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{SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT 256 8 "Cycloids" }}{PARA 256 "
" 0 "" {TEXT -1 21 "Math 151, Spring 2002" }}{PARA 256 "" 0 "" {TEXT 
-1 11 "J. Gerlach " }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT 257 15 "Regular Cycloid" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 137 "r
estart;\nr := 1: N := 1.5:\nx := t - r*sin(t/r):\ny := r - r*cos(t/r):
\nplot([x,y,t=0..2*N*Pi],color=blue, thickness=2,scaling=constrained);
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 
0 "" {TEXT 258 11 "Hypocycloid" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 217 "
restart;\nR := 1: r := R/7: N:=3:\nx := (R-r)*cos(t) + r*cos((R-r)*t/r
):\ny := (R-r)*sin(t) - r*sin((R-r)*t/r):\nplot([[x,y,t=0..2*N*Pi],[R*
cos(t),R*sin(t),t=0..2*Pi]],color=[blue,black], thickness=2,scaling=co
nstrained);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT 259 10 "Epicycloid" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 218 "restart;\nR := 1: r := R/3: N:= 3:\nx := (R+r)*cos(t
) - r*cos((R+r)*t/r):\ny := (R+r)*sin(t) - r*sin((R+r)*t/r):\nplot([[x
,y,t=0..2*N*Pi],[R*cos(t),R*sin(t),t=0..2*Pi]],color=[blue,black], thi
ckness=2,scaling=constrained);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 260 60 "Amusement Park Ride\n
Not a cycloid, yet an interesting orbit." }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 207 "restart;\nR := 1: r := R/3: a :=12:  N:= 1:\nx := R*
cos(t) + r*cos(a*t):\ny := R*sin(t) + r*sin(a*t):\nplot([[x,y,t=0..2*N
*Pi],[R*cos(t),R*sin(t),t=0..2*Pi]],color=[blue,black], thickness=2,sc
aling=constrained);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
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