@ 2#$capmƻ =03jYy̿ @ ƿƿ"0̿HH3| !W KWith thanks to Annie Fetter of Math Forum for amazing Sketchpad expertise!e! !W`)p!WP)̿` p̿o! ƿƿ"!'HHŹpPż0 (ŹpŹ0 -Can you do better than this inter-seed angle?e? źż0Źźż0nt DocumentsŷMh)!P ƿƿ"8)HH3|) ASeeds are marked by "x"; move the inter-seed angle HERE...right -->-->  * `,P)P%*@@%tions! ƿƿ"8HH3|$a@ 'Drag the CENTER point to move seed-head  ʀ@$`)$`<da; ƿƿ"0;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 ƿƿ"0c`HH3|c8Double-click these BUTTONS to move to that pre-set anglele Pc`c@dd@0b18 tur~׳xAunc[ ƿƿ"N TG?? ?P;t8??p0;C5D#   ƿƿ"Mdh@;w??@??HHAD#@ o  ;ƿƿ"=B@=H=;=C@ =H=={ this is rp>,.=;=B  -H=;=B x >=;4 P@ ƿƿ"=P@ \=K=P@0 this is theta;t=K=Q0=S=PHH;k=P1==Q=E ƿƿ"=E =@=E0\~ this is r^2;W=@=Fp=H=EPHH;t=E;== ƿƿ"this is i, our sliderh`???0h0TR??PhTRP~U< ƿƿ"1260' k/~k0'k0;0kD B 6; ƿƿ"0' k/~k0'k0;0k%B` : ƿƿ"D*P:p6\6=6,6# 6 6DC ?` ƿƿ"C?@HH;p?0?CڀC /4ler% ƿƿ"A(0U` BDCc 5@@!P ƿƿ"0@@HH3|@p :What's the best angle to have between SEEDS in a seedhead?d? Note Pa@ ` Stationery?Recent Applica+2  ƿƿ"&,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 ƿƿ"AA6HH&60¨@ .38 ƿƿ"AB8HH3|8C@ .3< ƿƿ"AC<HH3|<0@C p ƿƿ"ADpHH3|&P¨ gl% ƿƿ"D*P:p6\6=6,6# 6 6C[BC_ LQI ƿƿ"D*P:p6\6=6,6# 6 6C4C 27? ƿƿ"D*P:p6\6=6,6# 6 6CډyBQ0   ƿƿ"m @#t`1{V:{(:{D:{(:arc aeAD#@C5D#?P%\ ƿƿ"m10 aliasAutomated Tasks Calculator ChooserConn 01260 = +.ƼƼzpƼPې40Ƽ>P.(Ƽ$Ƽ> > h@ƼH 0.$\ƼƽwƼ ƽPƽ=ƽn\' '**th@ƽuDistance(0 to 1260) = (tҐ4ƽƿNƽt \ƽ`ƽ*>`ƽ`OxƿO*ƽlvƽƽ`ƿOx ƾljƾ0DGƾ Dg ƾ@;$ƾ0ƿ@ƾ`)ƾ*Dєhƾƾƾ¬ƾ,40ª¬@ƿƿƾ"Hnƾr8|.$ƿcªccV @ƿƿ0"HPh 5U  ƿƿ"l0< <<=;%B`D B? -i  ƿƿ"jJ \.`O d6 g9 -J DCCڀC?4N  ƿƿ"c1 dd66-B`66-1d`66`CڀCB,{?h/Y^B)b$ ƿƿ6" <- Zoom ->pWT4.,> >p U(>p?B(PB`Cc&3  ƿƿ"n?@^,L5CCHDCBCCBBJCJ¨@C@?