GSP4QThat document was created with a newer version of Sketchpad and cannot be opened.|This document was created with a newer version of Sketchpad. Some information may be lost. The document will open as a copy.$-LInstructions` a b c d e f g h i j k l m n o p q _ ,#GSP4_W_0554/Mar 2 20040#` Arial '''$'$'$'$'$'$'$'$'$'$' $' $' %'&'8'8'8'9':' >    >>><0>>>>>>>>>>>>>>>>>>>>>>>><0>>>>>>>>>>>>>>>>>>>r.# h@@s@@Ћ@t@@p@r@@P@Y@)@@r@4(@ 4\.B@: &@  nQ\aAx6(n 6\.B@: &n   nQ\aAy='n   n((> n    nQ\aAExample n    nQ\aACreditsn>>>>>>>>>>>>>>>>>>>>><0>>>>>>>>><->><->>>>>>><->>>>>{"nEЉ@J@@B@p@@C(@`i@@Dh@`l@@A        > $   7$nQ\aA Hide Edges-# QThat document was created with a newer version of Sketchpad and cannot be opened.|This document was created with a newer version of Sketchpad. Some information may be lost. The document will open as a copy.$FLRegular Four-Sided Pyramid` a b c d e f g h i j k l m n o p q _ ,#GSP4_W_0554/Mar 2 20040#` Arial    '''$'$'$'$'$'$'$'$'$'$' $' $' %'&'8'8'8'9':' P ~ C<0> ^0`0C@\.խ@`0C@?   C V P  /<0> `0`0C@\.խ@`0C@?   /B Ab@@@C@Z@@@M`@pz@@zeroH@pz@@APo7@@ APozero'<ￜPɥwg) V@B@xww?A'@<?`0C@*?M'4R@xww@*?one4Rxww*?W'4@?*?zero'4*?zero'4@?*?C'4*?C'4@?*?A'4*?A'4@N?*?AP'4Nǿ*?AP'  AP'one'@   ?j  @c2'.#    ?Pitch.# 4@?*?W'' 4*?W''  ?bm 4@?*?one' 4*?one' ?bo' ?bp'   zDo@E '?S?O  ENP?ratio T,i?y?AOi ?bli ?bni ! .# "?p.#/3 #  <0>> "$>@F   rUSpin!C'n>  $"   /$ Move AO->O $$An濘53^?) F@>OAO' $$rϥwg) V@>OAO'#4(@RQ?@RQ?*? ratio'@#4(@RQ?RQĿ*? ratio'!4(@RQ?@RQ?*?E'!4(@RQ?RQĿ*?E'"4@N?*?O'0 3)j <0>` J0 `` & sqrt[1 - k*k]>  "-   C$ Move O->AO'>  ".   W$ Move O->AO'$0'  <0>m9e 0/?bfe.# /#?bge.# #0?bhe.#40#/UUUUUU?p2eU 1!?bje.# !2?bke.#42!1UUUUUU?p3eU "3 @c3e.#?  +&m 0 07j <0>` J0  `m10 ? @p4 @  DO@AF AAFAP' C .#C4(@RQ?@RQ?*?AF'C4(@RQ?RQĿ*?AF'D4@N?*?AP''D4Nǿ*?AP''/3 E'  <0>nQ\aAm[1]n GF?bc].# FC?bd].# CG?be].#4GCFUUUUUU?p1]0 3UJn <0>` N0 ` `` m8]! Oone' Pone'one'' 21.#)H}@u@@SCJ''!TS4E; & S' nQ\aAx8(nV 8`0C@: &n SW nQ\aAy='n VX C8nYC@L SZ @c1'ZS "L'' \S$rϥwg) V@NL''/ ]V?al - V^AJ ]_ #D U`?ay \S$?rϥwg) VNL''/ bV?an - VcAL bd #B eU?ba \S$F-D>￝MfNL''/ gV?ak - VhAI gi #A ej?av jU?ax4`Uj4eUj> n   c*nQ\aAShow Triangle ABEn j`?aow/ \V?amw - VqAKw \r #C Us?azw es?auw5`jes4eUs> w   P*nQ\aAShow Triangle BCE4nsU`> y   v*nQ\aAShow Triangle CDEn s`?arw> $laftu{pk   "4.nQ\aAShow permanent edges*A3n jY  <0>B3n jY  <0>A3n eY  <0>B3n eY  <0>0 3n~}j  <0>` J0|Y|YOQg hHjTg |@```` nQ\aA[uv][z]0 3n}~j <0>` J0|Y|YOQg hHjTg |@```` nQ\aA[uv][z]A3n UY  <0>B3n UY  <0>0 3nj <0>` J0|Y|YOQg hHjTg |@```` nQ\aA[uv][x]0 3nj <0>` J0|Y|YOQg hHjTg |@```` nQ\aA[uv][y]0 3n}~j <0>` J0|Y|YOQg hHjTg |@```` nQ\aA[uv][x]0 3n~}j <0>` J0|Y|YOQg hHjTg |@```` nQ\aA[uv][y]0 3nj <0>` J0 ``` nQ\aAABEA3n sY  <0>B3n sY  <0>0 3nj <0>` J0|Y|YOQg hHjTg |@```` nQ\aA[uv][x]0 3nj <0>` J0|Y|YOQg hHjTg |@```` nQ\aA[uv][z]0 3n}~j  <0>` J0|Y|YOQg hHjTg |@```` nQ\aA[uv][x]0 3nj  <0>` J0|Y|YOQg hHjTg |@```` nQ\aA[uv][y]0 3nj <0>` J0 ``` nQ\aAADC0 3n p C<0>` P0 A5p6jTg |=  `` nQ\aAinvis!nej j0 3 n C<0>` N0 A5p6jTg |= `` nQ\aAvis!nej j0 3j <0>` J0|Y|YOQg hHjTg |@```` nQ\aA[uv][z]0 3nj <0>` J0 ``` nQ\aABCE0 3n p C<0>` P0 A5p6jTg |=  `` nQ\aAinvis!neU U0 3 p C<0>` P0 A5p6jTg |=  `` nQ\aAinvis!nse e0 3 n C<0>` N0 A5p6jTg |= `` nQ\aAvis!nse e0 3 n C<0>` N0 A5p6jTg |= `` nQ\aAvis!neU UA3 `Y  <0>B3 `Y  <0>0 3j <0>` J0|Y|YOQg hHjTg |@```` nQ\aA[uv][x]0 3n~}j <0>` J0|Y|YOQg hHjTg |@```` nQ\aA[uv][z]0 3nj <0>` J0|Y|YOQg hHjTg |@```` nQ\aA[uv][y]0 3nj <0>` J0 ``` nQ\aADAE0 3n p C<0>` P0 A5p6jTg |=  `` nQ\aAinvis!nUj j0 3 p C<0>` P0 A5p6jTg |=  `` nQ\aAinvis!n`j j0 3 n C<0>` N0 A5p6jTg |= `` nQ\aAvis!n`j j0 3 n C<0>` N0 A5p6jTg |= `` nQ\aAvis!nUj j0 3j <0>` J0|Y|YOQg hHjTg |@```` nQ\aA[uv][y]0 3nj <0>` J0 ``` nQ\aACDE0 3n p C<0>` P0 A5p6jTg |=  `` nQ\aAinvis!nUs s0 3 n C<0>` N0 A5p6jTg |= `` nQ\aAvis!n`U U0 3 p C<0>` P0 A5p6jTg |=  `` nQ\aAinvis!n`U U0 3 n C<0>` N0 A5p6jTg |= `` nQ\aAvis!n`s s0 3 p C<0>` P0 A5p6jTg |=  `` nQ\aAinvis!n`s s> $   "^.nQ\aAHide invisible edges*0 3n n C<0>` N0 A5p6jTg |= `` nQ\aAvis!nUs s> $   "I,nQ\aAHide visible edgessC8nYC@K> m   *nQ\aAShow Triangle DAE> nv   0nQ\aAShow Quadrilateral ABCD0 3nr *<0>` R0 Hh   ``` 0 3r ><0>` R0 Hh   ``` 0 3r R<0>` R0 Hh   ``` 0 3r f<0>` R0 Hh   ``` 0 3v z<0>` V0 Hh   ````  O^  <0> >0?YY@??&nQ\aA vertex colort |> nU   ;P&nQ\aA Hide Point Et0 3n f '<0> F0H` ` Kn UK?> j   ;c&nQ\aA Hide Point At0 3n f '<0> F0H` ` Kn jK?> e   ;v&nQ\aA Hide Point Bt> ns   ;&nQ\aA Hide Point Ct0 3n f '<0> F0H` ` Kn sK?> `   ;&nQ\aA Hide Point Dt0 3n f '<0> F0H` ` Kn `K?0 3 f '<0> F0H` ` K eK?44~!>~q.#86#>|".#>    "|,nQ\aAShow smart vertices> n   X"6nQ\aAHide/Show permanent vertices Onb  <0> B0?YY@?? $nQ\aA color[ABE]e o-0 3n f <0> F0&;6 )ĉo ` `K4qn nK$@ O^  0<0> >0?YY@??$nQ\aA color[BCE]e 0oG0 3n f <0> F0&;6)ĉo ` `K4n wK$@ Ob  J<0> B0?YY@?? $nQ\aA color[CDE]e Joa0 3n f <0> F0&;6)ĉo ` `K4~n yK$@ Od  d<0> D0?YY@?? $nQ\aA color[DAE]e do{0 3n f <0> F0&;6)ĉo ` `K4n mK$@ Ob  ~<0> B0?YY@?? $nQ\aA color[ABCD] ~v0 3n f <0> F0&;6)ĉo ` `K5n vK $@>    "$nQ\aA Hide facesn0. > .