 .42905 .71793 .41796 .71185 Metetra .719 .848 .943 r .41796 .71185 .42905 .71793 .44787 .70902 .43689 .70303 Metetra .73 .853 .939 r .43689 .70303 .44787 .70902 .4668 .69953 .45593 .69359 Metetra .743 .857 .933 r .45593 .69359 .4668 .69953 .48581 .68939 .47507 .68345 Metetra .756 .859 .926 r .47507 .68345 .48581 .68939 .50491 .67854 .49429 .67251 Metetra .77 .86 .916 r .49429 .67251 .50491 .67854 .52409 .66693 .5136 .6607 Metetra .783 .858 .906 r .5136 .6607 .52409 .66693 .54332 .65452 .53296 .64795 Metetra .795 .852 .894 r .53296 .64795 .54332 .65452 .56261 .64133 .55238 .63425 Metetra .803 .843 .881 r .55238 .63425 .56261 .64133 .58193 .62741 .57183 .61964 Metetra .809 .832 .868 r .57183 .61964 .58193 .62741 .60128 .61287 .59129 .60423 Metetra .81 .817 .856 r .59129 .60423 .60128 .61287 .62066 .59786 .61078 .58824 Metetra .807 .801 .846 r .61078 .58824 .62066 .59786 .64006 .5826 .63027 .57192 Metetra .801 .785 .838 r .63027 .57192 .64006 .5826 .65948 .56732 .64978 .55559 Metetra .792 .769 .831 r .64978 .55559 .65948 .56732 .67895 .55224 .66932 .53954 Metetra .782 .754 .828 r .66932 .53954 .67895 .55224 .69846 .53757 .68891 .52404 Metetra .77 .741 .826 r .68891 .52404 .69846 .53757 .71805 .52345 .70857 .50926 Metetra .759 .73 .826 r .70857 .50926 .71805 .52345 .73772 .50998 .72831 .49531 Metetra .748 .722 .828 r .72831 .49531 .73772 .50998 .75749 .4972 .74817 .48221 Metetra .737 .715 .83 r .74817 .48221 .75749 .4972 .77738 .48511 .76814 .46992 Metetra .728 .711 .834 r .76814 .46992 .77738 .48511 .7974 .47366 .78825 .45839 Metetra .72 .708 .838 r .78825 .45839 .7974 .47366 .81755 .46281 .8085 .44753 Metetra .713 .706 .842 r .8085 .44753 .81755 .46281 .83784 .45249 .82889 .43725 Metetra .706 .705 .847 r .82889 .43725 .83784 .45249 .85828 .44264 .84944 .42747 Metetra .701 .705 .851 r .84944 .42747 .85828 .44264 .87887 .43319 .87014 .41811 Metetra .696 .706 .855 r .87014 .41811 .87887 .43319 .89962 .42407 .891 .40909 Metetra .692 .707 .859 r .891 .40909 .89962 .42407 .92052 .41525 .91202 .40036 Metetra .689 .708 .863 r .91202 .40036 .92052 .41525 .94158 .40667 .9332 .39186 Metetra .681 .826 .953 r .33174 .73576 .34338 .74245 .36184 .73537 .3503 .72883 Metetra .687 .831 .953 r .3503 .72883 .36184 .73537 .38043 .72795 .36898 .72157 Metetra .694 .838 .952 r .36898 .72157 .38043 .72795 .39914 .72013 .38778 .71392 Metetra .703 .844 .95 r .38778 .71392 .39914 .72013 .41796 .71185 .40671 .7058 Metetra .714 .851 .947 r .40671 .7058 .41796 .71185 .43689 .70303 .42575 .69714 Metetra .726 .857 .943 r .42575 .69714 .43689 .70303 .45593 .69359 .4449 .68783 Metetra .74 .863 .938 r .4449 .68783 .45593 .69359 .47507 .68345 .46416 .67776 Metetra .755 .867 .93 r .46416 .67776 .47507 .68345 .49429 .67251 .48351 .66682 Metetra .771 .869 .92 r .48351 .66682 .49429 .67251 .5136 .6607 .50294 .65487 Metetra .787 .868 .908 r .50294 .65487 .5136 .6607 .53296 .64795 .52245 .64182 Metetra .801 .863 .895 r .52245 .64182 .53296 .64795 .55238 .63425 .542 .62761 Metetra .813 .854 .88 r .542 .62761 .55238 .63425 .57183 .61964 .56158 .61225 Metetra .82 .841 .864 r .56158 .61225 .57183 .61964 .59129 .60423 .58117 .59586 Metetra .822 .824 .85 r .58117 .59586 .59129 .60423 .61078 .58824 .60076 .57869 Metetra .819 .805 .838 r .60076 .57869 .61078 .58824 .63027 .57192 .62035 .5611 Metetra .811 .786 .829 r .62035 .5611 .63027 .57192 .64978 .55559 .63995 .5435 Metetra .8 .767 .823 r .63995 .5435 .64978 .55559 .66932 .53954 .65957 .52631 Metetra .787 .75 .819 r .65957 .52631 .66932 .53954 .68891 .52404 .67923 .50987 Metetra .773 .735 .818 r .67923 .50987 .68891 .52404 .70857 .50926 .69895 .49439 Metetra .76 .724 .819 r .69895 .49439 .70857 .50926 .72831 .49531 .71877 .47996 Metetra .747 .715 .822 r .71877 .47996 .72831 .49531 .74817 .48221 .73871 .46658 Metetra .735 .709 .826 r .73871 .46658 .74817 .48221 .76814 .46992 .75877 .45417 Metetra .725 .705 .83 r .75877 .45417 .76814 .46992 .78825 .45839 .77897 .44263 Metetra .717 .702 .835 r .77897 .44263 .78825 .45839 .8085 .44753 .79932 .43184 Metetra .709 .701 .841 r .79932 .43184 .8085 .44753 .82889 .43725 .81983 .42166 Metetra .703 .701 .846 r .81983 .42166 .82889 .43725 .84944 .42747 .84048 .41201 Metetra .697 .702 .851 r .84048 .41201 .84944 .42747 .87014 .41811 .8613 .40278 Metetra .693 .703 .855 r .8613 .40278 .87014 .41811 .891 .40909 .88228 .3939 Metetra .689 .705 .86 r .88228 .3939 .891 .40909 .91202 .40036 .90342 .38529 Metetra .686 .707 .864 r .90342 .38529 .91202 .40036 .9332 .39186 .92473 .3769 Metetra .675 .823 .955 r .31994 .72892 .33174 .73576 .3503 .72883 .33858 .72216 Metetra .681 .83 .955 r .33858 .72216 .3503 .72883 .36898 .72157 .35735 .71509 Metetra .688 .836 .955 r .35735 .71509 .36898 .72157 .38778 .71392 .37625 .70764 Metetra .696 .844 .954 r .37625 .70764 .38778 .71392 .40671 .7058 .39528 .69975 Metetra .706 .852 .952 r .39528 .69975 .40671 .7058 .42575 .69714 .41442 .69131 Metetra .719 .86 .948 r .41442 .69131 .42575 .69714 .4449 .68783 .43369 .68221 Metetra .734 .867 .943 r .43369 .68221 .4449 .68783 .46416 .67776 .45307 .67232 Metetra .751 .874 .936 r .45307 .67232 .46416 .67776 .48351 .66682 .47255 .66148 Metetra .77 .879 .926 r .47255 .66148 .48351 .66682 .50294 .65487 .49212 .64951 Metetra .789 .88 .912 r .49212 .64951 .50294 .65487 .52245 .64182 .51176 .63624 Metetra .808 .876 .896 r .51176 .63624 .52245 .64182 .542 .62761 .53146 .62156 Metetra .823 .867 .879 r .53146 .62156 .542 .62761 .56158 .61225 .55118 .6054 Metetra .833 .852 .86 r .55118 .6054 .56158 .61225 .58117 .59586 .57091 .58789 Metetra .836 .832 .843 r .57091 .58789 .58117 .59586 .60076 .57869 .59062 .5693 Metetra .832 .81 .829 r .59062 .5693 .60076 .57869 .62035 .5611 .61031 .55014 Metetra .822 .786 .819 r .61031 .55014 .62035 .5611 .63995 .5435 .62999 .53099 Metetra .808 .764 .812 r .62999 .53099 .63995 .5435 .65957 .52631 .64968 .51243 Metetra .792 .744 .809 r .64968 .51243 .65957 .52631 .67923 .50987 .6694 .49491 Metetra .775 .728 .809 r .6694 .49491 .67923 .50987 .69895 .49439 .6892 .47869 Metetra .759 .716 .812 r .6892 .47869 .69895 .49439 .71877 .47996 .7091 .46382 Metetra .745 .707 .816 r .7091 .46382 .71877 .47996 .73871 .46658 .72912 .45025 Metetra .732 .701 .821 r .72912 .45025 .73871 .46658 .75877 .45417 .74927 .43783 Metetra .721 .698 .827 r .74927 .43783 .75877 .45417 .77897 .44263 .76957 .42638 Metetra .712 .697 .833 r .76957 .42638 .77897 .44263 .79932 .43184 .79003 .41575 Metetra .705 .697 .84 r .79003 .41575 .79932 .43184 .81983 .42166 .81065 .40576 Metetra .699 .698 .846 r .81065 .40576 .81983 .42166 .84048 .41201 .83142 .3963 Metetra .694 .699 .851 r .83142 .3963 .84048 .41201 .8613 .40278 .85236 .38725 Metetra .689 .701 .856 r .85236 .38725 .8613 .40278 .88228 .3939 .87346 .37854 Metetra .686 .704 .861 r .87346 .37854 .88228 .3939 .90342 .38529 .89473 .37008 Metetra .683 .706 .865 r .89473 .37008 .90342 .38529 .92473 .3769 .91616 .36182 Metetra .669 .82 .956 r .30797 .72187 .31994 .72892 .33858 .72216 .3267 .7153 Metetra .674 .826 .957 r .3267 .7153 .33858 .72216 .35735 .71509 .34556 .70844 Metetra .68 .834 .957 r .34556 .70844 .35735 .71509 .37625 .70764 .36455 .70124 Metetra .688 .842 .957 r .36455 .70124 .37625 .70764 .39528 .69975 .38367 .69362 Metetra .698 .851 .956 r .38367 .69362 .39528 .69975 .41442 .69131 .40292 .68547 Metetra .71 .861 .954 r .40292 .68547 .41442 .69131 .43369 .68221 .4223 .67669 Metetra .725 .871 .949 r .4223 .67669 .43369 .68221 .45307 .67232 .44179 .66709 Metetra .744 .88 .942 r .44179 .66709 .45307 .67232 .47255 .66148 .4614 .65649 Metetra .765 .888 .932 r .4614 .65649 .47255 .66148 .49212 .64951 .48111 .64466 Metetra .789 .893 .918 r .48111 .64466 .49212 .64951 .51176 .63624 .5009 .63133 Metetr