(*********************************************************************** Mathematica-Compatible Notebook This notebook can be used on any computer system with Mathematica 4.0, MathReader 4.0, or any compatible application. 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). NOTE: If you modify the data for this notebook not in a Mathematica- compatible application, you must delete the line below containing the word CacheID, otherwise Mathematica-compatible applications may try to use invalid cache data. 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[ 582685, 17139]*) (*NotebookOutlinePosition[ 583339, 17162]*) (* CellTagsIndexPosition[ 583295, 17158]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell["\<\ Evaluate these Cells, in order, to see an animation for Riemann Rectangles \ being rotated to create a volume by washers. 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0 r F P 0 g s .64864 .46961 m .65317 .46896 L .69234 .46426 L .695 .697 0 r F .65167 .49358 m .65148 .4824 L .65027 .48256 L .396 0 0 r F .65126 .46923 m .65109 .45864 L .64864 .46961 L F .69234 .46426 m .65317 .46896 L .72152 .4591 L .695 .697 0 r F .6388 .47375 m .6453 .47101 L p .69234 .46426 L F P 0 g s .63799 .48326 m .58548 .4903 L p .64458 .48305 L 0 0 .518 r F P 0 g s .64678 .48276 m .63799 .48326 L p .64458 .48305 L 0 0 .518 r F P 0 g s .63689 .47455 m .58444 .48198 L p .64317 .47132 L .695 .697 0 r F P 0 g s .6453 .47101 m .63689 .47455 L p .64317 .47132 L .695 .697 0 r F P 0 g s .58548 .4903 m .59533 .48963 L p .64458 .48305 L 0 0 .518 r F P 0 g s .59722 .4895 m .59533 .48963 L p .59673 .48957 L 0 0 .518 r F P 0 g s .59673 .48957 m .59533 .48963 L .59492 .48968 L 0 0 .518 r F .56994 .49232 m .58295 .4914 L p .59673 .48957 L F P 0 g s .59653 .49919 m .59653 .48947 L .59616 .48952 L .393 0 0 r F .59653 .49919 m .59912 .49887 L .59793 .48928 L F .59653 .49919 m .59793 .48928 L .59653 .48947 L F .59533 .48963 m .58456 .49036 L p .59492 .48968 L 0 0 .518 r F P 0 g s .58444 .48198 m .59393 .47838 L p .64317 .47132 L .695 .697 0 r F P 0 g s .59574 .47813 m .59652 .47801 L .5954 .46897 L .393 0 0 r F .59574 .47813 m .5954 .46897 L .59537 .47818 L F .56895 .48438 m .58151 .47975 L p .59528 .47777 L .695 .697 0 r F P 0 g s .59393 .47838 m .5954 .46897 L .59281 .46936 L .393 0 0 r F .59537 .47818 m .5954 .46897 L .59393 .47838 L F .59653 .49919 m .59616 .48952 L .59533 .48963 L F .58456 .49036 m .56994 .49232 L p .5927 .48998 L 0 0 .518 r F P 0 g s .5927 .48998 m .59492 .48968 L .58456 .49036 L 0 0 .518 r F .58566 .50113 m .58467 .49118 L .58443 .49121 L .394 0 0 r F .58202 .47967 m .58224 .47964 L .58108 .47028 L F .58418 .50132 m .58492 .50123 L .58369 .49131 L F .58418 .50132 m .58369 .49131 L .58319 .49137 L F .58492 .50123 m .58393 .49127 L .58369 .49131 L F .58295 .4914 m .5688 .4924 L p .58266 .49144 L 0 0 .518 r F P 0 g s .58224 .47964 m .58182 .47017 L .58108 .47028 L .394 0 0 r F .58276 .47957 m .58182 .47017 L .58224 .47964 L F .58202 .47967 m .58108 .47028 L .58191 .47969 L F .58151 .47975 m .58108 .47028 L .58034 .47039 L F .58191 .47969 m .58108 .47028 L .58151 .47975 L F .58418 .50132 m .58319 .49137 L .58295 .4914 L F .5688 .4924 m .55355 .49445 L p .57876 .49196 L 0 0 .518 r F P 0 g s .57876 .49196 m .58266 .49144 L .5688 .4924 L 0 0 .518 r F .57427 .50395 m .57504 .50386 L .57369 .49293 L .398 0 0 r F .57427 .50395 m .57369 .49293 L .57317 .493 L F .57504 .50386 m .57393 .4929 L .57369 .49293 L F .57292 .49303 m .54354 .49518 L p .57168 .4932 L 0 0 .518 r F P 0 g s .5721 .48009 m .57158 .46967 L .57082 .46979 L .398 0 0 r F .57263 .48001 m .57158 .46967 L .5721 .48009 L F .57187 .48013 m .57082 .46979 L .57176 .48014 L F .57133 .4802 m .57082 .46979 L .57006 .46991 L F .57176 .48014 m .57082 .46979 L .57133 .4802 L F .57427 .50395 m .57317 .493 L .57292 .49303 L F .54354 .49518 m .37308 .51815 L p .47413 .50619 L 0 0 .518 r F P 0 g s .47413 .50619 m .57168 .4932 L .54354 .49518 L 0 0 .518 r F .44992 .52709 m .45031 .511 L .44802 .5113 L .42 0 0 r F .45077 .49199 m .45115 .47667 L .4458 .49274 L F .44319 .47407 m .59866 .44772 L p .59754 .44803 L .729 .686 0 r F P 0 g s .44402 .47785 m .44345 .47413 L .44288 .47423 L .304 0 0 r F .44288 .47423 m .44319 .47407 L p .59754 .44803 L .729 .686 0 r F P 0 g s .44402 .47785 m .45115 .47667 L .44458 .45555 L .304 0 0 r F .43843 .45616 m .59399 .42685 L p .59024 .42819 L .739 .656 0 r F P 0 g s .43744 .45689 m .43843 .45616 L p .59024 .42819 L .739 .656 0 r F P 0 g s .43246 .43888 m .58837 .40661 L p .58634 .4075 L .73 .612 0 r F P 0 g s .44071 .45627 m .44458 .45555 L .4391 .43792 L .304 0 0 r F .44071 .45627 m .4391 .43792 L .43793 .43816 L F .44402 .47785 m .44458 .45555 L .44071 .45627 L F .43196 .43939 m .43246 .43888 L p .58634 .4075 L .73 .612 0 r F P 0 g s .45115 .47667 m .44396 .42869 L .43671 .43025 L .304 0 0 r F .45115 .47667 m .45838 .47547 L .44396 .42869 L F .45838 .47547 m .45131 .42711 L .44396 .42869 L F .45838 .47547 m .46572 .47426 L .45131 .42711 L F .46572 .47426 m .45877 .42551 L .45131 .42711 L F .46572 .47426 m .47316 .47303 L .45877 .42551 L F .47316 .47303 m .46635 .42388 L .45877 .42551 L F .47316 .47303 m .48071 .47178 L .46635 .42388 L F .48071 .47178 m .47403 .42223 L .46635 .42388 L F .48071 .47178 m .48838 .47051 L .47403 .42223 L F .48838 .47051 m .48184 .42055 L .47403 .42223 L F .48838 .47051 m .49616 .46922 L .48184 .42055 L F .49616 .46922 m .48976 .41885 L .48184 .42055 L F .49616 .46922 m .50405 .46791 L .48976 .41885 L F .50405 .46791 m .49781 .41712 L .48976 .41885 L F .50405 .46791 m .51207 .46659 L .49781 .41712 L F .51207 .46659 m .50598 .41536 L .49781 .41712 L F .51207 .46659 m .52021 .46524 L .50598 .41536 L F .52021 .46524 m .51428 .41358 L .50598 .41536 L F .52021 .46524 m .52847 .46387 L .51428 .41358 L F .52847 .46387 m .5227 .41177 L .51428 .41358 L F .52847 .46387 m .53686 .46248 L .5227 .41177 L F .53686 .46248 m .53127 .40993 L .5227 .41177 L F .53686 .46248 m .54538 .46107 L .53127 .40993 L F .54538 .46107 m .53997 .40806 L .53127 .40993 L F .54538 .46107 m .55404 .45964 L .53997 .40806 L F .55404 .45964 m .54881 .40616 L .53997 .40806 L F .55404 .45964 m .56283 .45818 L .54881 .40616 L F .56283 .45818 m .5578 .40423 L .54881 .40616 L F .56283 .45818 m .57177 .4567 L .5578 .40423 L F .57067 .45258 m .56915 .43215 L .56542 .43285 L F .57139 .45246 m .56774 .41134 L .57067 .45258 L F .56774 .41134 m .56693 .40227 L .56761 .41137 L F .56774 .41134 m .56761 .41137 L .57067 .45258 L F .57177 .4567 m .57139 .45246 L .57067 .45258 L F .57177 .4567 m .58085 .4552 L .56693 .40227 L F .58085 .4552 m .57621 .40027 L .56693 .40227 L F .58085 .4552 m .59007 .45367 L .57621 .40027 L F .58837 .40661 m .58799 .40716 L p .58634 .4075 L .73 .612 0 r F P 0 g s .59007 .45367 m .58565 .39825 L .57621 .40027 L .304 0 0 r F .59399 .42685 m .59323 .42763 L p .59024 .42819 L .739 .656 0 r F P 0 g s .59866 .44772 m .59842 .44788 L p .59754 .44803 L .729 .686 0 r F P 0 g s .59007 .45367 m .59945 .45212 L .58565 .39825 L .304 0 0 r F .5421 .48573 m .37181 .51018 L p .47173 .48266 L .729 .686 0 r F P 0 g s .47173 .48266 m .59754 .44803 L .56897 .46746 L .729 .686 0 r F .47173 .48266 m .56897 .46746 L .5421 .48573 L F .37181 .51018 m .44288 .47423 L p .59754 .44803 L F P 0 g s .39979 .49602 m .46739 .47194 L .4971 .47568 L .739 .656 0 r F .39979 .49602 m .4971 .47568 L .54101 .4812 L F .54101 .4812 m .37072 .50638 L p .39979 .49602 L F P 0 g s .46739 .47194 m .59024 .42819 L .56476 .45563 L .739 .656 0 r F .46739 .47194 m .56476 .45563 L .54101 .4812 L F .44288 .47423 m .43671 .43025 L .42957 .43178 L .304 0 0 r F .44345 .47413 m .43671 .43025 L .44288 .47423 L F .37072 .50638 m .43744 .45689 L p .59024 .42819 L .739 .656 0 r F P 0 g s .38461 .49607 m .46472 .4609 L .48579 .46539 L .73 .612 0 r F .38461 .49607 m .48579 .46539 L .53969 .47689 L F .53969 .47689 m .36935 .50277 L p .38461 .49607 L F P 0 g s .56542 .43285 m .56693 .40227 L .5578 .40423 L .304 0 0 r F .56915 .43215 m .56693 .40227 L .56542 .43285 L F .46472 .4609 m .58634 .4075 L .56216 .44347 L .73 .612 0 r F .46472 .4609 m .56216 .44347 L .53969 .47689 L F .58799 .40716 m .56293 .44333 L p .58634 .4075 L F P 0 g s .56293 .44333 m .53969 .47689 L p .56216 .44347 L .73 .612 0 r F P 0 g s .58634 .4075 m .56293 .44333 L .56216 .44347 L .73 .612 0 r F .59323 .42763 m .56617 .45539 L p .59024 .42819 L .739 .656 0 r F P 0 g s .56617 .45539 m .54101 .4812 L p .56476 .45563 L .739 .656 0 r F P 0 g s .59024 .42819 m .56617 .45539 L .56476 .45563 L .739 .656 0 r F .59842 .44788 m .56938 .46739 L p .59754 .44803 L .729 .686 0 r F P 0 g s .56938 .46739 m .5421 .48573 L p .56897 .46746 L .729 .686 0 r F P 0 g s .59754 .44803 m .56938 .46739 L .56897 .46746 L .729 .686 0 r F .57006 .46991 m .57082 .46979 L .57015 .46727 L .267 0 0 r F .57006 .46991 m .57015 .46727 L .56945 .46738 L F .57006 .46991 m .56945 .46738 L .56938 .46739 L F .56954 .46729 m .58423 .46499 L p .58395 .46511 L .729 .686 0 r F P 0 g s .57082 .46979 m .57021 .46726 L .57015 .46727 L .267 0 0 r F .56938 .46739 m .56954 .46729 L p .58395 .46511 L .729 .686 0 r F P 0 g s .57082 .46979 m .57158 .46967 L .56769 .45514 L .267 0 0 r F .56666 .45489 m .58136 .45242 L p .58043 .453 L .739 .656 0 r F P 0 g s .56617 .45539 m .56666 .45489 L p .58043 .453 L .739 .656 0 r F P 0 g s .56318 .44298 m .57791 .44034 L p .57742 .44074 L .73 .612 0 r F P 0 g s .56728 .45521 m .56769 .45514 L .56446 .44306 L .267 0 0 r F .56728 .45521 m .56446 .44306 L .56434 .44308 L F .56293 .44333 m .56318 .44298 L p .57742 .44074 L .73 .612 0 r F P 0 g s .57015 .46727 m .56306 .43782 L .56229 .43796 L .267 0 0 r F .57021 .46726 m .56306 .43782 L .57015 .46727 L F .56945 .46738 m .57015 .46727 L .56229 .43796 L F .56652 .45533 m .56229 .43796 L .56648 .45534 L F .56648 .45534 m .56356 .44322 L .56617 .45539 L F .56356 .44322 m .56347 .44324 L .56617 .45539 L F .56617 .45539 m .56347 .44324 L .56293 .44333 L F .57158 .46967 m .56382 .43768 L .56306 .43782 L F .57158 .46967 m .57234 .46955 L .56382 .43768 L F .57234 .46955 m .56459 .43754 L .56382 .43768 L F .57234 .46955 m .57311 .46944 L .56459 .43754 L F .57311 .46944 m .56536 .4374 L .56459 .43754 L F .57311 .46944 m .57387 .46932 L .56536 .4374 L F .57387 .46932 m .56613 .43725 L .56536 .4374 L F .57387 .46932 m .57464 .4692 L .56613 .43725 L F .57464 .4692 m .5669 .43711 L .56613 .43725 L F .57464 .4692 m .57541 .46908 L .57473 .46655 L F .57403 .46666 m .57473 .46655 L .5669 .43711 L F .57464 .4692 m .57473 .46655 L .57403 .46666 L F .57541 .46908 m .56767 .43697 L .5669 .43711 L F .57541 .46908 m .57617 .46896 L .56767 .43697 L F .57229 .45437 m .56844 .43683 L .56767 .43697 L F .57617 .46896 m .57265 .45431 L .57229 .45437 L F .57265 .45431 m .56844 .43683 L .57229 .45437 L F .57082 .46979 m .56769 .45514 L .56728 .45521 L F .56945 .46738 m .56652 .45533 L .56938 .46739 L F .56652 .45533 m .56648 .45534 L .56938 .46739 L F .56938 .46739 m .56648 .45534 L .56617 .45539 L F .57617 .46896 m .57694 .46885 L .56844 .43683 L F .57694 .46885 m .56921 .43669 L .56844 .43683 L F .57694 .46885 m .57771 .46873 L .56921 .43669 L F .57771 .46873 m .56999 .43654 L .56921 .43669 L F .57771 .46873 m .57848 .46861 L .56999 .43654 L F .57848 .46861 m .57076 .4364 L .56999 .43654 L F .57848 .46861 m .57926 .46849 L .57076 .4364 L F .57926 .46849 m .57154 .43626 L .57076 .4364 L F .57926 .46849 m .58003 .46837 L .57154 .43626 L F .58003 .46837 m .57231 .43612 L .57154 .43626 L F .58003 .46837 m .5808 .46825 L .57231 .43612 L F .5808 .46825 m .57309 .43597 L .57231 .43612 L F .5808 .46825 m .58158 .46813 L .57309 .43597 L F .57449 .44127 m .57387 .43583 L .57309 .43597 L F .58158 .46813 m .57514 .44115 L .57449 .44127 L F .57514 .44115 m .57387 .43583 L .57449 .44127 L F .58158 .46813 m .58236 .46801 L .57387 .43583 L F .58236 .46801 m .57465 .43569 L .57387 .43583 L F .58236 .46801 m .58313 .46789 L .57465 .43569 L F .58313 .46789 m .57543 .43554 L .57465 .43569 L F .58313 .46789 m .58391 .46777 L .57543 .43554 L F .57791 .44034 m .57767 .4407 L p .57742 .44074 L .73 .612 0 r F P 0 g s .58391 .46777 m .57622 .4354 L .57543 .43554 L .267 0 0 r F .58136 .45242 m .58088 .45293 L p .58043 .453 L .739 .656 0 r F P 0 g s .58423 .46499 m .58408 .46509 L p .58395 .46511 L .729 .686 0 r F P 0 g s .58391 .46777 m .58469 .46765 L .57622 .4354 L .267 0 0 r F .57263 .45791 m .56617 .45539 L .58043 .453 L .739 .656 0 r F .54959 .4724 m .56201 .45966 L p .57263 .45791 L F P 0 g s .56201 .45966 m .56617 .45539 L p .57263 .45791 L .739 .656 0 r F P 0 g s .56278 .46311 m .54753 .46557 L p .56991 .44699 L .73 .612 0 r F P 0 g s .56991 .44699 m .57742 .44074 L .57378 .44631 L .73 .612 0 r F .56991 .44699 m .57378 .44631 L .56278 .46311 L F .57767 .4407 m .57396 .44628 L p .57742 .44074 L F P 0 g s .57396 .44628 m .56278 .46311 L p .57378 .44631 L .73 .612 0 r F P 0 g s .57742 .44074 m .57396 .44628 L .57378 .44631 L .73 .612 0 r F .56482 .47004 m .54959 .4724 L p .57263 .45791 L .739 .656 0 r F P 0 g s .57263 .45791 m .58043 .453 L .57652 .45727 L .739 .656 0 r F .57263 .45791 m .57652 .45727 L .56482 .47004 L F .56652 .4773 m .55129 .47955 L p .57579 .46872 L .729 .686 0 r F P 0 g s .57579 .46872 m .58395 .46511 L .57964 .46812 L .729 .686 0 r F .57579 .46872 m .57964 .46812 L .56652 .4773 L F .58034 .47039 m .58108 .47028 L .58048 .46799 L .261 0 0 r F .58408 .46509 m .57974 .46811 L p .58395 .46511 L .729 .686 0 r F P 0 g s .57974 .46811 m .56652 .4773 L p .57964 .46812 L .729 .686 0 r F P 0 g s .58395 .46511 m .57974 .46811 L .57964 .46812 L .729 .686 0 r F .57579 .46872 m .56938 .46739 L .58395 .46511 L F .55129 .47955 m .56491 .4704 L p .57579 .46872 L F P 0 g s .56491 .4704 m .56938 .46739 L p .57579 .46872 L .729 .686 0 r F P 0 g s .57974 .46811 m .5772 .45716 L .57686 .45722 L .261 0 0 r F .58034 .47039 m .5798 .4681 L .57974 .46811 L F .58034 .47039 m .57987 .46809 L .5798 .4681 L F .58034 .47039 m .58048 .46799 L .57987 .46809 L F .57987 .46801 m .5941 .46582 L p .5938 .46594 L .729 .686 0 r F P 0 g s .58108 .47028 m .58054 .46799 L .58048 .46799 L .261 0 0 r F .57974 .46811 m .57987 .46801 L p .5938 .46594 L .729 .686 0 r F P 0 g s .58108 .47028 m .58182 .47017 L .57833 .45697 L .261 0 0 r F .58088 .45293 m .57686 .45722 L p .58043 .453 L .739 .656 0 r F P 0 g s .58043 .453 m .57686 .45722 L .57652 .45727 L .739 .656 0 r F .56991 .44699 m .56293 .44333 L .57742 .44074 L .73 .612 0 r F .54753 .46557 