@ 2!u$capmYy̿ @ 4ҌJ4YR!Y0̿HH3| !W KWith thanks to Annie Fetter of Math Forum for amazing Sketchpad expertise!e! !W`)p!WP)̿` p̿o! 4ҌJ4YR!Y!'HHŹpPż0 (ŹpŹ0 -Can you do better than this inter-seed angle?e? źż0Źźż0nt DocumentsŷMh)!P 4ҌJ4YR!Y8)HH3|) ASeeds are marked by "x"; move the inter-seed angle HERE...right -->-->  * `,P)P%*@@%tions! 4ҌJ4YR!Y8HH3|$a@ 'Drag the CENTER point to move seed-head  ʀ@$`)$`<da; 4ҌJ4YR!Y0;HH3|;@F SThese spiral seed patterns should be straight lines but are slightly curved. This is because the angle-rotation is not exactly 90, 180 or 270 degrees due to limitations of the screen (pixel resolution).c` 0 4ҌJ4YR!Y0c`HH3|c8Double-click these BUTTONS to move to that pre-set anglele Pc`c@dd@0b18 tur~׳xAunc[ 4ҌJ4YR!YN TG?? ?P;t8??p0;C5D#   4ҌJ4YR!YMdh@;w??@??HHAD#@ o  ;4ҌJ4YR!Y=B@=H=;=C@ =H=={ this is rp>,.=;=B  -H=;=B x >=;4 P@ 4ҌJ4YR!Y=P@ \=K=P@0 this is theta;t=K=Q0=S=PHH;k=P1==Q=E 4ҌJ4YR!Y=E =@=E0\~ this is r^2;W=@=Fp=H=EPHH;t=E;== 4ҌJ4YR!Ythis is i, our sliderh`???0h0TR??PhTRP~U< 4ҌJ4YR!Y1260' k/~k0'k0;0kD B 6; 4ҌJ4YR!Y0' k/~k0'k0;0k%B` : 4ҌJ4YR!YD*P:p6\6=6,6# 6 6DC ?` 4ҌJ4YR!YC?@HH;p?0?CڀC /4ler% 4ҌJ4YR!YA(0U` BDCc 5@@!P 4ҌJ4YR!Y0@@HH3|@p :What's the best angle to have between SEEDS in a seedhead?d? Note Pa@ ` Stationery?Recent Applica+2  4ҌJ4YR!Y&,HHDp -DpDDbThe best angle must have NO gaps which waste space and evenly space the seeds about the seed head.d. Seeds are marked by "x"; move the inter-seed angle on the right --> -->->ght -->>wwwwww6 4ҌJ4YR!YAA6HH&60¨@ .38 4ҌJ4YR!YAB8HH3|8C@ .3< 4ҌJ4YR!YAC<HH3|<0@C p 4ҌJ4YR!YADpHH3|&P¨ gl% 4ҌJ4YR!YD*P:p6\6=6,6# 6 6C[BC_ LQI 4ҌJ4YR!YD*P:p6\6=6,6# 6 6C4C 27? 4ҌJ4YR!YD*P:p6\6=6,6# 6 6CډyBQ0   4ҌJ4YR!Ym @#t`1{V:{(:{D:{(:arc aeAD#@C5D#?P%\ 4ҌJ4YR!Ym10 aliasAutomated Tasks Calculator ChooserConn 01260 = R9 8|TX҂98t4<;3  ŅŃł$Ņņ=>,;n<48(ݥ8W r9 J4YRJ4YR98Ƭ2ݥ<Distance(0 to 1260) = <99@ݡ:H׫T29@0r:9@XX : Dަh:H<<:{ݟh\r9Ԁ J YRŏh 9:D:T`HH3|:0_ :0( @_ :2Ƭ2++ : :\(Y:W 4:ߘ_ 5U  4ҌJ4YR!Yl0< <<=;%B`D B? -i  4ҌJ4YR!YjJ \.