Minimalist:
k[t_] := KnotData[{3, 1}, "SpaceCurve"][t];
lenlen[r_] := N@Integrate[Total[D[k[t], t]^2], {t, 0, 2 Pir}];
pts[n_] := Solve[Integrate[Total[D[k[t], t]^2], {t, 0, t1}]Solve[len[t1] == lenlen[2 Pi] #/n , t1, Reals] & /@ Range[n];Range[n + 1];
k[t1]
Graphics3D@Tube[k[t1] /. # & /@ (Flatten@pts@30), .1]
Minimalist:
k[t_] := KnotData[{3, 1}, "SpaceCurve"][t];
len = N@Integrate[Total[D[k[t], t]^2], {t, 0, 2 Pi}];
pts[n_] := Solve[Integrate[Total[D[k[t], t]^2], {t, 0, t1}] == len #/n ,t1,Reals] & /@ Range[n];
k[t1] /. # & /@ (Flatten@pts@30)
Minimalist:
k[t_] := KnotData[{3, 1}, "SpaceCurve"][t];
len[r_] := N@Integrate[Total[D[k[t], t]^2], {t, 0, r}];
pts[n_] := Solve[len[t1] == len[2 Pi] #/n, t1, Reals] & /@ Range[n + 1];
Graphics3D@Tube[k[t1] /. # & /@ (Flatten@pts@30), .1]