#O Cn ".# - ED@@@C@@@B@؅@@A@؅@5@?P[1]f.#$"/>@Y/7C.#K5 K$@    X.nQ\aALink to InstructionseXknD>Dpx-#YQThat document was created with a newer version of Sketchpad and cannot be opened.|This document was created with a newer version of Sketchpad. Some information may be lost. The document will open as a copy.$H LCredits` a b c d e f g h i j k l m n o p q _ ,#GSP4_W_0554/Mar 2 20040#` Arial9x  '''$'mtr$'nme$' fj$'ms$'$'$'$'$'$' $' $' %'&'8'8'8'9':' @@*',<0>>*'g     2nQ\aAHome2a n<  < Y!http://www.keypress.com/sketchpad2nQ\aASketchpad Resource CenterY nh  h  Lhttp://www.keypress.com/sketchpad/general_resources/advanced_sketch_gallery/0nQ\aAAdvanced Sketch Gallery nDB,.>,n$$->V-Z)mtrnP@ v@4(mtr@ 4\.B@: &nme@  nQ\aAx6(mtrn 6\.B@: &nmen   nQ\aAy='n   -# {A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$LVisibility Index ArialxoxnQ\aACorsnQ\aABnQ\aAA'nQ\aAS[1]A3   <0>A3   J<0>A3   5<0>B3   ]<0>B3   ^H<0>B3   ]2<0>0 ! j ^`<0>Vl D J0|Y|YOQg hHjTg |@```` nQ\aA[uv][z]0 !n j ^x<0>Vl D J0|Y|YOQg hHjTg |@```` nQ\aA[uv][y]0 !n  j ^<0>Vl D J0|Y|YOQg hHjTg |@```` nQ\aA[uv][x]0 !n j ^<0>Vl D J0 ``` &nQ\aA =V[{2}{3}{4}]/#Visibility - V. Dubrovsky 10/03 For three succesively selected points A, B, C the tool returns V=+1 if the triangle ABC is oriented positively (counterclockwise) and V=-1 otherwise. Thanks to Nick Jackiw for improvement of the labeling in this tool.s{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$ LSmart Edge Arial d   nQ\aABmYEnQ\aAAV@ !@^  <0> >0  @T @pUnQ\aAV[2]  !n^  <0> >0  @T @pUnQ\aAV[1] 0 !n n <0> N0 A5p6jTg |= `` nQ\aAvis0 !n p <0> P0 A5p6jTg |=  `` nQ\aAinvis!n !  /#Smart Edge - V. Dubrovsky 10/03 Click two endpoints A and B of an edge of a polyhedron and then the visibility indices V_1 and V_2 of the two adjacent faces. The edge thus created will become dashed on the invisible side of the polyhedron. {A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$LBlinker Arial  !^  <0> >0  @T @U$nQ\aA Visibility  !n^  <0> >0  @T @UnQ\aAColor ?nnQ\aAFace0 ! f <0> F0H` ` >    m(nQ\aAHide Face P[1]cK?^n K?f/#Blinker - V. Dubrovsky 9/04 Click an object (such as the interior of a face, an edge, or a vertex), the Color parameter, and the Visiblity parameter. Press the Hide button that appears. Then the object will be replaced by its parametrically colored copy which exists only if Visibility is nonnegative and whose color is defined by the Color parameter.