(************** Content-type: application/mathematica ************** CreatedBy='Mathematica 5.2' 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[ 302556, 8180]*) (*NotebookOutlinePosition[ 303238, 8203]*) (* CellTagsIndexPosition[ 303194, 8199]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell[TextData[{ Cell[BoxData[ \(TraditionalForm\`X\^\(\(y\)\(\ \)\) = \ y\^x\)]], "\nby Debra Woods" }], "Title"], Cell[CellGroupData[{ Cell[TextData[{ "A professor at the ISMAA conference came to the booth with a problem that \ came up in his class. He asked if we can visualize the solution to\n\n", Cell[BoxData[ \(TraditionalForm\`x\^y = \ y\^x\)]], ". \n\nFirst he wanted to see a 3D plot of it:" }], "Section"], Cell[CellGroupData[{ Cell[BoxData[ \(\(plt = Plot3D[x^y - y^x, {x, 0, 5}, {y, 0, 5}];\)\)], "Input", CellChangeTimes -> {{3.38427736587219*^9, 3.384277400791089*^9}, \ {3.38427747241092*^9, 3.38427747920268*^9}}], Cell[BoxData[ RowBox[{\(Power::"indet"\), \(\(:\)\(\ \)\), "\<\"Indeterminate \ expression \\!\\(0.`\\^0.`\\) encountered. \\!\\(\\*ButtonBox[\\\"More\ \[Ellipsis]\\\", ButtonStyle->\\\"RefGuideLinkText\\\", ButtonFrame->None, \ ButtonData:>\\\"General::indet\\\"]\\)\"\>"}]], "Message"], Cell[BoxData[ RowBox[{\(Power::"indet"\), \(\(:\)\(\ \)\), "\<\"Indeterminate \ expression \\!\\(0.`\\^0.`\\) encountered. \\!\\(\\*ButtonBox[\\\"More\ \[Ellipsis]\\\", ButtonStyle->\\\"RefGuideLinkText\\\", ButtonFrame->None, \ ButtonData:>\\\"General::indet\\\"]\\)\"\>"}]], "Message"], Cell[BoxData[ RowBox[{\(Power::"indet"\), 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.39431 Metetra .591 .42 .619 r .85147 .39431 .87334 .51816 .88787 .40116 .87754 .38616 Metetra .664 .741 .907 r .87754 .38616 .88787 .40116 .914 .39306 .90384 .37793 Metetra .664 .741 .907 r .90384 .37793 .914 .39306 .94036 .3849 .93037 .36962 Metetra .708 .761 .893 r .33441 .63243 .34835 .64468 .37089 .63457 .35707 .62235 Metetra .719 .765 .889 r .35707 .62235 .37089 .63457 .39361 .62341 .37991 .61136 Metetra .726 .77 .888 r .37991 .61136 .39361 .62341 .41648 .61147 .40291 .59978 Metetra .726 .778 .893 r .40291 .59978 .41648 .61147 .43948 .59941 .42605 .58824 Metetra .714 .786 .908 r .42605 .58824 .43948 .59941 .46259 .58827 .44929 .57763 Metetra .682 .79 .932 r .44929 .57763 .46259 .58827 .4858 .57947 .47265 .56907 Metetra .613 .779 .96 r .47265 .56907 .4858 .57947 .50918 .57471 .49617 .56379 Metetra .49 .725 .976 r .49617 .56379 .50918 .57471 .5328 .57591 .5199 .5631 Metetra .321 .608 .951 r .5199 .5631 .5328 .57591 .55681 .58516 .54397 .56827 Metetra .175 .455 .881 r .54397 .56827 .55681 .58516 .58143 .60455 .56852 .58037 Metetra .132 .335 .799 r .56852 .58037 .58143 .60455 .60694 .63598 .59372 .6001 Metetra .188 .284 .731 r .59372 .6001 .60694 .63598 .63365 .68083 .61975 .62738 Metetra .285 .283 .682 r .61975 .62738 .63365 .68083 .65958 .67947 .64675 .66089 Metetra .568 .656 .895 r .64675 .66089 .65958 .67947 .68558 .67237 .67309 .6591 Metetra .645 .763 .934 r .67309 .6591 .68558 .67237 .71181 .66521 .6995 .65181 Metetra .645 .763 .934 r .6995 .65181 .71181 .66521 .73829 .65798 .72615 .64446 Metetra .645 .763 .934 r .72615 .64446 .73829 .65798 .76501 .65069 .75305 .63703 Metetra .645 .763 .934 r .75305 .63703 .76501 .65069 .79199 .64332 .78021 .62954 Metetra .971 .754 .553 r .78021 .62954 .79199 .64332 .81922 .63589 .79801 .50492 Metetra .764 .536 .589 r .79801 .50492 .81922 .63589 .83582 .51157 .8148 .38742 Metetra .59 .418 .617 r .8148 .38742 .83582 .51157 .85147 .39431 .8408 .3792 Metetra .664 .741 .907 r .8408 .3792 .85147 .39431 .87754 .38616 .86704 .3709 Metetra .664 .741 .907 r .86704 .3709 .87754 .38616 .90384 .37793 .89351 .36254 Metetra .664 .741 .907 r .89351 .36254 .90384 .37793 .93037 .36962 .92022 .35409 Metetra .706 .761 .895 r .32024 .61998 .33441 .63243 .35707 .62235 .34303 .60994 Metetra .716 .764 .891 r .34303 .60994 .35707 .62235 .37991 .61136 .366 .59914 Metetra .72 .77 .892 r .366 .59914 .37991 .61136 .40291 .59978 .38912 .58792 Metetra .718 .777 .899 r .38912 .58792 .40291 .59978 .42605 .58824 .41238 .5769 Metetra .705 .785 .913 r .41238 .5769 .42605 .58824 .44929 .57763 .43576 .5668 Metetra .676 .789 .934 r .43576 .5668 .44929 .57763 .47265 .56907 .45927 .55848 Metetra .62 .781 .958 r .45927 .55848 .47265 .56907 .49617 .56379 .48293 .55282 Metetra .531 .745 .973 r .48293 .55282 .49617 .56379 .5199 .5631 .5068 .55065 Metetra .421 .67 .965 r .5068 .55065 .5199 .5631 .54397 .56827 .53096 .55266 Metetra .329 .569 .927 r .53096 .55266 .54397 .56827 .56852 .58037 .55551 .5593 Metetra .298 .476 .867 r .55551 .5593 .56852 .58037 .59372 .6001 .58057 .57053 Metetra .332 .417 .799 r .58057 .57053 .59372 .6001 .61975 .62738 .60621 .58561 Metetra .398 .394 .738 r .60621 .58561 .61975 .62738 .64675 .66089 .63249 .60266 Metetra .469 .395 .691 r .63249 .60266 .64675 .66089 .67309 .6591 .65933 .61814 Metetra .498 .463 .749 r .65933 .61814 .67309 .6591 .6995 .65181 .68641 .62618 Metetra .652 .631 .817 r .68641 .62618 .6995 .65181 .72615 .64446 .71309 .61775 Metetra .819 .694 .726 r .71309 .61775 .72615 .64446 .75305 .63703 .73819 .58031 Metetra .825 .618 .624 r .73819 .58031 .75305 .63703 .78021 .62954 .75991 .49823 Metetra .764 .536 .589 r .75991 .49823 .78021 .62954 .79801 .50492 .77786 .38047 Metetra .588 .416 .616 r .77786 .38047 .79801 .50492 .8148 .38742 .80379 .37218 Metetra .664 .741 .907 r .80379 .37218 .8148 .38742 .8408 .3792 .82996 .36383 Metetra .664 .741 .907 r .82996 .36383 .8408 .3792 .86704 .3709 .85636 .3554 Metetra .664 .741 .907 r .85636 .3554 .86704 .3709 .89351 .36254 .88301 .34689 Metetra .664 .741 .907 r .88301 .34689 .89351 .36254 .92022 .35409 .9099 .3383 Metetra .704 .76 .896 r .30586 .60734 .32024 .61998 .34303 .60994 .32876 .59735 Metetra .711 .764 .894 r .32876 .59735 .34303 .60994 .366 .59914 .35185 .58674 Metetra .714 .769 .896 r .35185 .58674 .366 .59914 .38912 .58792 .3751 .57591 Metetra .71 .776 .904 r .3751 .57591 .38912 .58792 .41238 .5769 .39849 .56538 Metetra .696 .783 .918 r .39849 .56538 .41238 .5769 .43576 .5668 .422 .55578 Metetra .669 .787 .937 r .422 .55578 .43576 .5668 .45927 .55848 .44565 .54771 Metetra .624 .782 .957 r .44565 .54771 .45927 .55848 .48293 .55282 .46945 .54177 Metetra .56 .757 .97 r .46945 .54177 .48293 .55282 .5068 .55065 .49347 .53846 Metetra .488 .709 .968 r .49347 .53846 .5068 .55065 .53096 .55266 .51775 .53809 Metetra .432 .644 .946 r .51775 .53809 .53096 .55266 .55551 .5593 .54236 .54069 Metetra .416 .577 .904 r .54236 .54069 .55551 .5593 .58057 .57053 .56738 .54587 Metetra .441 .524 .847 r .56738 .54587 .58057 .57053 .60621 .58561 .59285 .55262 Metetra .489 .492 .787 r .59285 .55262 .60621 .58561 .63249 .60266 .61876 .55902 Metetra .544 .48 .734 r .61876 .55902 .63249 .60266 .65933 .61814 .645 .56193 Metetra .599 .483 .693 r .645 .56193 .65933 .61814 .68641 .62618 .67129 .55655 Metetra .653 .498 .661 r .67129 .55655 .68641 .62618 .71309 .61775 .69709 .53607 Metetra .706 .521 .635 r .69709 .53607 .71309 .61775 .73819 .58031 .72151 .49148 Metetra .764 .553 .612 r .72151 .49148 .73819 .58031 .75991 .49823 .74323 .41199 Metetra .706 .515 .628 r .74323 .41199 .75991 .49823 .77786 .38047 .76649 .36512 Metetra .664 .741 .907 r .76649 .36512 .77786 .38047 .80379 .37218 .79259 .3567 Metetra .664 .741 .907 r .79259 .3567 .80379 .37218 .82996 .36383 .81892 .3482 Metetra .664 .741 .907 r .81892 .3482 .82996 .36383 .85636 .3554 .8455 .33962 Metetra .664 .741 .907 r .8455 .33962 .85636 .3554 .88301 .34689 .87232 .33097 Metetra .664 .741 .907 r .87232 .33097 .88301 .34689 .9099 .3383 .89939 .32223 Metetra .701 .76 .897 r .29124 .5945 .30586 .60734 .32876 .59735 .31427 .58457 Metetra .707 .763 .896 r .31427 .58457 .32876 .59735 .35185 .58674 .33748 .57418 Metetra .707 .768 .9 r .33748 .57418 .35185 .58674 .3751 .57591 .36085 .56373 Metetra .701 .775 .909 r .36085 .56373 .3751 .57591 .39849 .56538 .38435 .5537 Metetra .687 .782 .923 r .38435 .5537 .39849 .56538 .422 .55578 .408 .54455 Metetra .662 .786 .94 r .408 .54455 .422 .55578 .44565 .54771 .43178 .53674 Metetra .625 .782 .957 r .43178 .53674 .44565 .54771 .46945 .54177 .45574 .53062 Metetra .579 .766 .968 r .45574 .53062 .46945 .54177 .49347 .53846 .4799 .52646 Metetra .532 .735 .968 r .4799 .52646 .49347 .53846 .51775 .53809 .50431 .52431 Metetra .499 .692 .955 r .50431 .52431 .51775 .53809 .54236 .54069 .52903 .524 Metetra .495 .647 .925 r .52903 .524 .54236 .54069 .56738 .54587 .55409 .52497 Metetra .517 .605 .88 r .55409 .52497 .56738 .54587 .59285 .55262 .57952 .5262 Metetra .557 .575 .828 r .57952 .5262 .59285 .55262 .61876 .55902 .60528 .52596 Metetra .604 .559 .777 r .60528 .52596 .61876 .55902 .645 .56193 .63127 .52166 Metetra .653 .556 .733 r .63127 .52166 .645 .56193 .67129 .55655 .65725 .50958 Metetra .705 .567 .696 r .65725 .50958 .67129 .55655 .69709 .53607 .6828 .48468 Metetra .76 .589 .665 r .6828 .48468 .69709 .53607 .72151 .49148 .70726 .44052 Metetra .822 .623 .634 r .70726 .44052 .72151 .49148 .74323 .41199 .72964 .36952 Metetra .692 .569 .711 r .72964 .36952 .74323 .41199 .76649 .36512 .75493 .34951 Metetra .664 .741 .907 r .75493 .34951 .76649 .36512 .79259 .3567 .7812 .34095 Metetra .664 .741 .907 r .7812 .34095 .79259 .3567 .81892 .3482 .8077 .33231 Metetra .664 .741 .907 r .8077 .33231 .81892 .3482 .8455 .33962 .83446 .32358 Metetra .664 .741 .907 r .83446 .32358 .8455 .33962 .87232 .33097 .86146 .31478 Metetra .664 .741 .907 r .86146 .31478 .87232 .33097 .89939 .32223 .88871 .30589 Metetra .699 .759 .899 r .27639 .58145 .29124 .5945 .31427 .58457 .29954 .57159 Metetra .702 .763 .899 r .29954 .57159 .31427 .58457 .33748 .57418 .32286 .56144 Metetra .7 .768 .904 r .32286 .56144 .33748 .57418 .36085 .56373 .34635 .55139 Metetra .692 .774 .914 r .34635 .55139 .36085 .56373 .38435 .5537 .36998 .54183 Metetra .678 .78 .927 r .36998 .54183 .38435 .5537 .408 .54455 .39374 .53312 Metetra .655 .784 .943 r .39374 .53312 .408 .54455 .43178 .53674 .41767 .52556 Metetra .625 .782 .956 r .41767 .52556 .43178 .53674 .45574 .53062 .44177 .51934 Metetra .591 .771 .966 r .44177 .51934 .45574 .53062 .4799 .52646 .46609 .51455 Metetra .56 .751 .967 r .46609 .51455 .4799 .52646 .50431 .52431 .49065 .51112 Metetra .542 .724 .958 r .49065 .51112 .50431 .52431 .52903 .524 .51549 .50877 Metetra .544 .694 .937 r .51549 .50877 .52903 .524 .55409 .52497 .54065 .50692 Metetra .566 .666 .905 r .54065 .50692 .55409 .52497 .57952 .5262 .56612 .50465 Metetra .602 .643 .863 r .56612 .50465 .57952 .5262 .60528 .52596 .59188 .50051 Metetra .646 .63 .82 r .59188 .50051 .60528 .52596 .63127 .52166 .61783 .4925 Metetra .695 .629 .778 r .61783 .4925 .63127 .52166 .65725 .50958 .64379 .47782 Metetra .748 .641 .741 r .64379 .47782 .65725 .50958 .6828 .48468 .66944 .45285 Metetra .809 .667 .706 r .66944 .45285 .6828 .48468 .70726 .44052 .69429 .41302 Metetra .878 .708 .666 r .69429 .41302 .70726 .44052 .72964 .36952 .71764 .35301 Metetra .781 .768 .842 r .71764 .35301 .72964 .36952 .75493 .34951 .74318 .33364 Metetra .664 .741 .907 r .74318 .33364 .75493 .34951 .7812 .34095 .76961 .32493 Metetra .664 .741 .907 r .76961 .32493 .7812 .34095 .8077 .33231 .79629 .31614 Metetra .664 .741 .907 r .79629 .31614 .8077 .33231 .83446 .32358 .82322 .30727 Metetra .664 .741 .907 r .82322 .30727 .83446 .32358 .86146 .31478 .85041 .29831 Metetra .664 .741 .907 r .85041 .29831 .86146 .31478 .88871 .30589 .87784 .28927 Metetra .696 .759 .9 r .26129 .56818 .27639 .58145 .29954 .57159 .28456 .55842 Metetra .697 .762 .902 r .28456 .55842 .29954 .57159 .32286 .56144 .308 .54852 Metetra .693 .767 .909 r .308 .54852 .32286 .56144 .34635 .55139 .3316 .53888 Metetra .683 .773 .919 r .3316 .53888 .34635 .55139 .36998 .54183 .35534 .52978 Metetra .669 .779 .932 r .35534 .52978 .36998 .54183 .39374 .53312 .37924 .52149 Metetra .648 .782 .945 r .37924 .52149 .39374 .53312 .41767 .52556 .4033 .51416 Metetra .624 .781 .957 r .4033 .51416 .41767 .52556 .44177 .51934 .42755 .5079 Metetra .599 .774 .964 r .42755 .5079 .44177 .51934 .46609 .51455 .45202 .50267 Metetra .578 .762 .966 r .45202 .50267 .46609 .51455 .49065 .51112 .47673 .49835 Metetra .568 .745 .96 r .47673 .49835 .49065 .51112 .51549 .50877 .50172 .49462 Metetra .574 .727 .946 r .50172 .49462 .51549 .50877 .54065 .50692 .52701 .49096 Metetra .595 .71 .924 r .52701 .49096 .54065 .50692 .56612 .50465 .55258 .4866 Metetra .628 .697 .894 r .55258 .4866 .56612 .50465 .59188 .50051 .57843 .48042 Metetra .67 .691 .861 r .57843 .48042 .59188 .50051 .61783 .4925 .60447 .47091 Metetra .719 .697 .828 r .60447 .47091 .61783 .4925 .64379 .47782 .63057 .45608 Metetra .777 .716 .795 r .63057 .45608 .64379 .47782 .66944 .45285 .65649 .43337 Metetra .845 .752 .761 r .65649 .43337 .66944 .45285 .69429 .41302 .68189 .39964 Metetra .922 .805 .713 r .68189 .39964 .69429 .41302 .71764 .35301 .70628 .3512 Metetra .923 .958 .787 r .70628 .3512 .71764 .35301 .74318 .33364 .73122 .3175 Metetra .664 .741 .907 r .73122 .3175 .74318 .33364 .76961 .32493 .75783 .30864 Metetra .664 .741 .907 r .75783 .30864 .76961 .32493 .79629 .31614 .78468 .29969 Metetra .664 .741 .907 r .78468 .29969 .79629 .31614 .82322 .30727 .81179 .29067 Metetra .664 .741 .907 r .81179 .29067 .82322 .30727 .85041 .29831 .83916 .28155 Metetra .664 .741 .907 r .83916 .28155 .85041 .29831 .87784 .28927 .86679 .27235 Metetra .692 .758 .902 r .24595 .55471 .26129 .56818 .28456 .55842 .26934 .54505 Metetra .691 .761 .906 r .26934 .54505 .28456 .55842 .308 .54852 .29289 .53544 Metetra .685 .766 .913 r .29289 .53544 .308 .54852 .3316 .53888 .31659 .5262 Metetra .674 .772 .924 r .31659 .5262 .3316 .53888 .35534 .52978 .34045 .51755 Metetra .66 .777 .936 r .34045 .51755 .35534 .52978 .37924 .52149 .36447 .50963 Metetra .642 .78 .947 r .36447 .50963 .37924 .52149 .4033 .51416 .38867 .50253 Metetra .622 .78 .957 r .38867 .50253 .4033 .51416 .42755 .5079 .41306 .49627 Metetra .603 .776 .963 r .41306 .49627 .42755 .5079 .45202 .50267 .43769 .49075 Metetra .589 .768 .965 r .43769 .49075 .45202 .50267 .47673 .49835 .46256 .48583 Metetra .584 .759 .962 r .46256 .48583 .47673 .49835 .50172 .49462 .4877 .48121 Metetra .59 .748 .953 r .4877 .48121 .50172 .49462 .52701 .49096 .51313 .47646 Metetra .608 .74 .938 r .51313 .47646 .52701 .49096 .55258 .4866 .53885 .47098 Metetra .637 .736 .92 r .53885 .47098 .55258 .4866 .57843 .48042 .56484 .46395 Metetra .675 .74 .899 r .56484 .46395 .57843 .48042 .60447 .47091 .59104 .45429 Metetra .723 .754 .877 r .59104 .45429 .60447 .47091 .63057 .45608 .61735 .44063 Metetra .782 .785 .855 r .61735 .44063 .63057 .45608 .65649 .43337 .64363 .42125 Metetra .854 .836 .828 r .64363 .42125 .65649 .43337 .68189 .39964 .66963 .39404 Metetra .931 .904 .775 r .66963 .39404 .68189 .39964 .70628 .3512 .69502 .35656 Metetra .957 .942 .637 r .69502 .35656 .70628 .3512 .73122 .3175 .71937 .306 Metetra .737 .84 .928 r .71937 .306 .73122 .3175 .75783 .30864 .74584 .29206 Metetra .664 .741 .907 r .74584 .29206 .75783 .30864 .78468 .29969 .77287 .28296 Metetra .664 .741 .907 r .77287 .28296 .78468 .29969 .81179 .29067 .80016 .27377 Metetra .664 .741 .907 r .80016 .27377 .81179 .29067 .83916 .28155 .82772 .2645 Metetra .664 .741 .907 r .82772 .2645 .83916 .28155 .86679 .27235 .85553 .25514 Metetra .688 .757 .904 r .23036 .541 .24595 .55471 .26934 .54505 .25386 .53149 Metetra .684 .76 .909 r .25386 .53149 .26934 .54505 .29289 .53544 .27751 .52219 Metetra .676 .765 .918 r .27751 .52219 .29289 .53544 .31659 .5262 .30132 .51336 Metetra .665 .77 .928 r .30132 .51336 .31659 .5262 .34045 .51755 .32529 .50512 Metetra .651 .775 .939 r .32529 .50512 .34045 .51755 .36447 .50963 .34943 .49755 Metetra .635 .778 .95 r .34943 .49755 .36447 .50963 .38867 .50253 .37376 .49067 Metetra .619 .779 .958 r .37376 .49067 .38867 .50253 .41306 .49627 .39831 .48442 Metetra .604 .777 .963 r .39831 .48442 .41306 .49627 .43769 .49075 .42308 .47872 Metetra .594 .772 .965 r .42308 .47872 .43769 .49075 .46256 .48583 .44811 .47341 Metetra .591 .767 .963 r .44811 .47341 .46256 .48583 .4877 .48121 .47342 .46825 Metetra .597 .762 .958 r .47342 .46825 .4877 .48121 .51313 .47646 .49901 .4629 Metetra .611 .759 .95 r .49901 .4629 .51313 .47646 .53885 .47098 .52489 .45693 Metetra .634 .761 .94 r .52489 .45693 .53885 .47098 .56484 .46395 .55104 .44976 Metetra .665 .772 .929 r .55104 .44976 .56484 .46395 .59104 .45429 .57743 .44068 Metetra .706 .794 .92 r .57743 .44068 .59104 .45429 .61735 .44063 .604 .42877 Metetra .758 .835 .91 r .604 .42877 .61735 .44063 .64363 .42125 .63064 .41294 Metetra .821 .897 .895 r .63064 .41294 .64363 .42125 .66963 .39404 .65721 .39186 Metetra .878 .972 .843 r .65721 .39186 .66963 .39404 .69502 .35656 .68349 .36397 Metetra .836 .97 .656 r .68349 .36397 .69502 .35656 .71937 .306 .70921 .32747 Metetra .70921 .32747 .71937 .306 .74584 .29206 .73399 .28041 Metetra .741 .845 .928 r .73399 .28041 .74584 .29206 .77287 .28296 .76085 .26593 Metetra .664 .741 .907 r .76085 .26593 .77287 .28296 .80016 .27377 .78833 .25658 Metetra .664 .741 .907 r .78833 .25658 .80016 .27377 .82772 .2645 .81607 .24714 Metetra .664 .741 .907 r .81607 .24714 .82772 .2645 .85553 .25514 .84407 .23761 Metetra .684 .756 .907 r .21451 .52708 .23036 .541 .25386 .53149 .23811 .51773 Metetra .677 .759 .913 r .23811 .51773 .25386 .53149 .27751 .52219 .26187 .50878 Metetra .667 .764 .922 r .26187 .50878 .27751 .52219 .30132 .51336 .28578 .50036 Metetra .656 .769 .933 r .28578 .50036 .30132 .51336 .32529 .50512 .30986 .49251 Metetra .642 .773 .943 r .30986 .49251 .32529 .50512 .34943 .49755 .33412 .48525 Metetra .629 .776 .952 r .33412 .48525 .34943 .49755 .37376 .49067 .35858 .47854 Metetra .615 .777 .958 r .35858 .47854 .37376 .49067 .39831 .48442 .38327 .47233 Metetra .604 .776 .963 r .38327 .47233 .39831 .48442 .42308 .47872 .4082 .46652 Metetra .597 .774 .965 r .4082 .46652 .42308 .47872 .44811 .47341 .43339 .46097 Metetra .594 .771 .964 r .43339 .46097 .44811 .47341 .47342 .46825 .45886 .45549 Metetra .598 .769 .962 r .45886 .45549 .47342 .46825 .49901 .4629 .48461 .44985 Metetra .607 .77 .958 r .48461 .44985 .49901 .4629 .52489 .45693 .51066 .44375 Metetra .623 .775 .954 r .51066 .44375 .52489 .45693 .55104 .44976 .53699 .43682 Metetra .645 .788 .951 r .53699 .43682 .55104 .44976 .57743 .44068 .56358 .42859 Metetra .674 .813 .95 r .56358 .42859 .57743 .44068 .604 .42877 .59041 .41852 Metetra .71 .854 .951 r .59041 .41852 .604 .42877 .63064 .41294 .6174 .40595 Metetra .751 .916 .947 r .6174 .40595 .63064 .41294 .65721 .39186 .64447 .39008 Metetra .774 .984 .903 r .64447 .39008 .65721 .39186 .68349 .36397 .6715 .37 Metetra .684 .956 .71 r .6715 .37 .68349 .36397 .70921 .32747 .69832 .34465 Metetra .69832 .34465 .70921 .32747 .73399 .28041 .72472 .31285 Metetra 0 0 .033 r .72472 .31285 .73399 .28041 .76085 .26593 .75042 .27328 Metetra .768 .949 .621 r .75042 .27328 .76085 .26593 .78833 .25658 .77628 .23909 Metetra .664 .741 .907 r .77628 .23909 .78833 .25658 .81607 .24714 .80421 .22948 Metetra .664 .741 .907 r .80421 .22948 .81607 .24714 .84407 .23761 .83241 .21978 Metetra .678 .755 .909 r .19839 .51291 .21451 .52708 .23811 .51773 .22209 .5038 Metetra .669 .758 .917 r .22209 .5038 .23811 .51773 .26187 .50878 .24594 .49522 Metetra .658 .763 .927 r .24594 .49522 .26187 .50878 .28578 .50036 .26995 .48719 Metetra .647 .768 .937 r .26995 .48719 .28578 .50036 .30986 .49251 .29414 .4797 Metetra .635 .772 .946 r .29414 .4797 .30986 .49251 .33412 .48525 .31852 .4727 Metetra .623 .775 .953 r .31852 .4727 .33412 .48525 .35858 .47854 .34312 .46615 Metetra .612 .776 .959 r .34312 .46615 .35858 .47854 .38327 .47233 .36795 .45998 Metetra .603 .775 .963 r .36795 .45998 .38327 .47233 .4082 .46652 .39304 .45409 Metetra .598 .774 .964 r .39304 .45409 .4082 .46652 .43339 .46097 .41839 .44838 Metetra .595 .773 .965 r .41839 .44838 .43339 .46097 .45886 .45549 .44402 .44272 Metetra .597 .772 .964 r .44402 .44272 .45886 .45549 .48461 .44985 .46994 .43695 Metetra .602 .774 .963 r .46994 .43695 .48461 .44985 .51066 .44375 .49615 .43089 Metetra .61 .78 .962 r .49615 .43089 .51066 .44375 .53699 .43682 .52266 .42431 Metetra .623 .792 .963 r .52266 .42431 .53699 .43682 .56358 .42859 .54946 .41694 Metetra .639 .813 .967 r .54946 .41694 .56358 .42859 .59041 .41852 .57653 .40848 Metetra .657 .847 .973 r .57653 .40848 .59041 .41852 .6174 .40595 .60384 .39855 Metetra .674 .897 .977 r .60384 .39855 .6174 .40595 .64447 .39008 .63134 .38673 Metetra .671 .952 .953 r .63134 .38673 .64447 .39008 .6715 .37 .65897 .37253 Metetra .585 .943 .818 r .65897 .37253 .6715 .37 .69832 .34465 .68664 .35539 Metetra .68664 .35539 .69832 .34465 .72472 .31285 .71423 .33467 Metetra .71423 .33467 .72472 .31285 .75042 .27328 .74161 .30966 