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The document will open as a copy. $[ [LBugs` a b c d e f g h i j k l m n o p q _ ,#GSP4_W_0554/Mar 3 20040#x Arial 0 '''$'$'$'$'$'$'$'$'$'$' $' $' %'&'8'8'8'9':' nQ\aABP@J@@nQ\aAAv@J@@F@f@@86i">tani/.#@nQ\aAC[1] l@q@@@l@@t@@  @@  @ @ @ @  .# -@  @  @ $ ]grV@ $ t?-RB?4"B "B B $ tտ-RB?4@"B B $ tտ-RB?4@"B B   -B  -B  -B  -B  -B  -B  -B  -B B  .# -B   -B   -B   -B   -B   -B   -B   -B  B #.#B ".#B !.#B (.#B $.#B %.#B &.#B '.# B .# B .#BnQ\aAH[1]V@q@@A@x@@\@@B}@@\@@ 45 @6@ 47 @8G[1] 75 :@ 45 <  @Drag/345=  W<0>3&nQ\aA Scale Factori!n23>.#!13>.#!03>.#!/3>.#!.3>.#!-3>.#!,3>.#!+3>.#!*3>.#!)3>.#! 3>.#! 3>.#>  45679;<   ,nQ\aAShow Ratio Segment"> n =9   |*nQ\aAScale 0.25:1t> n =7   |(nQ\aAScale 0.5:1> n =;   |*nQ\aAScale 0.75:1tn545O45P45Q45>  =5   &nQ\aA Scale 1:1> n =O   &nQ\aA Scale 2:1> n =P   &nQ\aA Scale 3:1> n =Q   &nQ\aA Scale 4:1> n0 45679;<OPQR   ,nQ\aAShow Ratio SegmentnDDpM1>><0>>><0>>pMl.# n   ,nQ\aAReturn to Main Menu*(n42u>s>>u> nX   *nQ\aAHide InstructionsVQThat 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. $>-LThe Golden Ratio` a b c d e f g h i j k l m n o p q _ ,#GSP4_W_0554/Mar 3 20040#x Arial   0'''$'$'$'$'$'$'$'$'$'$' $' $' %'&'8'8'8'9':') &@}@4(@ 4bXI@: &@  nQ\aAx6(n 6bX,A@: &n  nQ\aAy='n  C8nC(@? <?8@?e" @  O^ mT<0>T3 s >0"?YY@??,nQ\aANumber of trianglesmTuh0 3n b m(<0>:/ B0ZII`nQ\aAxAbn@G@@2Radius of plotted circleЖ@G@@  @@M@@,Width of scale markĖ@N@@ @nQ\aAB@M@@nQ\aAAPs@M@@nQ\aAO@R@@nQ\aAP@R@@ @nQ\aAA{hw@O7j@@  @  $   Dt$nQ\aA Move Pointa> n '   D$nQ\aA Move Pointa> n )   D$nQ\aA Move Pointang@`d@@0p@ k@@u@@d@@{@j@@H@d@> @X!"#$%&')*+,-.   v:&nQ\aA Hide Objects> n<')*+,-.   vP&nQ\aA Hide Objects> n ')*+,-.   vf&nQ\aA Hide ObjectsC8nC??C@  FC8C@? HC8C@?2 JC8C@? LC8C@?4 NC8C@? PC8C@?6 RC8C @? TC8C"@?8 VC8C$@? 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Some information may be lost. The document will open as a copy. $0LRatio and Music` a b c d e f g h i j k l m n o p q _ ,#GSP4_W_0554/Mar 3 20040#x Arial   0'''$'$'$'$'$'$'$'$'$'$' $' $' %'&'8'8'8'9':') &@}@4(@ 4bXI@: &@  nQ\aAx6(n 6bX,A@: &n  nQ\aAy='n  C8nC(@? <?8@?athser @  O^ mT<0>:/ >0"?YY@??,nQ\aANumber of trianglesmTuh0 3n b m(<0>:/ B0ZII`nQ\aAxAbn@G@@2Radius of plotted circleЖ@G@@  @@M@@,Width of scale markĖ@N@@ @nQ\aAB@M@@nQ\aAAPs@M@@nQ\aAO@R@@nQ\aAP@R@@ @nQ\aAA{hw@O7j@@  @  $   Dt$nQ\aA Move Pointa> n '   D$nQ\aA Move Pointa> n )   D$nQ\aA Move Pointang@`d@@0p@ k@@u@@d@@{@j@@H@d@> @X!"