Hypocycloid::usage="A hypocycloid is a curve drawn by a point P on the circle C of radius b when C rolls on the inside of a circle with center in O and radius a. References: Stewart, James. Cálculo de una variable. Trascendentes tempranas. Cengage LearningCengage: México, pp. 644, 645, 2012; Personal.";
In[]:=
Animatea=4;b=1;​​g1=Circle[{0,0},4];​​g2=Circle[{(a-b)Cos[θ],(a-b)Sin[θ]},b]/.θt1-0.01;​​g3=Point(a-b)Cos[θ]+bCos
a-b
b
θ,(a-b)Sin[θ]-bSin
a-b
b
θ/.θt1-0.01;​​g4=ParametricPlot(a-b)Cos[θ]+bCos
a-b
b
θ,(a-b)Sin[θ]-bSin
a-b
b
θ,{θ,0,t1},PlotStyleDashed,ColorFunction->"Aquamarine";​​​​Show[{g4,Graphics[{Red,Thick,PointSize[0.018],g3}],Graphics[{Black,g1}],Graphics[{Purple,Thick,g2}]},AxesTrue,AxesOrigin{0,0},BoxRatiosAutomatic,PerformanceGoal"Quality"],{t1,0.01,2π,0.1},AnimationRunningFalse
Out[]=
t1
In[]:=
ParametricPlot[{4
3
(Cos[θ])
,4
3
(Sin[θ])
},{θ,0,2π}]
Out[]=
Esta curva se llama hipocicloide de cuatro cúspides, o un astroide.