Mathematica and fun!

Usefull.nb

(*So sometimes I just want to show something very fast and I want for mathematica to do it for me, so after tryng very hard I came up with this*)
(*Previews and evalueates an expression*)
preview[x_] := 
 TraditionalForm[
  Row[{TraditionalForm[HoldForm[x]], "=", 
    x}]]; SetAttributes[preview, HoldFirst]
    
   
a = {6, 3, 0};
b = {9, 6, 0};
c = {9, 3, 3};
d = {6, 6, 3};
points = {{"a", a}, {"b", b}, {"c", c}, {"d", d}};
Print[preview[a]]; Print[preview[b]];
Print[preview[c]]; Print[preview[d]];
Print[Show[
  Graphics3D[{Red, PointSize[0.06], Point[Map[#[[2]] &, points]]}], 
  Graphics3D[{Gray, 
    Text[Style[#[[1]], Bold, FontSize -> 18], 1 #[[2]]] & /@ points}],
   Graphics3D@Line[{{a, b}, {b, c}, {c, d}, {d, a}, {d, b}, {a, c}}], 
  Boxed -> False]]
Print["Versuch der schewerpunkt ABC zu finden"]
Print[Row[{preview[e = (a + b)/2], 
    " Das ist Mittelpunkt von AB, Ich nenne es punkt e"}]];
points = {{"a", a}, {"b", b}, {"c", c}, {"d", d}, {"e", e}}; Print[
 Show[Graphics3D[{Red, PointSize[0.06], 
    Point[Map[#[[2]] &, points]]}], 
  Graphics3D[{Gray, 
    Text[Style[#[[1]], Bold, FontSize -> 18], 1 #[[2]]] & /@ points}],
   Graphics3D@Line[{{a, b}, {b, c}, {c, d}, {d, a}, {d, b}, {a, c}}], 
  Boxed -> False]]
Print[Row[{preview[e + \[Lambda] (c - e)], " Das ist Gerade EC"}]]
Print[Show[
  Graphics3D[{Red, PointSize[0.06], Point[Map[#[[2]] &, points]]}], 
  Graphics3D[{Gray, 
    Text[Style[#[[1]], Bold, FontSize -> 18], 1 #[[2]]] & /@ points}],
   Graphics3D@
   Line[{{a, b}, {b, c}, {c, d}, {d, a}, {d, b}, {a, c}, {e, c}}], 
  Boxed -> False]]
Print[Row[{preview[S1 = (c - e)*1/3 + e], 
   " Das ist der schwerpunkt von ABC, weil \[Lambda]=1/3 von EC der \
Schwerpunkt sein musst, ich nenne es S1"}]]
points = {{"a", a}, {"b", b}, {"c", c}, {"d", d}, {"e", e}, {"S1", 
    S1}};
Print[Show[
  Graphics3D[{Red, PointSize[0.06], Point[Map[#[[2]] &, points]]}], 
  Graphics3D[{Gray, 
    Text[Style[#[[1]], Bold, FontSize -> 18], 1 #[[2]]] & /@ points}],
   Graphics3D@
   Line[{{a, b}, {b, c}, {c, d}, {d, a}, {d, b}, {a, c}, {e, c}}], 
  Boxed -> False]]
Print["Versuch der schewerpunkt BCD zu finden"]
Print[Row[{preview[f = (b + c)/2], 
    " Das ist Mittelpunkt von BC, Ich nenne es punkt f"}]];
Print[Row[{preview[f + \[Lambda] (d - f)], " Das ist Gerade FD"}]]
Print[Row[{preview[S2 = (d - f)*1/3 + f], 
   " Das ist der schwerpunkt von BCD, weil \[Lambda]=1/3 von FD der \
Schwerpunkt sein musst, ich nenne es S2"}]]
points = {{"a", a}, {"b", b}, {"c", c}, {"d", d}, {"S1", S1}, {"S2", 
    S2}, {"e", e}, {"f", f}};
Print[Show[
  Graphics3D[{Red, PointSize[0.06], Point[Map[#[[2]] &, points]]}], 
  Graphics3D[{Gray, 
    Text[Style[#[[1]], Bold, FontSize -> 18], 1 #[[2]]] & /@ points}],
   Graphics3D@
   Line[{{a, b}, {b, c}, {c, d}, {d, a}, {d, b}, {a, c}, {e, c}, {f, 
      d}}], Boxed -> False]]
Print[Row[{TraditionalForm[
    HoldForm[S1 + \[Lambda] (d - S1) == S2 + \[Lambda] (a - S2)]], 
   "Der Schnittpunkt zwischen S1d und S2a ist der Schwerpunkt des \
Tetraeder"}]]
Print["Schwerpunkt ist {7.5,4.5,1.5} weil \[Lambda]=0.25, ich nenne \
es p"]
p = {7.5, 4.5, 1.5}
points = {{"a", a}, {"b", b}, {"c", c}, {"d", d}, {"S1", S1}, {"S2", 
    S2}, {"p", p}};
Print[Show[
  Graphics3D[{Red, PointSize[0.06], Point[Map[#[[2]] &, points]]}], 
  Graphics3D[{Gray, 
    Text[Style[#[[1]], Bold, FontSize -> 18], 1 #[[2]]] & /@ points}],
   Graphics3D@
   Line[{{a, b}, {b, c}, {c, d}, {d, a}, {d, b}, {a, c}, {S1, d}, {S2,
       a}}], Boxed -> False]]