`O d6 g9 -J DCCڀC?4N  4ҌJ4YR!Yc1 dd66-B`66-1d`66`CڀCB,{?h/Y^B)b$ 4ҌJ4YR!6Y <- Zoom ->pWT4.,> >p U(>p?B(PB`Cc&3  4ҌJ4YR!Yn?@^,L5CCHDCBCCBBJCJ¨@C@?-3  4ҌJ4YR!Yo?V,LB7`BxH¤CCCC2[CfrC@C?3  4ҌJ4YR!Yp&h\z`pp ` C¨?  4ҌJ4YR!YqHH3| & ¨¨@?v  4ҌJ4YR! YAIHH3|/05 bDC gl 4ҌJ4YR! YDrag me to change angle4.,Ǡ U(`B(C[BC_f  4ҌJ4YR!YkCڀCC[BC_?&4Nler 4ҌJ4YR!"Y a1 PlayerApplications Foldr aliasAutomated Tasks CalaCڀCB,뾷#oDCC[BC_AA14N?V&-@X 4ҌJ4YR!Y 90 (1/4 turn)pWT4.,> >p U(>p?B(P &-_@ 4ҌJ4YR!Y180 (1/2 turn)d34.,0,Z) U(0ꪠB( """"&M)  4ҌJ4YR!Ym16 aliasAutomated Tasks Calculator ChooserConn arc angle a1 =  8|TX҂98t4<;3  ŅŃł$Ņņ=>,;n<48(ݥ8W r9 J4YRJ4YR98Ƭ2ݥ<!Angle between successive seeds = <99@ݡ:H׫T29@0r:9@XX : Dަh:H<<:{ݟh\r9Ԁ J YRŏh 9:D:T`HH3|:0_ :0( @_ :2Ƭ2++ : :\(Y:W 4:ߘ_ (O œ 4ҌJ4YR!Ym28;*n*n*n*n=d@=  {D:arc angle a1}{360} = 8|TX҂98t4<;3  ŅŃł$Ņņ=>,;n<48(ݥ8W r9 J4YRJ4YR98Ƭ2ݥ<!Fraction of turn between seeds = <99@ݡ:H׫T29@0r:9@XX : Dަh:H<<:{ݟh\r9Ԁ J YRŏh 9:D:T`HH3|:0_ :0( @_ :2Ƭ2++ : :\(Y:W 4:ߘ_ 9@+#(=B 4ҌJ4YR! YO?HH;w?@0?BD#D  @E> 4ҌJ4YR! Yi' k/~k0'k0;0kĭHB N N #?4ҌJ4YR!2Y BDCc@E,X  4ҌJ4YR!Ynearly phi=0.618 turns4.,> >p U(>p?B(P """"& 4ҌJ4YR!YAIH3|/05 bCvC: %#i 4ҌJ4YR!Ym21 aliasAutomated Tasks Calculator ChooserConn OM = c angle a1}{360} = 8|TX҂98t4<;3  ŅŃł$Ņņ=>,;n<48(ݥ8W r9 J4YRJ4YR98Ƭ2ݥ<F = tion of turn between seeds = <99@ݡ:H׫T29@0r:9@XX : Dަh:H<<:{ݟh\r9Ԁ J YRŏh 9:D:T`HH3|:0_ :0( @_ :2Ƭ2++ : :\(Y:W 4:ߘ_ -g 4ҌJ4YR!Ym2r aliasAutomated Tasks Calculator ChooserConn 0i = c angle a1}{360} = 8|TX҂98t4<;3  ŅŃł$Ņņ=>,;n<48(ݥ8W r9 J4YRJ4YR98Ƭ2ݥ<i = tion of turn between seeds = <99@ݡ:H׫T29@0r:9@XX : Dަh:H<<:{ݟh\r9Ԁ J YRŏh 9:D:T`HH3|:0_ :0( @_ :2Ƭ2++ : :\(Y:W 4:ߘ_ .N 7" 4ҌJ4YR!5Y œy"$D 2kpk }k$"9xE- BDCՀBDA?Q/ޱN " 4ҌJ4YR!4Y œx'99k09;@kG9;PWkkzCcCyCc?Q/-@A 