# Mathematical Experiment 11

 Draw the graphs of the first six Chebyshev polynomials in the interval  [-1,1].> m:=[cos(x),cos(n*x),x=0..Pi]; > plot({m\$n=1..6},axes=none); ¡@
 Draw this pretty leaf:> w:=1+cos(t)/2:z:=t/6-sin(2*t)/12:x:=w*cos(z):y:=w*sin(z): > plot([x,y,t=0..12*Pi],axes=none,scaling=constrained);
 Draw the graphs of the polynomials given by the binomial expansions > restart; > m:=[x,binomial(100,k)*x^(100-k)*(1-x)^k,x=0..1]: > plot({m\$k=0..100},axes=none); ¡@ ¡@
 Construct this pattern of the "sunflower": > r:=exp(t); > m:=64; > a:=plot([[r*cos(t+2*Pi*k/m),r*sin(t+2*Pi*k/m),t=3..5]\$k=1..m], scaling=constrained,color=red,axes=none): > b:=plot([[r*cos(t+2*Pi*k/m),-r*sin(t+2*Pi*k/m),t=3..5]\$k=1..m], scaling=constrained,color=blue,axes=none): > with(plots): > display(a,b); Reference: T. Cook: The Curves of Life. ¡@ ¡@
 Construct he graph given in polar coordinates by [0,4p]
 Construct this interesting drawing: > plot(2-cos(3*t)-cos(31*3*t/32),t=0..64*Pi,coords=polar, numpoints=1000,axes=none,scaling=constrained); Reference: William F. Rigge, Envelope Rosettes, Amer. Math. Monthly, (1920), p. 152.
 Draw this interesting pattern: > plot(2-cos(7*t)-cos(31*7*t/32),t=0..64*Pi,coords=polar, numpoints=1000,axes=none,scaling=constrained);
 Draw this interesting pattern: > plot(100+t+15*cos(3.05*t), t = 0 .. 200, coords = polar, axes = none,scaling=constrained); ¡@