-3  ƿƿ"o?V,LB7`BxH¤CCCC2[CfrC@C?3  ƿƿ"p&h\z`pp ` C¨?  ƿƿ"qHH3| & ¨¨@?v  ƿƿ "AIHH3|/05 bDC rw ƿƿ "Drag me to change angle4.,Ǡ U(`B(CϔCjs#(=B ƿƿ "O?HH;w?@0?BD#D  @E> ƿƿ "i' k/~k0'k0;0kĭHB N N #?ƿƿ2 "BDCc@E,X q  ƿƿ"kCڀCCϔCjs?&4Nler ƿƿ" "a1 PlayerApplications Foldr aliasAutomated Tasks CalaCڀCB,#gjDCCϔCjsAA.4N?&-@X ƿƿ" 90 (1/4 turn)pWT4.,> >p U(>p?B(P &-_@ ƿƿ"180 (1/2 turn)d34.,0,Z) U(0ꪠB( & ƿƿ"nearly phi=0.618 turns4.,> >p U(>p?B(P """"& ƿƿ"AIH3|/05 bCvC: %#i ƿƿ"m21 aliasAutomated Tasks Calculator ChooserConn OM = = +.ƼƼzpƼPې40Ƽ>P.(Ƽ$Ƽ> > h@ƼH 0.$\ƼƽwƼ ƽPƽ=ƽn\' '**th@ƽuF = ance(0 to 1260) = (tҐ4ƽƿNƽt \ƽ`ƽ*>`ƽ`OxƿO*ƽlvƽƽ`ƿOx ƾljƾ0DGƾ Dg ƾ@;$ƾ0ƿ@ƾ`)ƾ*Dєhƾƾƾ¬ƾ,40ª¬@ƿƿƾ"Hnƾr8|.$ƿcªccV @ƿƿ0"HPh'g ƿƿ"m2r aliasAutomated Tasks Calculator ChooserConn 0i = = +.ƼƼzpƼPې40Ƽ>P.(Ƽ$Ƽ> > h@ƼH 0.$\ƼƽwƼ ƽPƽ=ƽn\' '**th@ƽui = ance(0 to 1260) = (tҐ4ƽƿNƽt \ƽ`ƽ*>`ƽ`OxƿO*ƽlvƽƽ`ƿOx ƾljƾ0DGƾ Dg ƾ@;$ƾ0ƿ@ƾ`)ƾ*Dєhƾƾƾ¬ƾ,40ª¬@ƿƿƾ"Hnƾr8|.$ƿcªccV @ƿƿ0"HPh(N 7" ƿƿ5 "#,y"$D 2kpk }k$"9xE- BDCՀBDA?Q)ޱN " ƿƿ4 "#,x'99k09;@kG9;PWkkzCcCyCc?Q)M)  ƿƿ"m16 aliasAutomated Tasks Calculator ChooserConn arc angle a1 = .ƼƼzpƼPې40Ƽ>P.(Ƽ$Ƽ> > h@ƼH 0.$\ƼƽwƼ ƽPƽ=ƽn\' '**th@ƽu!Angle between successive seeds = 4ƽƿNƽt \ƽ`ƽ*>`ƽ`OxƿO*ƽlvƽƽ`ƿOx ƾljƾ0DGƾ Dg ƾ@;$ƾ0ƿ@ƾ`)ƾ*Dєhƾƾƾ¬ƾ,40ª¬@ƿƿƾ"Hnƾr8|.$ƿcªccV @ƿƿ0"HPh+-@A ƿƿ"270 (3/4 turn)pWT4.,> >p U(>p?B(P """"/& [" ƿƿ"m22I{| } Text Format  {D:F{!:*}10}{1cm} = ƼƼzpƼPې40Ƽ>P.(Ƽ$Ƽ> > h@ƼH 0.$\ƼƽwƼ ƽPƽ=ƽn\' '**th@ƽu F*10/1cm = en successive seeds = 4ƽƿNƽt \ƽ`ƽ*>`ƽ`OxƿO*ƽlvƽƽ`ƿOx ƾljƾ0DGƾ Dg ƾ@;$ƾ0ƿ@ƾ`)ƾ*Dєhƾƾƾ¬ƾ,40ª¬@ƿƿƾ"Hnƾr8|.$ƿcªccV @ƿƿ0"HPh Aŋ0]%w" ƿƿ"m11;*n*n*n*n?9 {D:01260}{0i} = } = ƼƼzpƼPې40Ƽ>P.(Ƽ$Ƽ> > h@ƼH 0.$\ƼƽwƼ ƽPƽ=ƽn\' '**th@ƽu'Distance(0 to 1260)/Distance(0 to i) = 4ƽƿNƽt \ƽ`ƽ*>`ƽ`OxƿO*ƽlvƽƽ`ƿOx ƾljƾ0DGƾ Dg ƾ@;$ƾ0ƿ@ƾ`)ƾ*Dєhƾƾƾ¬ƾ,40ª¬@ƿƿƾ"Hnƾr8|.