sfera[u_,v_]:={Cos[v]Cos[u],Cos[v]Sin[u],Sin[v]}

(* sfera unitaria: {Cos[v]Cos[u],Cos[v]Sin[u],Sin[v]}  *)
(* "paralleli": v=cost    "meridiani": u=cost   *)

(* "parallelo": v=0 (equatore) *)

sfera[u,0]

Table[k^2,{k,1,5}]

Table[k^2,{k,1,20,3}]

sfera[u_,v_]:={Cos[v]Cos[u],Cos[v]Sin[u],Sin[v]}

sfera[u,0.2]

Cos[0.2]

Table[k,{k,1,5}]

Table[k,{k,{2,4,15,7,3}}]

sfera[u_,v_]:={Cos[v]Cos[u],Cos[v]Sin[u],Sin[v]}

{0,0.2,0.2+0.19,0.39+0.18,0.57+0.17,0.74+0.16}

N[2Pi/28]

Sum[c^k,{k,0,4}]

Manipulate[Table[0.2*Sum[c^k,{k,0,m}],{m,0,4}],{{c,1},0.1,3}]

Table[0.2*Sum[0.95^k,{k,0,m}],{m,0,4}]

{0,0.2,0.2+0.19,0.39+0.18,0.57+0.17,0.74+0.16}

Table[0.2*Sum[0.95^k,{k,0,m}],{m,0,4}]

vm[m_,c_,vin_]:=vin*Sum[c^k,{k,0,m}]

sfera[u_,v_]:={Cos[v]Cos[u],Cos[v]Sin[u],Sin[v]}

tas[u0_,v0_,ur_,vr_]:=Show[{ParametricPlot3D[sfera[u0-ur,v],{v,v0-vr,v0+vr}],
ParametricPlot3D[sfera[u0+ur,v],{v,v0-vr,v0+vr}],
ParametricPlot3D[sfera[u,v0-vr],{u,u0-ur,u0+ur}],
ParametricPlot3D[sfera[u,v0+vr],{u,u0-ur,u0+ur}]}]

Show[{
ParametricPlot3D[sfera[u,v],{u,0,2Pi},{v,0,Pi/2},Mesh->None,PlotStyle->Opacity[0.5]],Table[ParametricPlot3D[sfera[u,k],{u,0,2Pi},PlotStyle->Thick],{k,Table[0.2*Sum[0.95^k,{k,0,m}],{m,0,4}]}],
Table[ParametricPlot3D[sfera[k,v],{v,0,0.2*Sum[0.95^k,{k,0,4}]},PlotStyle->Thick],{k,0,2Pi,2Pi/28}],
Graphics3D[Point[Table[sfera[k+Pi/28,vm[0,0.95,0.2*1/2]],{k,0,2Pi,2Pi/28}]]],
Table[tas[k+Pi/28,vm[0,0.95,0.2*1/2],0.05,0.05],{k,0,2Pi,2Pi/28}],
Table[Graphics3D[Point[Table[sfera[k+Pi/28,vm[m,0.95,0.2]+(vm[m+1,0.95,0.2]-vm[m,0.95,0.2])*1/2],{k,0,2Pi,2Pi/28}]]],{m,0,3}]
}]

Show[{
ParametricPlot3D[sfera[u,v],{u,0,2Pi},{v,0,Pi/2},Mesh->None,PlotStyle->Opacity[0.5]],Table[ParametricPlot3D[sfera[u,k],{u,0,2Pi},PlotStyle->Thick],{k,{0,0.2,0.2+0.19,0.39+0.18,0.57+0.17,0.74+0.16}}],
Table[ParametricPlot3D[sfera[k,v],{v,0,0.90},PlotStyle->Thick],{k,0,2Pi,2Pi/28}]
}]

N[2Pi/28*Cos[0.2]]/N[2Pi/28]

%*0.2

N[2Pi/28*Cos[0.2]]/0.2

N[2Pi/28*Cos[0.39]]/0.19

N[2Pi/28]

N[2Pi/28*Cos[0.2]]

N[2Pi/28]-N[2Pi/28*Cos[0.2]]

Manipulate[Show[{
ParametricPlot3D[sfera[u,v],{u,0,2Pi},{v,0,Pi/2},Mesh->None,PlotStyle->Opacity[0.5]],Table[ParametricPlot3D[sfera[u,v],{u,0,2Pi},PlotStyle->Thick],{v,0,}],
Table[ParametricPlot3D[sfera[k,v],{v,0,0.88},PlotStyle->Thick],{k,0,2Pi,2Pi/28}]
}],{c,0.001,1}]