4ҌJ4YR!Y270 (3/4 turn)pWT4.,> >p U(>p?B(P """"1& [œ 4ҌJ4YR!Ym22I{| } Text Format  {D:F{!:*}10}{1cm} = } = 8|TX҂98t4<;3  ŅŃł$Ņņ=>,;n<48(ݥ8W r9 J4YRJ4YR98Ƭ2ݥ< F*10/1cm = turn between seeds = <99@ݡ:H׫T29@0r:9@XX : Dަh:H<<:{ݟh\r9Ԁ J YRŏh 9:D:T`HH3|:0_ :0( @_ :2Ƭ2++ : :\(Y:W 4:ߘ_  Aŋ2]%wœ 4ҌJ4YR!Ym11;*n*n*n*n?9 {D:01260}{0i} = } = } = 8|TX҂98t4<;3  ŅŃł$Ņņ=>,;n<48(ݥ8W r9 J4YRJ4YR98Ƭ2ݥ<'Distance(0 to 1260)/Distance(0 to i) = <99@ݡ:H׫T29@0r:9@XX : Dަh:H<<:{ݟh\r9Ԁ J YRŏh 9:D:T`HH3|:0_ :0( @_ :2Ƭ2++ : :\(Y:W 4:ߘ_ 39E0œ 4ҌJ4YR!Ym3;*n*n*n*n?̰@T  trunc{(:FH{!:*}100} = = 8|TX҂98t4<;3  ŅŃł$Ņņ=>,;n<48(ݥ8W r9 J4YRJ4YR98Ƭ2ݥ<trunc[Distance(F to H)*100] = to i) = <99@ݡ:H׫T29@0r:9@XX : Dަh:H<<:{ݟh\r9Ԁ J YRŏh 9:D:T`HH3|:0_ :0( @_ :2Ƭ2++ : :\(Y:W 4:ߘ_ j2d3/4p 4ҌJ4YR!YAEpHH3|BDCc 54)Ŝ 4ҌJ4YR!Ym23I{| } Text Format   i{!:*}{(:{D:F{!:*}10}{1cm}} = 8|TX҂98t4<;3  ŅŃł$Ņņ=>,;n<48(ݥ8W r9 J4YRJ4YR98Ƭ2ݥ<i * F = stance(F to H)*100] = to i) = <99@ݡ:H׫T29@0r:9@XX : Dަh:H<<:{ݟh\r9Ԁ J YRŏh 9:D:T`HH3|:0_ :0( @_ :2Ƭ2++ : :\(Y:W 4:ߘ_ 37  œt 4ҌJ4YR!Ym24I{| } Text Format  /{D:{(:arc angle a1}{!:*}(i * F){!:*}1cm}{1} = ҂98t4<;3  ŅŃł$Ņņ=>,;n<48(ݥ8W r9 J4YRJ4YR98Ƭ2ݥ<!(Arc Angle(a1))*(i * F)*1cm/1 = i) = <99@ݡ:H׫T29@0r:9@XX : Dަh:H<<:{ݟh\r9Ԁ J YRŏh 9:D:T`HH3|:0_ :0( @_ :2Ƭ2++ : :\(Y:W 4:ߘ_  Aŋ<5+;6ŕ  4ҌJ4YR!Ym25;*n*n*n*nh`p9  ({D:{(:arc angle a1}{!:*}(i * F)}{1cm} = {1} = ҂98t4<;3  ŅŃł$Ņņ=>,;n<48(ݥ8W r9 J4YRJ4YR98Ƭ2ݥ<(Arc Angle(a1))*(i * F)/1cm = = i) = <99@ݡ:H׫T29@0r:9@XX : Dަh:H<<:{ݟh\r9Ԁ J YRŏh 9:D:T`HH3|:0_ :0( @_ :2Ƭ2++ : :\(Y:W 4:ߘ_ Aŋ+;`œ 4ҌJ4YR!Ym27I{| } Text Format  @{D:{V:{(:{D:{(:arc angle a1}{!:*}(i * F){!:*}1cm}{1}}}}{100} = <;3  ŅŃł$Ņņ=>,;n<48(ݥ8W r9 J4YRJ4YR98Ƭ2ݥ<-sqrt[((Arc Angle(a1))*(i * F)*1cm/1)]/100 = <99@ݡ:H׫T29@0r:9@XX : Dަh:H<<:{ݟh\r9Ԁ J YRŏh 9:D:T`HH3|:0_ :0( @_ :2Ƭ2++ : :\(Y:W 4:ߘ_ 5d<-2"ler 4ҌJ4YR!ah'ʞp4ҌJ4YR!?YQo PlayerApplications Foldr aliasAutomated Tasks Cala?.3;=<>?