m .5591 .44887 L p .56991 .44699 L F P 0 g s .5591 .44887 m .56293 .44333 L p .56991 .44699 L .73 .612 0 r F P 0 g s .58108 .47028 m .57833 .45697 L .57793 .45704 L .261 0 0 r F .57729 .45676 m .59152 .45441 L p .59055 .45497 L .739 .656 0 r F P 0 g s .58048 .46799 m .5779 .45704 L .5776 .45709 L .261 0 0 r F .57686 .45722 m .57729 .45676 L p .59055 .45497 L .739 .656 0 r F P 0 g s .58054 .46799 m .57532 .44604 L .58048 .46799 L .261 0 0 r F .57418 .44595 m .58844 .44346 L p .58792 .44384 L .73 .612 0 r F P 0 g s .57396 .44628 m .57418 .44595 L p .58792 .44384 L .73 .612 0 r F P 0 g s .57532 .44604 m .57419 .44127 L .57531 .44604 L .261 0 0 r F .57532 .44604 m .57531 .44604 L .58048 .46799 L F .5776 .45709 m .57419 .44127 L .57345 .4414 L F .5779 .45704 m .57419 .44127 L .5776 .45709 L F .57793 .45704 m .57833 .45697 L .57544 .44602 L F .57793 .45704 m .57544 .44602 L .57532 .44604 L F .5772 .45716 m .5776 .45709 L .57345 .4414 L F .5772 .45716 m .57458 .44617 L .57686 .45722 L F .57458 .44617 m .57448 .44619 L .57686 .45722 L F .57686 .45722 m .57448 .44619 L .57396 .44628 L F .58182 .47017 m .57493 .44113 L .57419 .44127 L F .58182 .47017 m .58256 .47006 L .57493 .44113 L F .58256 .47006 m .57567 .441 L .57493 .44113 L F .58256 .47006 m .5833 .46994 L .57567 .441 L F .5833 .46994 m .57641 .44087 L .57567 .441 L F .5833 .46994 m .58404 .46983 L .57641 .44087 L F .58404 .46983 m .57716 .44074 L .57641 .44087 L F .58404 .46983 m .58478 .46972 L .58418 .46742 L F .58349 .46753 m .58418 .46742 L .57716 .44074 L F .58404 .46983 m .58418 .46742 L .58349 .46753 L F .58478 .46972 m .5779 .4406 L .57716 .44074 L F .58478 .46972 m .58552 .4696 L .5779 .4406 L F .58552 .4696 m .57865 .44047 L .5779 .4406 L F .58552 .4696 m .58627 .46949 L .57865 .44047 L F .58279 .45624 m .5794 .44034 L .57865 .44047 L F .58627 .46949 m .58313 .45618 L .58279 .45624 L F .58313 .45618 m .5794 .44034 L .58279 .45624 L F .5798 .4681 m .5772 .45716 L .57974 .46811 L F .5798 .4681 m .5776 .45709 L .5772 .45716 L F .57987 .46809 m .5776 .45709 L .5798 .4681 L F .57987 .46809 m .58048 .46799 L .5776 .45709 L F .58627 .46949 m .58701 .46938 L .5794 .44034 L F .58701 .46938 m .58015 .4402 L .5794 .44034 L F .58701 .46938 m .58776 .46926 L .58015 .4402 L F .58776 .46926 m .58089 .44007 L .58015 .4402 L F .58776 .46926 m .5885 .46915 L .58089 .44007 L F .5885 .46915 m .58164 .43993 L .58089 .44007 L F .5885 .46915 m .58925 .46904 L .58164 .43993 L F .58925 .46904 m .5824 .4398 L .58164 .43993 L F .58925 .46904 m .59 .46892 L .5824 .4398 L F .59 .46892 m .58315 .43966 L .5824 .4398 L F .59 .46892 m .59075 .46881 L .58315 .43966 L F .59075 .46881 m .5839 .43953 L .58315 .43966 L F .59075 .46881 m .5915 .4687 L .5839 .43953 L F .58515 .44433 m .58466 .43939 L .5839 .43953 L F .5915 .4687 m .58578 .44422 L .58515 .44433 L F .58578 .44422 m .58466 .43939 L .58515 .44433 L F .5915 .4687 m .59225 .46858 L .58466 .43939 L F .59225 .46858 m .58541 .43926 L .58466 .43939 L F .59225 .46858 m .593 .46847 L .58541 .43926 L F .593 .46847 m .58617 .43912 L .58541 .43926 L F .593 .46847 m .59376 .46835 L .58617 .43912 L F .58844 .44346 m .58823 .44379 L p .58792 .44384 L .73 .612 0 r F P 0 g s .59152 .45441 m .59111 .45487 L p .59055 .45497 L .739 .656 0 r F P 0 g s .59376 .46835 m .58692 .43899 L .58617 .43912 L .261 0 0 r F .58681 .45709 m .57686 .45722 L .59055 .45497 L .739 .656 0 r F .56579 .46901 m .5752 .45898 L p .58681 .45709 L F P 0 g s .5752 .45898 m .57686 .45722 L p .58681 .45709 L .739 .656 0 r F P 0 g s .57686 .45722 m .56482 .47004 L p .57652 .45727 L .739 .656 0 r F P 0 g s .57829 .45941 m .56367 .46178 L p .5843 .44652 L .73 .612 0 r F P 0 g s .5843 .44652 m .58792 .44384 L .5865 .44614 L .73 .612 0 r F .5843 .44652 m .5865 .44614 L .57829 .45941 L F .5941 .46582 m .59397 .46591 L p .5938 .46594 L .729 .686 0 r F P 0 g s .59376 .46835 m .59451 .46824 L .58692 .43899 L .261 0 0 r F .58823 .44379 m .57829 .45941 L p .58792 .44384 L .73 .612 0 r F P 0 g s .56367 .46178 m .57396 .44628 L p .58792 .44384 L .73 .612 0 r F P 0 g s .58676 .4461 m .58817 .44106 L .58557 .44152 L .258 0 0 r F .5804 .46674 m .56579 .46901 L p .58681 .45709 L .739 .656 0 r F P 0 g s .58681 .45709 m .59055 .45497 L .58903 .45673 L .739 .656 0 r F .58681 .45709 m .58903 .45673 L .5804 .46674 L F .58216 .47441 m .56756 .47657 L p .58992 .46751 L .729 .686 0 r F P 0 g s .58992 .46751 m .5938 .46594 L .5921 .46718 L .729 .686 0 r F .58992 .46751 m .5921 .46718 L .58216 .47441 L F .59281 .46936 m .5954 .46897 L .59483 .46676 L .258 0 0 r F .59397 .46591 m .59224 .46716 L p .5938 .46594 L .729 .686 0 r F P 0 g s .59224 .46716 m .58216 .47441 L p .5921 .46718 L .729 .686 0 r F P 0 g s .5938 .46594 m .59224 .46716 L .5921 .46718 L .729 .686 0 r F .58992 .46751 m .57974 .46811 L .5938 .46594 L F .56756 .47657 m .57795 .46935 L p .58992 .46751 L F P 0 g s .57795 .46935 m .57974 .46811 L p .58992 .46751 L .729 .686 0 r F P 0 g s .59224 .46716 m .59069 .45645 L .5895 .45665 L .258 0 0 r F .59281 .46936 m .59244 .46713 L .59224 .46716 L F .59281 .46936 m .59269 .46709 L .59244 .46713 L F .59281 .46936 m .59483 .46676 L .59269 .46709 L F .59236 .46707 m .64366 .45919 L p .64281 .45939 L .729 .686 0 r F P 0 g s .5954 .46897 m .59503 .46673 L .59483 .46676 L .258 0 0 r F .59224 .46716 m .59236 .46707 L p .64281 .45939 L .729 .686 0 r F P 0 g s .5954 .46897 m .598 .46858 L .5947 .4558 L .258 0 0 r F .5899 .45621 m .64124 .44782 L p .63838 .44868 L .739 .656 0 r F P 0 g s .5895 .45665 m .5899 .45621 L p .63838 .44868 L .739 .656 0 r F P 0 g s .58696 .44578 m .6384 .43689 L p .63685 .43745 L .73 .612 0 r F P 0 g s .59329 .45603 m .5947 .4558 L .59196 .4452 L .258 0 0 r F .59329 .45603 m .59196 .4452 L .59154 .44527 L F .58676 .4461 m .58696 .44578 L p .63685 .43745 L .73 .612 0 r F P 0 g s .59483 .46676 m .59077 .4406 L .58817 .44106 L .258 0 0 r F .59503 .46673 m .59077 .4406 L .59483 .46676 L F .59111 .45487 m .5804 .46674 L p .59055 .45497 L .739 .656 0 r F P 0 g s .59069 .45645 m .5921 .45623 L .58817 .44106 L .258 0 0 r F .5895 .45665 m .58857 .44579 L .58676 .4461 L F .59069 .45645 m .58817 .44106 L .5895 .45665 L F .598 .46858 m .59339 .44014 L .59077 .4406 L F .598 .46858 m .60061 .46818 L .59339 .44014 L F .60061 .46818 m .59603 .43967 L .59339 .44014 L F .60061 .46818 m .60323 .46778 L .59603 .43967 L F .60323 .46778 m .59867 .4392 L .59603 .43967 L F .60323 .46778 m .60586 .46738 L .59867 .4392 L F .60586 .46738 m .60133 .43873 L .59867 .4392 L F .60586 .46738 m .60851 .46698 L .60133 .43873 L F .60851 .46698 m .60399 .43826 L .60133 .43873 L F .60851 .46698 m .61117 .46658 L .60399 .43826 L F .61117 .46658 m .60668 .43779 L .60399 .43826 L F .61117 .46658 m .61384 .46618 L .60668 .43779 L F .61384 .46618 m .60937 .43731 L .60668 .43779 L F .61384 .46618 m .61652 .46577 L .61596 .46352 L F .61349 .4639 m .61596 .46352 L .60937 .43731 L F .61384 .46618 m .61596 .46352 L .61349 .4639 L F .61326 .45278 m .61207 .43683 L .60937 .43731 L F .61652 .46577 m .61449 .45257 L .61326 .45278 L F .61449 .45257 m .61207 .43683 L .61326 .45278 L F .5954 .46897 m .5947 .4558 L .59329 .45603 L F .59244 .46713 m .59069 .45645 L .59224 .46716 L F .59244 .46713 m .5921 .45623 L .59069 .45645 L F .59269 .46709 m .5921 .45623 L .59244 .46713 L F .59269 .46709 m .59483 .46676 L .5921 .45623 L F .61652 .46577 m .61922 .46536 L .61207 .43683 L F .61325 .44152 m .61479 .43635 L .61207 .43683 L F .61922 .46536 m .61552 .44113 L .61325 .44152 L F .61552 .44113 m .61479 .43635 L .61325 .44152 L F .61922 .46536 m .62193 .46495 L .61479 .43635 L F .62193 .46495 m .61752 .43587 L .61479 .43635 L F .62193 .46495 m .62465 .46454 L .61752 .43587 L F .62465 .46454 m .62027 .43538 L .61752 .43587 L F .62465 .46454 m .62738 .46413 L .62027 .43538 L F .62738 .46413 m .62302 .4349 L .62027 .43538 L F .62738 .46413 m .63012 .46371 L .62302 .4349 L F .63012 .46371 m .62579 .43441 L .62302 .4349 L F .63012 .46371 m .63288 .46329 L .62579 .43441 L F .63288 .46329 m .62858 .43391 L .62579 .43441 L F .63288 .46329 m .63565 .46287 L .62858 .43391 L F .62974 .43868 m .63137 .43342 L .62858 .43391 L F .63565 .46287 m .63208 .43827 L .62974 .43868 L F .63208 .43827 m .63137 .43342 L .62974 .43868 L F .64086 .43229 m .64337 .42629 L .63959 .42698 L .263 0 0 r F .64683 .45657 m .72262 .4448 L p .72148 .44506 L .729 .686 0 r F P 0 g s .64733 .45922 m .64701 .45662 L .64671 .45667 L .263 0 0 r F .64671 .45667 m .64683 .45657 L p .72148 .44506 L .729 .686 0 r F P 0 g s .64105 .43193 m .71713 .41849 L p .71504 .4192 L .73 .612 0 r F P 0 g s .64395 .43174 m .64105 .43193 L .71504 .4192 L .73 .612 0 r F .64417 .44402 m .72005 .43141 L p .71622 .4325 L .739 .656 0 r F P 0 g s .64733 .45922 m .65109 .45864 L .64756 .44388 L .263 0 0 r F .64733 .45922 m .64756 .44388 L .64586 .44417 L F .6438 .44451 m .64417 .44402 L p .71622 .4325 L .739 .656 0 r F P 0 g s .64733 .45922 m .64464 .43162 L .64402 .43173 L .263 0 0 r F .64671 .45667 m .64402 .43173 L .64086 .43229 L F .64701 .45662 m .64402 .43173 L .64671 .45667 L F .65109 .45864 m .64717 .42561 L .64337 .42629 L F .65109 .45864 m .65487 .45806 L .64717 .42561 L F .63565 .46287 m .63844 .46245 L .63521 .4492 L .258 0 0 r F .6337 .44944 m .63521 .4492 L .63137 .43342 L F .63565 .46287 m .63521 .4492 L .6337 .44944 L F .65487 .45806 m .651 .42491 L .64717 .42561 L .263 0 0 r F .65487 .45806 m .65868 .45748 L .651 .42491 L F .65868 .45748 m .65485 .42422 L .651 .42491 L F .65868 .45748 m .66251 .45689 L .65485 .42422 L F .66251 .45689 m .65872 .42351 L .65485 .42422 L F .66251 .45689 m .66636 .4563 L .65872 .42351 L F .66636 .4563 m .66262 .42281 L .65872 .42351 L F .66636 .4563 m .67025 .45571 L .66262 .42281 L F .67025 .45571 m .66655 .4221 L .66262 .42281 L F .67025 .45571 m .67415 .45511 L .66655 .4221 L F .67415 .45511 m .6705 .42138 L .66655 .4221 L F .67415 .45511 m .67808 .45451 L .6705 .42138 L F .67462 .4394 m .67448 .42066 L .6705 .42138 L F .67808 .45451 m .67644 .4391 L .67462 .4394 L F .67644 .4391 m .67448 .42066 L .67462 .4394 L F .63844 .46245 m .63418 .43292 L .63137 .43342 L .258 0 0 r F .63844 .46245 m .64124 .46203 L .64068 .45972 L F .6381 .46012 m .64068 .45972 L .63418 .43292 L F .63844 .46245 m .64068 .45972 L .6381 .46012 L F .67808 .45451 m .68204 .4539 L .67448 .42066 L .263 0 0 r F .67572 .42613 m .67848 .41994 L .67448 .42066 L F .68204 .4539 m .67907 .42554 L .67572 .42613 L F .67907 .42554 m .67848 .41994 L .67572 .42613 L F .6384 .43689 m .63823 .43721 L p .63685 .43745 L .73 .612 0 r F P 0 g s .64124 .44782 m .6409 .44827 L p .63838 .44868 L .739 .656 0 r F P 0 g s .64124 .46203 m .63701 .43242 L .63418 .43292 L .258 0 0 r F .64366 .45919 m .64355 .45928 L p .64281 .45939 L .729 .686 0 r F P 0 g s .64124 .46203 m .64405 .4616 L .63701 .43242 L .258 0 0 r F .68204 .4539 m .68602 .4533 L .68542 .45066 L .263 0 0 r F .68176 .45123 m .68542 .45066 L .67848 .41994 L F .68204 .4539 m .68542 .45066 L .68176 .45123 L F .68602 .4533 m .68251 .41921 L .67848 .41994 L F .68602 .4533 m .69002 .45268 L .68251 .41921 L F .69002 .45268 m .68657 .41847 L .68251 .41921 L F .69002 .45268 m .69406 .45206 L .68657 .41847 L F .69406 .45206 m .69065 .41773 L .68657 .41847 L F .69406 .45206 m .69812 .45144 L .69065 .41773 L F .69812 .45144 m .69476 .41699 L .69065 .41773 L F .69812 .45144 m .7022 .45082 L .69476 .41699 L F .7022 .45082 m .69889 .41624 L .69476 .41699 L F .7022 .45082 m .70631 .45019 L .69889 .41624 L F .70631 .45019 m .70306 .41549 L .69889 .41624 L F .70631 .45019 m .71045 .44955 L .70306 .41549 L F .71045 .44955 m .70725 .41473 L .70306 .41549 L F .71045 .44955 m .71462 .44892 L .70725 .41473 L F .71462 .44892 m .71147 .41396 L .70725 .41473 L F .71462 .44892 m .71881 .44828 L .71147 .41396 L F .71713 .41849 m .717 .41885 L p .71504 .4192 L .73 .612 0 r F P 0 g s .72005 .43141 m .71977 .43191 L p .71622 .4325 L .739 .656 0 r F P 0 g s .71881 .44828 m .71572 .41319 L .71147 .41396 L .263 0 0 r F .72262 .4448 m .72253 .4449 L p .72148 .44506 L .729 .686 0 r F P 0 g s .71881 .44828 m .72303 .44763 L .71572 .41319 L .263 0 0 r F .7153 .4528 m .63723 .46451 L p .72148 .44506 L .729 .686 0 r F P 0 g s .72253 .4449 m .7153 .4528 L p .72148 .44506 L .729 .686 0 r F P 0 g s .71344 .4432 m .6353 .45553 L p .71622 .4325 L .739 .656 0 r F P 0 g s .68752 .44067 m .6438 .44451 L .71622 .4325 L .739 .656 0 r F .6409 .44827 m .6438 .44451 L p .68752 .44067 L F P 0 g s .64586 .44417 m .64756 .44388 L .64464 .43162 L .263 0 0 r F .71132 .43398 m .63304 .44692 L p .71504 .4192 L .73 .612 0 r F P 0 g s .717 .41885 m .71132 .43398 L p .71504 .4192 L .73 .612 0 r F P 0 g s .69226 .4518 m .64671 .45667 L .72148 .44506 L .729 .686 0 r F .63723 .46451 m .64355 .45928 L p .69226 .4518 L F P 0 g s .64355 .45928 m .64671 .45667 L p .69226 .4518 L .729 .686 0 r F P 0 g s .71977 .43191 m .71344 .4432 L p .71622 .4325 L .739 .656 0 r F P 0 g s .6353 .45553 m .6409 .44827 L p .68752 .44067 L .739 .656 0 r F P 0 g s .64402 .43173 m .64464 .43162 L .64337 .42629 L .263 0 0 r F .63823 .43721 m .64086 .43229 L p .68633 .4289 L .73 .612 0 r F P 0 g s .64086 .43229 m .64105 .43193 L p .64395 .43174 L .73 .612 0 r F P 0 g s .64086 .43229 m .64395 .43174 L .68633 .4289 L .73 .612 0 r F .64402 .43173 m .64337 .42629 L .64086 .43229 L .263 0 0 r F .68633 .4289 m .64395 .43174 L .71504 .4192 L .73 .612 0 r F .63304 .44692 m .63823 .43721 L p .68633 .4289 L F P 0 g s .63154 .44972 m .579 .45829 L p .63685 .43745 L .73 .612 0 r F P 0 g s .63823 .43721 m .63154 .44972 L p .63685 .43745 L .73 .612 0 r F P 0 g s .63364 .45768 m .58118 .46587 L p .63838 .44868 L .739 .656 0 r F P 0 g s .6409 .44827 m .63364 .45768 L p .63838 .44868 L .739 .656 0 r F P 0 g s .63543 .46599 m .583 .4738 L p .64281 .45939 L .729 .686 0 r F P 0 g s .64355 .45928 m .63543 .46599 L p .64281 .45939 L .729 .686 0 r F P 0 g s .579 .45829 m .58676 .4461 L p .63685 .43745 L .73 .612 0 r F P 0 g s .59154 .44527 m .59196 .4452 L .59077 .4406 L .258 0 0 r F .58118 .46587 m .5895 .45665 L p .63838 .44868 L .739 .656 0 r F P 0 g s .583 .4738 m .59224 .46716 L p .64281 .45939 L .729 .686 0 r F P 0 g s .58857 .44579 m .58817 .44106 L .58676 .4461 L .258 0 0 r F .57532 .44604 m .57544 .44602 L .57419 .44127 L .261 0 0 r F .57458 .44617 m .57345 .4414 L .57448 .44619 L F .57396 .44628 m .57345 .4414 L .57271 .44153 L F .57448 .44619 m .57345 .4414 L .57396 .44628 L F .56434 .44308 m .56446 .44306 L .56306 .43782 L .267 0 0 r