GSP4yQThat 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.$-LInstructions` a b c d e f g h i j k l m n o p q _ ,#GSP4_M_0580XUB/May 5 20060#HArial Geneva '''$'$'$'$'$'$'$'$'$'$' $' $' %'&'8'8'8'9':'>   >>><0>>>>>>>>>>>>>>>>>>>>>>>><0>>>>>>>>>>>>>>>>>>>o.#h@@s@Ћ@t@p@r@P@Y@)@r@4( 4\.B@: &  nQ\aAx6( 6\.B@: &   nQ\aAy='   ((>     nQ\aAExample     nQ\aACredits>>>>>>>>>>>>>>>>>>>>><0>>>>>>>>><->><->>>>>>><->>>>>EЉ@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_M_0580XUB/May 5 20060#HArial Geneva     '''$'$'$'$'$'$'$'$'$'$' $' $' %'&'8'8'8'9':' P~ C<0> ^0`0C@\.խ@`0C@?   CS P /<0> `0`0C@\.խ@`0C@?   /?Ab@@C@Z@@M`@pz@zeroH@pz@APo7@ APozero'<ￜPɥwg) V@pX<@xww?A'@<?H<@*?M'4pXL@xww@*?one4pXLxww*?W'p4@?*?zero'4*?zero'4@?*?C'4*?C'4@?*?A'4*?A'4@N?*?AP'4Nǿ*?AP'  AP'one'@   ?j  @c2'.#    ?Pitch.# 4@?*?W'' 4*?W''  ?bm 4@?*?one' 4*?one' ?bo' ?bp'   zDo@E '?S?O  ENP?ratio T,i?y?AOi ?bli ?bni ! .# "?p.#/3 #  <0>uc> "$>@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'$0'  <0>Wucm9e 0/?bfe.# /#?bge.# #0?bhe.#40#/UUUUUU?p2e 1!?bje.# !2?bke.#42!1UUUUUU?p3e "3 @c3e.#?  +&m 0 07j <0> J0  `m10 ? @p4 @  DO@AF AAFAP' C .#C4"@RQ?@RQ?*?AF'C4"@RQ?RQĿ*?AF'D4@N?*?AP''D4Nǿ*?AP''/3 E'  <0>WucnQ\aAm[1] GF?bc].# FC?bd].# CG?be].#4GCFUUUUUU?p1]0 3Jn <0> N0 ` `` m8]! Oone' Pone'one'' 21.#)H}@u@SCJ''!TS4E; & S' nQ\aAx8(V 8`0C@: & SW nQ\aAy=' VX C8YC@L SZ @c1'ZS "L'' \S$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 ABE j`?aow/ \V?amw - VqAKw \r #C Us?azw es?auw5`jes4eUs> w   P*nQ\aAShow Triangle BCE4sU`> y   v*nQ\aAShow Triangle CDE s`?arw> $laftu{pk   "4.nQ\aAShow permanent edges*A3 jY  <0>4ucB3 jY  <0>4ucA3 eY  <0>4ucB3 eY  <0>4uc0 3~}j  <0> J0|Y|YOQg hHjTg |@```` nQ\aA[uv][z]0 3}~j <0> J0|Y|YOQg hHjTg |@```` nQ\aA[uv][z]A3 UY  <0>4ucB3 UY  <0>4uc0 3j <0> J0|Y|YOQg hHjTg |@```` nQ\aA[uv][x]0 3j <0> J0|Y|YOQg hHjTg |@```` nQ\aA[uv][y]0 3}~j <0> J0|Y|YOQg hHjTg |@```` nQ\aA[uv][x]0 3~}j <0> J0|Y|YOQg hHjTg |@```` nQ\aA[uv][y]0 3j <0> J0 ``` nQ\aAABEA3 sY  <0>4ucB3 sY  <0>4uc0 3j <0> J0|Y|YOQg hHjTg |@```` nQ\aA[uv][x]0 3j <0> J0|Y|YOQg hHjTg |@```` nQ\aA[uv][z]0 3}~j  <0> J0|Y|YOQg hHjTg |@```` nQ\aA[uv][x]0 3j  <0> J0|Y|YOQg hHjTg |@```` nQ\aA[uv][y]0 3j <0> J0 ``` nQ\aAADC0 3 p C<0> P0 A5p6jTg |=  `` nQ\aAinvis!ej j0 3 n C<0> N0 A5p6jTg |= `` nQ\aAvis!ej j0 3j <0> J0|Y|YOQg hHjTg |@```` nQ\aA[uv][z]0 3j <0> J0 ``` nQ\aABCE0 3 p C<0> P0 A5p6jTg |=  `` nQ\aAinvis!eU U0 3 p C<0> P0 A5p6jTg |=  `` nQ\aAinvis!se e0 3 n C<0> N0 A5p6jTg |= `` nQ\aAvis!se e0 3 n C<0> N0 A5p6jTg |= `` nQ\aAvis!eU UA3 `Y  <0>4ucB3 `Y  <0>4uc0 3j <0> J0|Y|YOQg hHjTg |@```` nQ\aA[uv][x]0 3~}j <0> J0|Y|YOQg hHjTg |@```` nQ\aA[uv][z]0 3j <0> J0|Y|YOQg hHjTg |@```` nQ\aA[uv][y]0 3j <0> J0 ``` nQ\aADAE0 3 p C<0> P0 A5p6jTg |=  `` nQ\aAinvis!Uj j0 3 p C<0> P0 A5p6jTg |=  `` nQ\aAinvis!`j j0 3 n C<0> N0 A5p6jTg |= `` nQ\aAvis!`j j0 3 n C<0> N0 A5p6jTg |= `` nQ\aAvis!Uj j0 3j <0> J0|Y|YOQg hHjTg |@```` nQ\aA[uv][y]0 3j <0> J0 ``` nQ\aACDE0 3 p C<0> P0 A5p6jTg |=  `` nQ\aAinvis!Us s0 3 n C<0> N0 A5p6jTg |= `` nQ\aAvis!