$ƿcªccV @ƿƿ0"HPh19E0" ƿƿ"m3;*n*n*n*n?̰@T  trunc{(:FH{!:*}100} = ƼƼzpƼPې40Ƽ>P.(Ƽ$Ƽ> > h@ƼH 0.$\ƼƽwƼ ƽPƽ=ƽn\' '**th@ƽutrunc[Distance(F to H)*100] = to i) = 4ƽƿNƽt \ƽ`ƽ*>`ƽ`OxƿO*ƽlvƽƽ`ƿOx ƾljƾ0DGƾ Dg ƾ@;$ƾ0ƿ@ƾ`)ƾ*Dєhƾƾƾ¬ƾ,40ª¬@ƿƿƾ"Hnƾr8|.$ƿcªccV @ƿƿ0"HPhj2d1/4p ƿƿ"AEpHH3|BDCc 32O " ƿƿ"m28;*n*n*n*n=d@=  {D:arc angle a1}{360} = ƼƼzpƼPې40Ƽ>P.(Ƽ$Ƽ> > h@ƼH 0.$\ƼƽwƼ ƽPƽ=ƽn\' '**th@ƽu!Fraction of turn between seeds = i) = 4ƽƿNƽt \ƽ`ƽ*>`ƽ`OxƿO*ƽlvƽƽ`ƿOx ƾljƾ0DGƾ Dg ƾ@;$ƾ0ƿ@ƾ`)ƾ*Dєhƾƾƾ¬ƾ,40ª¬@ƿƿƾ"Hnƾr8|.$ƿcªccV @ƿƿ0"HPh9@4)" ƿƿ"m23I{| } Text Format   i{!:*}{(:{D:F{!:*}10}{1cm}} = ƼzpƼPې40Ƽ>P.(Ƽ$Ƽ> > h@ƼH 0.$\ƼƽwƼ ƽPƽ=ƽn\' '**th@ƽui * F = of turn between seeds = i) = 4ƽƿNƽt \ƽ`ƽ*>`ƽ`OxƿO*ƽlvƽƽ`ƿOx ƾljƾ0DGƾ Dg ƾ@;$ƾ0ƿ@ƾ`)ƾ*Dєhƾƾƾ¬ƾ,40ª¬@ƿƿƾ"Hnƾr8|.$ƿcªccV @ƿƿ0"HPh16  " ƿƿ"m24I{| } Text Format  /{D:{(:arc angle a1}{!:*}(i * F){!:*}1cm}{1} = Pې40Ƽ>P.(Ƽ$Ƽ> > h@ƼH 0.$\ƼƽwƼ ƽPƽ=ƽn\' '**th@ƽu!(Arc Angle(a1))*(i * F)*1cm/1 = i) = 4ƽƿNƽt \ƽ`ƽ*>`ƽ`OxƿO*ƽlvƽƽ`ƿOx ƾljƾ0DGƾ Dg ƾ@;$ƾ0ƿ@ƾ`)ƾ*Dєhƾƾƾ¬ƾ,40ª¬@ƿƿƾ"Hnƾr8|.$ƿcªccV @ƿƿ0"HPh Aŋ<54;6" ƿƿ"m25;*n*n*n*nh`p9  ({D:{(:arc angle a1}{!:*}(i * F)}{1cm} = {1} = Pې40Ƽ>P.(Ƽ$Ƽ> > h@ƼH 0.$\ƼƽwƼ ƽPƽ=ƽn\' '**th@ƽu(Arc Angle(a1))*(i * F)/1cm = = i) = 4ƽƿNƽt \ƽ`ƽ*>`ƽ`OxƿO*ƽlvƽƽ`ƿOx ƾljƾ0DGƾ Dg ƾ@;$ƾ0ƿ@ƾ`)ƾ*Dєhƾƾƾ¬ƾ,40ª¬@ƿƿƾ"Hnƾr8|.$ƿcªccV @ƿƿ0"HPhAŋ4;`" ƿƿ"m27I{| } Text Format  @{D:{V:{(:{D:{(:arc angle a1}{!:*}(i * F){!:*}1cm}{1}}}}{100} = P.(Ƽ$Ƽ> > h@ƼH 0.$\ƼƽwƼ ƽPƽ=ƽn\' '**th@ƽu-sqrt[((Arc Angle(a1))*(i * F)*1cm/1)]/100 = ƽƿNƽt \ƽ`ƽ*>`ƽ`OxƿO*ƽlvƽƽ`ƿOx ƾljƾ0DGƾ Dg ƾ@;$ƾ0ƿ@ƾ`)ƾ*Dєhƾƾƾ¬ƾ,40ª¬@ƿƿƾ"Hnƾr8|.$ƿcªccV @ƿƿ0"HPh5d<ler ƿƿ<"Qo PlayerApplications Foldr aliasAutomated Tasks CalaA%Cz =)>^j'ʞpƿƿ?"Qo PlayerApplications Foldr aliasAutomated Tasks Cala?(1;=<>?