Lösungen/Solutions/
B1S2Ue/Ex13

L = Lektion/ Leçon   -- Sprechstunde / heures de consultation
W = Work / Arbeit / Travail
A  =Anhang/  Annexe / Appendice

Ueb/Ex 1      W

Individuelle Lösung. • Solution individuelle.

1

p[n_] := 
      5 {Re[E^(I ((n - 1) 2  Pi/8) + Pi/8)],  
            Im[E^(I ((n - 1) 2  Pi/8) + Pi/8)], 
            Floor[n/9] (Sqrt[5] - 1)/2}/((Sqrt[5] - 1)/
              2)

tab31 = Table[p[k], {k, 1, 16}] // N

tab21 = 
      Table[{p[k][[1]], p[k][[2]]}, {k, 1, 8}] // 
        N

mp21 = Join[{PointSize[0.02]}, Map[Point, tab21]]

v[t_] := t (p[3] - p[6]) + p[3]; 
solv1 = Solve[v[t][[2]] == 0, {t}] // Flatten

s = {v[t][[1]], v[t][[2]], 10 (Sqrt[5] - 1)/2} /. 
          solv1  // N

mp22 = Join[mp21, {Point[{s[[1]], s[[2]]}]}]

Show[Graphics[mp22], AspectRatio -> Automatic];

tab32 = 
      Join[Table[{Re[(p[k][[1]] + 
                      I p[k][[2]]) E^(I 10/320 2  Pi)], 
              Im[(p[k][[1]] + 
                      I p[k][[2]]) E^(I 10/320 2  Pi)], p[
                  k][[3]]}, {k, 1, 
              16}], 
{{Re[(s[[1]] + 
                      I s[[2]]) E^(I 10/320 2  Pi)], 
              Im[(s[[1]] + I s[[2]]) E^(I 10/320 2  Pi)], 
              s[[3]]}}] // N

mp31 = Join[{PointSize[0.02]}, Map[Point, tab32]]

Show[Graphics3D[mp31], AspectRatio -> Automatic];

pp[k_] := tab32[[k]]

tab33 = 
      Join[Table[{pp[k][[1]], 
              Re[(p[k][[2]] + 
                      I p[k][[3]]) E^(I 14/320 2  Pi)], 
              Im[(p[k][[2]] + 
                      I p[k][[3]]) E^(I 14/320 2  
                        Pi)]}, {k, 1, Length[tab32]}]] // N

pp1[k_] := tab33[[k]]

mp32 = Join[{PointSize[0.02]}, Map[Point, tab33]]

Show[Graphics3D[mp32], AspectRatio -> Automatic];

li1 = 
      Table[Line[{pp1[1 + Mod[k,  8]], pp1[1 + Mod[k + 1, 8]]}], {k, 1, 
          8}]

li2 = 
      Table[Line[{pp1[9 + Mod[k, 8]], pp1[9 + Mod[k + 1, 8]]}], {k, 1, 
          8}]

li3 = 
      Table[Line[{pp1[1 + Mod[k,  8]], pp1[9 + Mod[k, 8]]}], {k, 1, 
          8}]

li4 = 
      Table[Line[{pp1[9 + Mod[k,  8]], pp1[17]}], {k, 1, 8}]

mp33 = Join[mp32, li1, li2, li3, li4]

Show[Graphics3D[mp33], AspectRatio -> Automatic];

Show[Graphics3D[mp33], ViewPoint -> {1.580,  2.700,  -1.240}, 
        AspectRatio -> Automatic];