`U U0 3 p C<0> P0 A5p6jTg |=  `` nQ\aAinvis!`U U0 3 n C<0> N0 A5p6jTg |= `` nQ\aAvis!`s s0 3 p C<0> P0 A5p6jTg |=  `` nQ\aAinvis!`s s> $   "^.nQ\aAHide invisible edges*0 3 n C<0> N0 A5p6jTg |= `` nQ\aAvis!Us s> $   "I,nQ\aAHide visible edgessC8YC@K> m   *nQ\aAShow Triangle DAE> v   0nQ\aAShow Quadrilateral ABCD0 3r *<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>g >0?YY@??&nQ\aA vertex colort z> U   ;P&nQ\aA Hide Point Et0 3 f '<0> F0H` ` K UK?> j   ;c&nQ\aA Hide Point At0 3 f '<0> F0H` ` K jK?> e   ;v&nQ\aA Hide Point Bt> s   ;&nQ\aA Hide Point Ct0 3 f '<0> F0H` ` K sK?> `   ;&nQ\aA Hide Point Dt0 3 f '<0> F0H` ` K `K?0 3 f '<0> F0H` ` K eK?44~!>~p.#86#>y".#>    "|,nQ\aAShow smart vertices>    X"6nQ\aAHide/Show permanent vertices Ob  <0> B0?YY@?? $nQ\aA color[ABE]e k(0 3 f <0> F0&;6 )ĉo ` `K4q nK$@ O^  0<0> >0?YY@??$nQ\aA color[BCE]e 0kB0 3 f <0> F0&;6)ĉo ` `K4 wK$@ Ob  J<0> B0?YY@?? $nQ\aA color[CDE]e Jk\0 3 f <0> F0&;6)ĉo ` `K4~ yK$@ Od  d<0> D0?YY@?? $nQ\aA color[DAE]e dkv0 3 f <0> F0&;6)ĉo ` `K4 mK$@ Ob  ~<0> B0?YY@?? $nQ\aA color[ABCD] ~r0 3 f <0> F0&;6)ĉo ` `K5 vK $@>    "$nQ\aA Hide faces0. > .#O C ".# - ED@@C@@B@؅@A@؅@5?P[1]f.#$"/>ara/6C.#K5 K$@    X.nQ\aALink to InstructionseXkD>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.$H LCredits` a b c d e f g h i j k l m n o p q _ ,#GSP4_M_0580XUB/May 5 20060#HArial Geneva   '''$'mtr$'nme$' fj$'ms$'$'$'$'$'$' $' $' %'&'8'8'8'9':'@@*',<0>>*'c    2nQ\aAHome2` <  < Yhttp://www.dynamicgeometry.com/2nQ\aASketchpad Resource CenterY d  d  Ihttp://www.dynamicgeometry.com/general_resources/advanced_sketch_gallery/0nQ\aAAdvanced Sketch Gallery DB,.>(,$$->-Z)mtrP@ v@4(mtr 4\.B@: &nme  nQ\aAx6(mtr 6\.B@: &nme   nQ\aAy='   -# O{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.$LVisibility IndexArialnQ\aACorsnQ\aABnQ\aAA'nQ\aAS[1]A3   <0>ӰA3   J<0>A3   5<0>ӰB3   ]<0>B3   ^H<0>ӰB3   ]2<0>0 ! j ^`<0> J0|Y|YOQg hHjTg |@```` nQ\aA[uv][z]0 ! j ^x<0> J0|Y|YOQg hHjTg |@```` nQ\aA[uv][y]0 !  j ^<0> J0|Y|YOQg hHjTg |@```` nQ\aA[uv][x]0 ! j ^<0> J0 ``` &nQ\aA =V[{2}{3}{4}]/#Visibility - V. Dubrovsky 10/03 For three succesively selected points A, B, C the tool returns V=+1 if the triangle ABC is oriented positively (counterclockwise) and V=-1 otherwise. Thanks to Nick Jackiw for improvement of the labeling in this tool.O{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$ LSmart EdgeArial GenevaB   nQ\aABmYEnQ\aAAV@ !^  <0>g >0  @T @pUnQ\aAV[2]  !^  <0> >0  @T @pUnQ\aAV[1] 0 ! n <0> N0 A5p6jTg |= `` nQ\aAvis0 ! p <0> P0 A5p6jTg |=  `` nQ\aAinvis! !  /#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. iO{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.$LBlinkerArial Geneva  !^  <0> >0  @T @U$nQ\aA Visibility  !^  <0>g >0  @T @UnQ\aAColor ?nQ\aAFace0 ! f <0> F0H` ` >    m(nQ\aAHide Face P[1] K?^ K?d/#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.