Metetra .12 0 .139 r .74161 .30966 .75042 .27328 .77628 .23909 .7686 .27957 Metetra .098 0 .167 r .7686 .27957 .77628 .23909 .80421 .22948 .79497 .24357 Metetra .635 .817 .396 r .79497 .24357 .80421 .22948 .83241 .21978 .82054 .20161 Metetra .672 .754 .912 r .182 .49851 .19839 .51291 .22209 .5038 .2058 .48968 Metetra .66 .757 .922 r .2058 .48968 .22209 .5038 .24594 .49522 .22973 .48151 Metetra .649 .762 .932 r .22973 .48151 .24594 .49522 .26995 .48719 .25384 .47387 Metetra .638 .767 .941 r .25384 .47387 .26995 .48719 .29414 .4797 .27813 .46669 Metetra .627 .77 .949 r .27813 .46669 .29414 .4797 .31852 .4727 .30264 .45992 Metetra .618 .773 .955 r .30264 .45992 .31852 .4727 .34312 .46615 .32737 .45348 Metetra .609 .774 .959 r .32737 .45348 .34312 .46615 .36795 .45998 .35235 .44732 Metetra .602 .774 .962 r .35235 .44732 .36795 .45998 .39304 .45409 .37758 .44136 Metetra .598 .774 .964 r .37758 .44136 .39304 .45409 .41839 .44838 .40309 .43553 Metetra .595 .773 .965 r .40309 .43553 .41839 .44838 .44402 .44272 .42888 .42974 Metetra .595 .773 .965 r .42888 .42974 .44402 .44272 .46994 .43695 .45497 .4239 Metetra .597 .774 .965 r .45497 .4239 .46994 .43695 .49615 .43089 .48136 .4179 Metetra .6 .778 .966 r .48136 .4179 .49615 .43089 .52266 .42431 .50805 .41162 Metetra .605 .787 .968 r .50805 .41162 .52266 .42431 .54946 .41694 .53505 .40492 Metetra .611 .802 .973 r .53505 .40492 .54946 .41694 .57653 .40848 .56234 .39765 Metetra .617 .826 .98 r .56234 .39765 .57653 .40848 .60384 .39855 .58992 .38961 Metetra .62 .86 .988 r .58992 .38961 .60384 .39855 .63134 .38673 .61777 .38061 Metetra .609 .901 .986 r .61777 .38061 .63134 .38673 .65897 .37253 .64586 .37042 Metetra .557 .925 .937 r .64586 .37042 .65897 .37253 .68664 .35539 .67416 .35877 Metetra .408 .851 .756 r .67416 .35877 .68664 .35539 .71423 .33467 .7026 .34538 Metetra .7026 .34538 .71423 .33467 .74161 .30966 .73114 .32991 Metetra .064 0 0 r .73114 .32991 .74161 .30966 .7686 .27957 .75969 .312 Metetra .207 0 .125 r .75969 .312 .7686 .27957 .79497 .24357 .78814 .29125 Metetra .293 0 .254 r .78814 .29125 .79497 .24357 .82054 .20161 .81638 .26723 Metetra .664 .752 .916 r .16533 .48386 .182 .49851 .2058 .48968 .18921 .47541 Metetra .65 .756 .927 r .18921 .47541 .2058 .48968 .22973 .48151 .21322 .46766 Metetra .639 .761 .936 r .21322 .46766 .22973 .48151 .25384 .47387 .23742 .46039 Metetra .63 .766 .945 r .23742 .46039 .25384 .47387 .27813 .46669 .26182 .45349 Metetra .621 .769 .951 r .26182 .45349 .27813 .46669 .30264 .45992 .28645 .44688 Metetra .613 .772 .956 r .28645 .44688 .30264 .45992 .32737 .45348 .31132 .44051 Metetra .607 .773 .959 r .31132 .44051 .32737 .45348 .35235 .44732 .33644 .43433 Metetra .602 .773 .962 r .33644 .43433 .35235 .44732 .37758 .44136 .36183 .42828 Metetra .598 .772 .963 r .36183 .42828 .37758 .44136 .40309 .43553 .3875 .42231 Metetra .596 .771 .964 r .3875 .42231 .40309 .43553 .42888 .42974 .41346 .41639 Metetra .595 .771 .964 r .41346 .41639 .42888 .42974 .45497 .4239 .43971 .41045 Metetra .595 .771 .964 r .43971 .41045 .45497 .4239 .48136 .4179 .46627 .40444 Metetra .595 .773 .965 r .46627 .40444 .48136 .4179 .50805 .41162 .49314 .39831 Metetra .596 .778 .967 r .49314 .39831 .50805 .41162 .53505 .40492 .52033 .39198 Metetra .597 .787 .971 r .52033 .39198 .53505 .40492 .56234 .39765 .54783 .3854 Metetra .598 .8 .977 r .54783 .3854 .56234 .39765 .58992 .38961 .57565 .37848 Metetra .596 .819 .985 r .57565 .37848 .58992 .38961 .61777 .38061 .60378 .37114 Metetra .588 .845 .993 r .60378 .37114 .61777 .38061 .64586 .37042 .63222 .36329 Metetra .567 .875 .994 r .63222 .36329 .64586 .37042 .67416 .35877 .66096 .35484 Metetra .513 .892 .963 r .66096 .35484 .67416 .35877 .7026 .34538 .68998 .34566 Metetra .394 .852 .848 r .68998 .34566 .7026 .34538 .73114 .32991 .71926 .33564 Metetra .71926 .33564 .73114 .32991 .75969 .312 .74877 .32465 Metetra .023 0 0 r .74877 .32465 .75969 .312 .78814 .29125 .77849 .31253 Metetra .182 0 0 r .77849 .31253 .78814 .29125 .81638 .26723 .80838 .29913 Metetra .653 .749 .92 r .14838 .46897 .16533 .48386 .18921 .47541 .17231 .461 Metetra .639 .755 .932 r .17231 .461 .18921 .47541 .21322 .46766 .1964 .4537 Metetra .63 .76 .941 r .1964 .4537 .21322 .46766 .23742 .46039 .22069 .44677 Metetra .622 .765 .948 r .22069 .44677 .23742 .46039 .26182 .45349 .2452 .44008 Metetra .616 .768 .953 r .2452 .44008 .26182 .45349 .28645 .44688 .26996 .43358 Metetra .61 .77 .957 r .26996 .43358 .28645 .44688 .31132 .44051 .29496 .42722 Metetra .606 .771 .959 r .29496 .42722 .31132 .44051 .33644 .43433 .32023 .42097 Metetra .603 .771 .961 r .32023 .42097 .33644 .43433 .36183 .42828 .34578 .41478 Metetra .6 .77 .961 r .34578 .41478 .36183 .42828 .3875 .42231 .37161 .40864 Metetra .598 .769 .961 r .37161 .40864 .3875 .42231 .41346 .41639 .39773 .40252 Metetra .597 .768 .961 r .39773 .40252 .41346 .41639 .43971 .41045 .42416 .3964 Metetra .596 .767 .961 r .42416 .3964 .43971 .41045 .46627 .40444 .45089 .39025 Metetra .596 .767 .961 r .45089 .39025 .46627 .40444 .49314 .39831 .47793 .38404 Metetra .596 .768 .962 r .47793 .38404 .49314 .39831 .52033 .39198 .5053 .37776 Metetra .595 .77 .963 r .5053 .37776 .52033 .39198 .54783 .3854 .533 .37137 Metetra .595 .775 .966 r .533 .37137 .54783 .3854 .57565 .37848 .56103 .36486 Metetra .593 .783 .971 r .56103 .36486 .57565 .37848 .60378 .37114 .58939 .3582 Metetra .59 .795 .978 r .58939 .3582 .60378 .37114 .63222 .36329 .61809 .35135 Metetra .584 .811 .986 r .61809 .35135 .63222 .36329 .66096 .35484 .64714 .34429 Metetra .573 .831 .994 r .64714 .34429 .66096 .35484 .68998 .34566 .67653 .33699 Metetra .551 .853 .998 r .67653 .33699 .68998 .34566 .71926 .33564 .70626 .32941 Metetra .509 .869 .986 r .70626 .32941 .71926 .33564 .74877 .32465 .73633 .32152 Metetra .429 .861 .931 r .73633 .32152 .74877 .32465 .77849 .31253 .76675 .31328 Metetra .292 .79 .796 r .76675 .31328 .77849 .31253 .80838 .29913 .79749 .30464 Metetra .639 .746 .926 r .13113 .45381 .14838 .46897 .17231 .461 .1551 .44649 Metetra .628 .754 .938 r .1551 .44649 .17231 .461 .1964 .4537 .17926 .43965 Metetra .621 .76 .946 r .17926 .43965 .1964 .4537 .22069 .44677 .20364 .43301 Metetra .616 .765 .951 r .20364 .43301 .22069 .44677 .2452 .44008 .22826 .42647 Metetra .612 .768 .955 r .22826 .42647 .2452 .44008 .26996 .43358 .25315 .42001 Metetra .609 .77 .957 r .25315 .42001 .26996 .43358 .29496 .42722 .2783 .4136 Metetra .606 .77 .958 r .2783 .4136 .29496 .42722 .32023 .42097 .30372 .4072 Metetra .605 .77 .959 r .30372 .4072 .32023 .42097 .34578 .41478 .32942 .40082 Metetra .603 .768 .959 r .32942 .40082 .34578 .41478 .37161 .40864 .35542 .39443 Metetra .603 .766 .958 r .35542 .39443 .37161 .40864 .39773 .40252 .38171 .38802 Metetra .602 .764 .957 r .38171 .38802 .39773 .40252 .42416 .3964 .40831 .38159 Metetra .602 .762 .955 r .40831 .38159 .42416 .3964 .45089 .39025 .43522 .37512 Metetra .602 .759 .954 r .43522 .37512 .45089 .39025 .47793 .38404 .46244 .36862 Metetra .602 .757 .953 r .46244 .36862 .47793 .38404 .5053 .37776 .48999 .36206 Metetra .602 .755 .952 r .48999 .36206 .5053 .37776 .533 .37137 .51786 .35544 Metetra .602 .754 .951 r .51786 .35544 .533 .37137 .56103 .36486 .54608 .34876 Metetra .602 .754 .951 r .54608 .34876 .56103 .36486 .58939 .3582 .57464 .34202 Metetra .601 .755 .952 r .57464 .34202 .58939 .3582 .61809 .35135 .60355 .33519 Metetra .601 .758 .954 r .60355 .33519 .61809 .35135 .64714 .34429 .63281 .32828 Metetra .599 .762 .957 r .63281 .32828 .64714 .34429 .67653 .33699 .66244 .32128 Metetra .598 .768 .961 r .66244 .32128 .67653 .33699 .70626 .32941 .69244 .31419 Metetra .595 .776 .967 r .69244 .31419 .70626 .32941 .73633 .32152 .72281 .30699 Metetra .591 .787 .974 r .72281 .30699 .73633 .32152 .76675 .31328 .75357 .29967 Metetra .584 .801 .982 r .75357 .29967 .76675 .31328 .79749 .30464 .78471 .29225 Metetra .62 .741 .933 r .11358 .43839 .13113 .45381 .1551 .44649 .13755 .43194 Metetra .615 .753 .944 r .13755 .43194 .1551 .44649 .17926 .43965 .16177 .42554 Metetra .613 .761 .95 r .16177 .42554 .17926 .43965 .20364 .43301 .18625 .41913 Metetra .611 .766 .954 r .18625 .41913 .20364 .43301 .22826 .42647 .21099 .41267 Metetra .61 .768 .956 r .21099 .41267 .22826 .42647 .25315 .42001 .23601 .40617 Metetra .609 .77 .957 r .23601 .40617 .25315 .42001 .2783 .4136 .26131 .39961 Metetra .608 .769 .957 r .26131 .39961 .2783 .4136 .30372 .4072 .28689 .393 Metetra .608 .768 .956 r .28689 .393 .30372 .4072 .32942 .40082 .31276 .38632 Metetra .609 .766 .955 r .31276 .38632 .32942 .40082 .35542 .39443 .33893 .37958 Metetra .609 .764 .953 r .33893 .37958 .35542 .39443 .38171 .38802 .3654 .37277 Metetra .61 .76 .951 r .3654 .37277 .38171 .38802 .40831 .38159 .39217 .36589 Metetra .61 .756 .948 r .39217 .36589 .40831 .38159 .43522 .37512 .41926 .35895 Metetra .611 .752 .945 r .41926 .35895 .43522 .37512 .46244 .36862 .44666 .35192 Metetra .612 .747 .942 r .44666 .35192 .46244 .36862 .48999 .36206 .47438 .34483 Metetra .613 .743 .938 r .47438 .34483 .48999 .36206 .51786 .35544 .50244 .33765 Metetra .613 .738 .934 r .50244 .33765 .51786 .35544 .54608 .34876 .53083 .3304 Metetra .614 .733 .93 r .53083 .3304 .54608 .34876 .57464 .34202 .55956 .32306 Metetra .614 .728 .927 r .55956 .32306 .57464 .34202 .60355 .33519 .58864 .31564 Metetra .615 .723 .923 r .58864 .31564 .60355 .33519 .63281 .32828 .61807 .30814 Metetra .615 .718 .919 r .61807 .30814 .63281 .32828 .66244 .32128 .64787 .30055 Metetra .616 .713 .915 r .64787 .30055 .66244 .32128 .69244 .31419 .67803 .29287 Metetra .616 .709 .911 r .67803 .29287 .69244 .31419 .72281 .30699 .70857 .2851 Metetra .616 .705 .908 r .70857 .2851 .72281 .30699 .75357 .29967 .73949 .27723 Metetra .616 .701 .905 r .73949 .27723 .75357 .29967 .78471 .29225 .77079 .26927 Metetra .592 .732 .941 r .09572 .42269 .11358 .43839 .13755 .43194 .11964 .41742 Metetra .603 .754 .95 r .11964 .41742 .13755 .43194 .16177 .42554 .14392 .41142 Metetra .606 .763 .954 r .14392 .41142 .16177 .42554 .18625 .41913 .16851 .40515 Metetra .608 .767 .956 r .16851 .40515 .18625 .41913 .21099 .41267 .19338 .39868 Metetra .609 .769 .957 r .19338 .39868 .21099 .41267 .23601 .40617 .21854 .39203 Metetra .611 .77 .956 r .21854 .39203 .23601 .40617 .26131 .39961 .244 .38523 Metetra .613 .769 .955 r .244 .38523 .26131 .39961 .28689 .393 .26975 .37829 Metetra .614 .767 .953 