\input mftmac
\medskip
$\5{mode\_setup};\ \5{screenstrokes};\ \2{path}p[],\2{stardot};\ p_{1}:=(0,10)%
\8{--}(2,2)\8{--}(10,0);$\par
$\2{def}\5{cc}=\5{clearit};\ \5{showit};\3{enddef};$\par
$\2{for}i=2,3,4\?:$\par
\quad$p[i]=p[i-1]\6{rotated}90;$\par
$\!\3{endfor};$\par
$\9The end of one curve must be the start of the next.\par
$p_{5}:=p_{4}\AM p_{3}\AM p_{2}\AM p_{1}\8{..}\1{cycle};$\par
\BL
$\2{fill}p_{5}\6{scaled}4\6{shifted}(50,50);$\par
$\2{fill}p_{5}\6{shifted}(50,50)\6{scaled}4;$\par
$\\{sscreen}(50\\{pt}\SH ,30\\{pt}\SH ,1\\{pt}\SH ,2);$\par
\BL
\font\stardot=stardot scaled 1440
\medskip\centerline{\stardot A}\medskip
\noindent These two aren't the same! Unlike Greek geometry, our
geometry does not take place `in' a void; rather, transformations
are done with reference to a coordinate
system.\footnote{${}^1$}{Just as our lives in Christ
should be ordered by the fundamental coordinate system: ``Take up your
cross and follow me.''} The first takes
$(2,2)\mapsto(8,8)\mapsto(58,58)$ while the second takes
$(2,2)\mapsto(52,52)\mapsto(208,208)$.

Now we can define:
\BL
$\2{stardot}:=p_{5}\6{scaled}.1;\ \5{cc};$\par
$\2{fill}\2{stardot}\6{scaled}30\6{shifted}(100,100);$\par
\BL
The -{}- operators above can't (unless we change p5 to
{\tt p5:=p4..p3..p2..p1..cycle;}) be replaced with -{}-{}- as
the following example shows:
\BL
$\2{pickup}\5{pencircle}\6{scaled}.1\\{pt};$\par
$\2{numeric}x,y;\ \2{path}p[];$\par
\BL
$z_{1}=(0,10);\ z_{2}=(2,2);\ z_{3}=(10,0);\ z_{4}=(2,-2);\ z_{5}=(0,-10);$\par
$z_{6}=(-2,-2);\ z_{7}=(-10,0);\ z_{8}=(-2,2);$\par
\BL
$p_{1}:=z_{1}\8{---}z_{2}\8{---}z_{3}\8{---}z_{4}\8{---}z_{5}\8{---}z_{6}%
\8{---}z_{7}\8{---}z_{8}\8{---}\1{cycle};$\par
$p_{2}:=z_{1}\8{---}z_{2}\8{---}z_{3}\AM z_{3}\8{---}z_{4}\8{---}z_{5}\AM z_{5}%
\8{---}z_{6}\8{---}z_{7}\AM z_{7}\8{---}z_{8}\8{---}\1{cycle};$\par
\BL
$\2{fill}p_{1}\6{scaled}5;$\par
$\2{message}\7"p1 scaled 5";\ \2{show}\\{currentpicture};\ \5{cc};$\par
$\2{fill}p_{2}\6{scaled}3;$\par
$\2{message}\7"p2 scaled 3";\ \2{show}\\{currentpicture};$\par
$\2{fill}p_{1}\6{scaled}5;$\par
$\\{sscreen}(50\\{pt}\SH ,20\\{pt}\SH ,1\\{pt}\SH ,2);$\par
\medskip\centerline{\stardot B}\medskip
\BL
\quad$\9Surprising, yes?\par
$\!\3{end};$\par
