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This is my first time evaluating Mathematica to study differential geometry (Curves and Geometry by Alfred Gray) before I consider buying the Mathematica cloud version. I simply wish to plot a cycloid

cycloid[a_,b_][t_] := {a t - b Sin[t], a - b Cos[t]};
α = cycloid[1, 1];
ParametricPlot[α[t], {t, -3 π, 3 π}, 
  PlotRange->{{-3 π, 3 π} {-2, 4}}, Ticks -> None]

However, it outputs a blank as shown

enter image description here

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  • $\begingroup$ ...and where is the definition of cycloid? $\endgroup$ – J. M.'s ennui Feb 15 at 12:20
  • $\begingroup$ @J.M. sorry I omitted a line. It is edited. $\endgroup$ – user9106985 Feb 15 at 12:26
  • $\begingroup$ Use := for the definition of cycloid, and = for the definition of α. $\endgroup$ – J. M.'s ennui Feb 15 at 12:29
  • $\begingroup$ Same issue. I have edited it again. $\endgroup$ – user9106985 Feb 15 at 12:36
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    $\begingroup$ @user9106985 Missing , in PlotRange definition! $\endgroup$ – Ulrich Neumann Feb 15 at 12:44
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Try this particular set first:

a = 2; b = 1; cycloid[ t_] := {a  t - b Sin[t], a - b Cos[t]};
ParametricPlot[
  cycloid[t], {t, -3 π, 3 π}, PlotRange -> All, 
  GridLines -> Automatic, PlotStyle -> {Thick, Red}, 
  AspectRatio -> 0.2
]
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