r .26975 .37829 .28689 .393 .31276 .38632 .2958 .37122 Metetra .616 .764 .95 r .2958 .37122 .31276 .38632 .33893 .37958 .32214 .36401 Metetra .618 .76 .947 r .32214 .36401 .33893 .37958 .3654 .37277 .34879 .35668 Metetra .619 .756 .944 r .34879 .35668 .3654 .37277 .39217 .36589 .37575 .34923 Metetra .621 .751 .939 r .37575 .34923 .39217 .36589 .41926 .35895 .40302 .34165 Metetra .622 .745 .935 r .40302 .34165 .41926 .35895 .44666 .35192 .4306 .33395 Metetra .623 .739 .93 r .4306 .33395 .44666 .35192 .47438 .34483 .45851 .32613 Metetra .624 .732 .924 r .45851 .32613 .47438 .34483 .50244 .33765 .48673 .31819 Metetra .625 .726 .919 r .48673 .31819 .50244 .33765 .53083 .3304 .51529 .31013 Metetra .626 .718 .913 r .51529 .31013 .53083 .3304 .55956 .32306 .54419 .30195 Metetra .627 .711 .907 r .54419 .30195 .55956 .32306 .58864 .31564 .57342 .29365 Metetra .627 .703 .9 r .57342 .29365 .58864 .31564 .61807 .30814 .603 .28523 Metetra .627 .696 .894 r .603 .28523 .61807 .30814 .64787 .30055 .63293 .27668 Metetra .627 .688 .887 r .63293 .27668 .64787 .30055 .67803 .29287 .66322 .26801 Metetra .627 .68 .88 r .66322 .26801 .67803 .29287 .70857 .2851 .69387 .25922 Metetra .627 .672 .874 r .69387 .25922 .70857 .2851 .73949 .27723 .72488 .2503 Metetra .626 .664 .867 r .72488 .2503 .73949 .27723 .77079 .26927 .75628 .24126 Metetra .551 .718 .951 r .07754 .40672 .09572 .42269 .11964 .41742 .10134 .40306 Metetra .591 .757 .957 r .10134 .40306 .11964 .41742 .14392 .41142 .12569 .39737 Metetra .601 .766 .958 r .12569 .39737 .14392 .41142 .16851 .40515 .15039 .39112 Metetra .607 .77 .958 r .15039 .39112 .16851 .40515 .19338 .39868 .17541 .3845 Metetra .612 .771 .957 r .17541 .3845 .19338 .39868 .21854 .39203 .20073 .37759 Metetra .616 .771 .955 r .20073 .37759 .21854 .39203 .244 .38523 .22636 .37042 Metetra .619 .769 .952 r .22636 .37042 .244 .38523 .26975 .37829 .25229 .36303 Metetra .622 .766 .948 r .25229 .36303 .26975 .37829 .2958 .37122 .27852 .35544 Metetra .625 .762 .944 r .27852 .35544 .2958 .37122 .32214 .36401 .30506 .34765 Metetra .628 .757 .94 r .30506 .34765 .32214 .36401 .34879 .35668 .3319 .33968 Metetra .63 .751 .935 r .3319 .33968 .34879 .35668 .37575 .34923 .35905 .33154 Metetra .631 .745 .93 r .35905 .33154 .37575 .34923 .40302 .34165 .3865 .32323 Metetra .633 .739 .924 r .3865 .32323 .40302 .34165 .4306 .33395 .41427 .31476 Metetra .634 .732 .919 r .41427 .31476 .4306 .33395 .45851 .32613 .44235 .30614 Metetra .635 .725 .913 r .44235 .30614 .45851 .32613 .48673 .31819 .47076 .29736 Metetra .636 .718 .906 r .47076 .29736 .48673 .31819 .51529 .31013 .49948 .28843 Metetra .636 .71 .9 r .49948 .28843 .51529 .31013 .54419 .30195 .52854 .27936 Metetra .637 .703 .894 r .52854 .27936 .54419 .30195 .57342 .29365 .55792 .27014 Metetra .637 .695 .888 r .55792 .27014 .57342 .29365 .603 .28523 .58764 .26078 Metetra .636 .688 .881 r .58764 .26078 .603 .28523 .63293 .27668 .61771 .25128 Metetra .636 .68 .875 r .61771 .25128 .63293 .27668 .66322 .26801 .64812 .24163 Metetra .636 .673 .869 r .64812 .24163 .66322 .26801 .69387 .25922 .67888 .23184 Metetra .635 .666 .862 r .67888 .23184 .69387 .25922 .72488 .2503 .70999 .22191 Metetra .634 .658 .856 r .70999 .22191 .72488 .2503 .75628 .24126 .74147 .21184 Metetra .483 .693 .96 r .05903 .39046 .07754 .40672 .10134 .40306 .0826 .38906 Metetra .582 .763 .965 r .0826 .38906 .10134 .40306 .12569 .39737 .10705 .38351 Metetra .599 .772 .963 r .10705 .38351 .12569 .39737 .15039 .39112 .13188 .37712 Metetra .609 .775 .96 r .13188 .37712 .15039 .39112 .17541 .3845 .15706 .37018 Metetra .617 .775 .956 r .15706 .37018 .17541 .3845 .20073 .37759 .18257 .36283 Metetra .623 .773 .952 r .18257 .36283 .20073 .37759 .22636 .37042 .20839 .35513 Metetra .628 .769 .947 r .20839 .35513 .22636 .37042 .25229 .36303 .23452 .34713 Metetra .632 .764 .942 r .23452 .34713 .25229 .36303 .27852 .35544 .26095 .33888 Metetra .635 .759 .937 r .26095 .33888 .27852 .35544 .30506 .34765 .28768 .3304 Metetra .638 .753 .932 r .28768 .3304 .30506 .34765 .3319 .33968 .31472 .3217 Metetra .64 .746 .926 r .31472 .3217 .3319 .33968 .35905 .33154 .34206 .31281 Metetra .641 .74 .92 r .34206 .31281 .35905 .33154 .3865 .32323 .36971 .30374 Metetra .642 .733 .915 r .36971 .30374 .3865 .32323 .41427 .31476 .39766 .29449 Metetra .643 .727 .909 r .39766 .29449 .41427 .31476 .44235 .30614 .42593 .28509 Metetra .644 .72 .904 r .42593 .28509 .44235 .30614 .47076 .29736 .45451 .27553 Metetra .644 .714 .898 r .45451 .27553 .47076 .29736 .49948 .28843 .4834 .26581 Metetra .644 .707 .893 r .4834 .26581 .49948 .28843 .52854 .27936 .51262 .25595 Metetra .644 .701 .888 r .51262 .25595 .52854 .27936 .55792 .27014 .54216 .24595 Metetra .644 .695 .883 r .54216 .24595 .55792 .27014 .58764 .26078 .57203 .23581 Metetra .643 .69 .878 r .57203 .23581 .58764 .26078 .61771 .25128 .60224 .22552 Metetra .643 .684 .874 r .60224 .22552 .61771 .25128 .64812 .24163 .63279 .2151 Metetra .642 .679 .869 r .63279 .2151 .64812 .24163 .67888 .23184 .66368 .20454 Metetra .642 .673 .865 r .66368 .20454 .67888 .23184 .70999 .22191 .69492 .19384 Metetra .641 .668 .86 r .69492 .19384 .70999 .22191 .74147 .21184 .72652 .183 Metetra .361 .637 .96 r .04019 .37391 .05903 .39046 .0826 .38906 .06334 .37583 Metetra .576 .776 .974 r .06334 .37583 .0826 .38906 .10705 .38351 .08792 .37014 Metetra .602 .784 .968 r .08792 .37014 .10705 .38351 .13188 .37712 .11294 .36332 Metetra .618 .784 .961 r .11294 .36332 .13188 .37712 .15706 .37018 .13832 .35578 Metetra .628 .781 .955 r .13832 .35578 .15706 .37018 .18257 .36283 .16405 .34772 Metetra .635 .776 .948 r .16405 .34772 .18257 .36283 .20839 .35513 .19009 .33925 Metetra .64 .769 .941 r .19009 .33925 .20839 .35513 .23452 .34713 .21643 .33047 Metetra .644 .762 .934 r .21643 .33047 .23452 .34713 .26095 .33888 .24308 .32142 Metetra .646 .755 .928 r .24308 .32142 .26095 .33888 .28768 .3304 .27002 .31216 Metetra .648 .748 .922 r .27002 .31216 .28768 .3304 .31472 .3217 .29726 .30271 Metetra .649 .741 .917 r .29726 .30271 .31472 .3217 .34206 .31281 .3248 .29308 Metetra .649 .735 .912 r .3248 .29308 .34206 .31281 .36971 .30374 .35264 .2833 Metetra .649 .729 .907 r .35264 .2833 .36971 .30374 .39766 .29449 .38077 .27337 Metetra .65 .723 .903 r .38077 .27337 .39766 .29449 .42593 .28509 .40922 .26331 Metetra .65 .718 .899 r .40922 .26331 .42593 .28509 .45451 .27553 .43797 .25311 Metetra .649 .714 .895 r .43797 .25311 .45451 .27553 .4834 .26581 .46704 .24278 Metetra .649 .709 .891 r .46704 .24278 .4834 .26581 .51262 .25595 .49642 .23232 Metetra .649 .705 .888 r .49642 .23232 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It is clear that equality holds when \ x=y. It is not clear how to parameterize the curved part however. Given just \ the little time that we had, I thought that maybe ", StyleBox["Mathematica", FontSlant->"Italic"], " would give me a hint on that, so:" }], "Section"], Cell[CellGroupData[{ Cell[BoxData[ \(Solve[x^2 \[Equal] 2^x, x]\)], "Input", CellLabel->"In[10]:=", CellChangeTimes -> {{3.384278974434753*^9, 3.384278984192822*^9}, \ {3.3842790517515907`*^9, 3.384279056703484*^9}}], Cell[BoxData[ RowBox[{\(InverseFunction::"ifun"\), \(\(:\)\(\ \)\), "\<\"Inverse \ functions are being used. Values may be lost for multivalued inverses. \\!\\(\ \\*ButtonBox[\\\"More\[Ellipsis]\\\", ButtonStyle->\\\"RefGuideLinkText\\\", \ ButtonFrame->None, ButtonData:>\\\"InverseFunction::ifun\\\"]\\)\"\>"}]], \ "Message", CellLabel->"From In[10]:="], Cell[BoxData[ RowBox[{\(InverseFunction::"ifun"\), \(\(:\)\(\ \)\), "\<\"Inverse \ functions are being used. 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Cell[CellGroupData[{ Cell["\<\ I personally think that is very pretty and artistic! It also looks \ better in version 6.0! Then, he asked about the point where there is only 1 solution. He had tried \ the following on a graphing calculator:\ \>", "Section"], Cell[BoxData[ \(f[x_, y_] := x^y - y^x\)], "Input", CellLabel->"In[15]:=", CellChangeTimes -> {{3.384278024900216*^9, 3.3842780428560877`*^9}}], Cell[CellGroupData[{ Cell[BoxData[ \(f[2.718, 2.7]\)], "Input", CellLabel->"In[16]:=", CellChangeTimes -> {{3.384278598554161*^9, 3.38427860449192*^9}}], Cell[BoxData[ \(0.0009182913583618557`\)], "Output", CellLabel->"Out[16]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(f[2.718, 2.75]\)], "Input", CellLabel->"In[17]:=", CellChangeTimes -> {3.3842786247297573`*^9}], Cell[BoxData[ \(0.0028707534119778444`\)], "Output", CellLabel->"Out[17]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(f[2.73, 2.718]\)], "Input", CellLabel->"In[18]:=", CellChangeTimes -> {{3.384278702369834*^9, 3.384278705591757*^9}}], Cell[BoxData[ \(\(-0.00038578622085161385`\)\)], "Output", CellLabel->"Out[18]="] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(f[2.7, 2.718]\)], "Input", CellLabel->"In[19]:=", CellChangeTimes -> {{3.384278721281579*^9, 3.384278725671784*^9}}], Cell[BoxData[ \(\(-0.0009182913583618557`\)\)], "Output", CellLabel->"Out[19]="] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["He then said, it is probably E. I said, let's see:", "Section"], Cell[CellGroupData[{ Cell[BoxData[ \(f[E, E]\)], "Input", CellLabel->"In[20]:="], Cell[BoxData[ \(0\)], "Output", CellLabel->"Out[20]="] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["\<\ Aha! In fact it is. Then I said, let's investigate the asymptote that the curve is approaching:\ \ \>", "Section"], Cell[CellGroupData[{ Cell[BoxData[ \(Limit[\(-\(\(x\ \ ProductLog[\(-\(Log[x]\/x\)\)]\)\/Log[x]\)\), x \[Rule] Infinity]\)], "Input", CellLabel->"In[21]:=", CellChangeTimes -> {{3.384338419955641*^9, 3.384338429082027*^9}}], Cell[BoxData[ \(1\)], "Output", CellLabel->"Out[21]="] }, Open ]] }, Open ]], Cell["He was going to take that to class to discuss with them.", "Section"], Cell["\<\ Here are some points for further investigation: a) Find a better parameterization of the curve. b) Find all integer solutions. c) Find all rational solutions.\ \>", "Section"] }, Open ]] }, FrontEndVersion->"5.2 for Microsoft Windows", ScreenRectangle->{{0, 1024}, {0, 688}}, WindowSize->{766, 661}, WindowMargins->{{4, Automatic}, {Automatic, 0}}, StyleDefinitions -> "TutorialBook.nb" ] (******************************************************************* Cached data follows. 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