Manipulate[Show[{
ParametricPlot3D[sfera[u,v],{u,0,2Pi},{v,0,Pi/2},Mesh->None,PlotStyle->Opacity[0.5]],Table[ParametricPlot3D[sfera[u,k],{u,0,2Pi},PlotStyle->Thick],{k,0,passov,passov}],
Table[ParametricPlot3D[sfera[k,v],{v,-.001,passov},PlotStyle->Thick],{k,0,2Pi,2Pi/28}]
}],{passov,0.001,Pi/2},ControlPlacement->Right]

Manipulate[Show[{
ParametricPlot3D[sfera[u,v],{u,0,2Pi},{v,0,Pi/2},Mesh->None,PlotStyle->Opacity[0.5]],Table[ParametricPlot3D[sfera[u,k],{u,0,2Pi},PlotStyle->Thick],{k,0,m*Pi/18,Pi/18}],
Table[ParametricPlot3D[sfera[k,v],{v,-.001,m*Pi/18},PlotStyle->Thick],{k,0,2Pi,2Pi/n}]
}],{m,0,20,1},{n,1,50,1},ControlPlacement->Right]

Manipulate[Show[{
ParametricPlot3D[sfera[u,v],{u,0,2Pi},{v,0,Pi/2},Mesh->None,PlotStyle->Opacity[0.5]],Table[ParametricPlot3D[sfera[u,k],{u,0,2Pi},PlotStyle->Thick],{k,0,m*Pi/18,Pi/18}]
}],{m,0,20,1}]

Show[{
ParametricPlot3D[sfera[u,v],{u,0,2Pi},{v,0,Pi/2},Mesh->None,PlotStyle->Opacity[0.5]],Table[ParametricPlot3D[sfera[u,k],{u,0,2Pi},PlotStyle->Thick],{k,0,6*Pi/18,Pi/18}]
}]

Show[{
ParametricPlot3D[sfera[u,v],{u,0,2Pi},{v,0,Pi/2},Mesh->None,PlotStyle->Opacity[0.5]],Table[ParametricPlot3D[sfera[u,k],{u,0,2Pi},PlotStyle->Thick],{k,0,Pi/3,Pi/18}]
}]

Show[{
ParametricPlot3D[sfera[u,v],{u,0,2Pi},{v,0,Pi/2},Mesh->None,PlotStyle->Opacity[0.5]],Table[ParametricPlot3D[sfera[u,k],{u,0,2Pi},PlotStyle->Thick],{k,0,Pi/3,Pi/9}]
}]

Show[{
ParametricPlot3D[sfera[u,v],{u,0,2Pi},{v,0,Pi/2},Mesh->None,PlotStyle->Opacity[0.5]],ParametricPlot3D[sfera[u,0],{u,0,2Pi},PlotStyle->Thick],
ParametricPlot3D[sfera[u,Pi/9],{u,0,2Pi},PlotStyle->Thick]
}]

Show[{ParametricPlot3D[{Cos[v]Cos[u],Cos[v]Sin[u],Sin[v]},{u,0,2Pi},{v,0,Pi/2},Mesh->None,PlotStyle->Opacity[0.5]],ParametricPlot3D[Table[{Cos[v]Cos[u],Cos[v]Sin[u],Sin[v]}/.u->2k*Pi/24,{k,0,23}],{v,0,3Pi/8},PlotStyle->{Red,Thick}],ParametricPlot3D[Table[{Cos[v]Cos[u],Cos[v]Sin[u],Sin[v]}/.v->2k*Pi/16,{k,0,6}],{u,0,2Pi},PlotStyle->{Red,Thick}]},ImageSize->200,AspectRatio->Automatic]

Show[{ParametricPlot3D[{Cos[v]Cos[u],Cos[v]Sin[u],Sin[v]},{u,0,2Pi},{v,0,5Pi/12},Mesh->None,PlotStyle->Opacity[0.5]],ParametricPlot3D[Table[{Cos[v]Cos[u],Cos[v]Sin[u],Sin[v]}/.u->2k*Pi/24,{k,0,23}],{v,0,5Pi/12},PlotStyle->{Red,Thick}],ParametricPlot3D[Table[{Cos[v]Cos[u],Cos[v]Sin[u],Sin[v]}/.v->2k*Pi/24,{k,0,6}],{u,0,2Pi},PlotStyle->{Red,Thick}]},ImageSize->400,AspectRatio->Automatic]