#$%&')*+,-.   v:&nQ\aA Hide Objects> n<')*+,-.   vP&nQ\aA Hide Objects> n ')*+,-.   vf&nQ\aA Hide ObjectsC8nC??C@  FC8C@? HC8C@?2 JC8C@? LC8C@?4 NC8C@? PC8C@?6 RC8C @? TC8C"@?8 VC8C$@? XC8C&@?10e Z @ F/ J\ - ]K - ]K/ L\ - `M - `M/ N\ - cO - cO/ P\ - fQ - fQ/ R\ - iS - iS/ T\ - lU - lU/ V\ - oW - oW/ X\ - rY - rY/ Z\ - u[ - u[ \ x?BB3 x  m<<0>f x z - \  |$ ࿥LXz?>@ects }$LXz??Nects | ffffff?/ H\ - I - I> T^adgjmpsvwtqnkheb_   I,nQ\aAShow Intersections5n}~  _^ ba ed hg kj nm qp ts wv \ uE]t?>  J   s$nQ\aA Point at 2e> n L   s$nQ\aA Point at 3e> n N   s$nQ\aA Point at 4e> n P   s$nQ\aA Point at 5e> n R   s$nQ\aA Point at 6e> n H   s$nQ\aA Point at 1en  nn00>E8n y>  x   >)2nQ\aAPlot number of triangles> nxz{   wNnQ\aA5Show a graphical model of the number of paving stonesnY@Z@@Y@~@@nQ\aAC0@k@@nQ\aAB@k@@nQ\aAC0@m@@nQ\aAB@m@@nQ\aACL@x@@nQ\aAB,@x@@nQ\aACD@ x@@nQ\aAB$@ x@@nQ\aAC@@e@@nQ\aABx@@e@@nQ\aACX@g@@nQ\aAB@g@@nQ\aAAFҞ@C‘s@@nQ\aAAFޅ@C‘s@@nQ\aAAF@C‘s@@nQ\aAAFҾ@C‘v@@nQ\aAAFҞ@C‘s@@ @  @֮9?vWov $LXz?N@raph   P=?< $LXz?N@raph   zc'5࿬OvX?v v $LXz?N@raph   P=?< $LXz?N@raph   T=?<  $LXz?N@raph   =߿ @   E:$nQ\aA Orient Page> n   :"nQ\aA Work Area> n   I nQ\aAReturnen,,C>eC2.# nP  P Jq4http://regentsprep.org/Regents/math/ratio/Tratio.htmBnQ\aA)Ratios and Music - Oswego School DistrictJqa nT  T J8http://www.musicmasterworks.com/WhereMathMeetsMusic.html?BnQ\aA)Where Math Meets Music - Joseph HeimillerJinDBFH/>o/FH>\.#npy@k@@z@m@@ .# @.# @c?!kXknQ\aAZ@K@@nQ\aAY{@Y@@.#.# .# .#.#  6 ?nQ\aAA[1] n.#-#VQThat 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. $(  LPractice` a b c d e f g h i j k l m n o p q _ ,#GSP4_W_0554/Mar 3 20040#x Arial   0'''$'$'$'$'$'$'$'$'$'$' $' $' %'&'8'8'8'9':') &@}@4(@ 4bXI@: &@  nQ\aAx6(n 6bX,A@: &n  nQ\aAy='n  C8nC(@? <?8@?eph Heim @  O^ mT<0>:/ >0"?YY@??,nQ\aANumber of trianglesmTuh0 3n b m(<0>:/ B0ZII`nQ\aAxAbn@G@@2Radius of plotted circleЖ@G@@  @@M@@,Width of scale markĖ@N@@ @nQ\aAB@M@@nQ\aAAPs@M@@nQ\aAO@R@@nQ\aAP@R@@ @nQ\aAA{hw@O7j@@  @  $   Dt$nQ\aA Move Pointa> n '   D$nQ\aA Move Pointa> n )   D$nQ\aA Move Pointang@`d@@0p@ k@@u@@d@@{@j@@H@d@> @X!"#$%&')*+,-.   v:&nQ\aA Hide Objects> n<')*+,-.   vP&nQ\aA Hide Objects> n ')*+,-.   vf&nQ\aA Hide ObjectsC8nC??C@  FC8C@? HC8C@?2 JC8C@? LC8C@?4 NC8C@? PC8C@?6 RC8C @? TC8C"@?8 VC8C$@? 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