%\input amstex
%\documentstyle{amsppt}
\magnification=\magstep2
\vsize=260truemm \hsize=150truemm\voffset=-15truemm
\footline{\hfil}


\input spline.sty
\def\whitemark#1{{\PSmarkradius=0.75\PSmarkradius
\PS{gsave 1 setgray}\PSmark{#1}\PS{grestore}}}

%For use in Philip's section
\def\biglines{\setPSlinewidth{1pt}}
\def\normallines{\setPSlinewidth{0.5pt}}
\def\LL{\biglines\PSline{2 1 14 1 14 5 10 5 10 3}\normallines}
\def\GG{\biglines\PSline{2 -1 14 -1 14 -5 10 -5 10 -3}\normallines}
\def\Gg{\biglines\PSline{2.3 -1 10 -1 10 -3.5 8 -3.5 8 -2}\normallines}

%You may try out other possibilities:
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%\def\GG{\biglines\spline{2 -1 14 -1 14 -5 10 -5 10 -3}\normallines}
%\def\Gg{\biglines\spline{2.3 -1 10 -1 10 -3.5 8 -3.5 8 -2}\normallines}




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%Fist do #1, setting the \PSunit
 #1\relax
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\line{\hss\vrule\PSpicture{#2}{#3}#4\endPSpicture\vrule}%
\hrule
}


%%%%%%%%%%%%%%%%%%%%%%%%%%  Figs  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\Fig abrahams-1
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\llcoords{-1 -1}
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\PScircle{0 0 1}\setPSlinewidth{2\PSlinewidth}
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\PScline{
 1        0
 0.8660   0.5
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-0.5      0.8660
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-0.8660  -0.5
-0.5 -0.8660
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0.5      -0.8660
0.8660   -0.5
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\Fig abrahams-2
%AT \PSunit=17truemm \PSpicture{3,5\PSunit}{3\PSunit}
\PSunit=17truemm \PSpicture{3,56\PSunit}{2.7\PSunit} \llcoords{-1.2 -1.2}
\setPSlinewidth{0.5\PSlinewidth}
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\LTX{$O$}{-0.1 -0.2}
\LTX{$(x,0)$}{0.9 -0.2}\LTX{$=B$}{0.8 -0.45}
\putPSmarks
 %35 degrees
\PSline{0 0 0.8192 0.5736 0.8192 0}\PSline{0.8192 0.5736 1 0}
\endPSpicture

\Fig abrahams-3
\PSunit=17truemm \PSpicture{8\PSunit}{2.75\PSunit}
\llcoords{-1 -1.7}
\putPSmarks
%left circle
\setPSlinewidth{0.5\PSlinewidth}
\PScircle{0 0 1.01}\setPSlinewidth{2\PSlinewidth}
\PScline{
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-0.8660  -0.5
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\setdash{4\PSlinewidth}
\PScline{
 0.8660   0.5
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-0.8660   0.5
-0.8660  -0.5
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%center circle
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%right circle
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\endPSpicture

\Fig abrahams-4
\PSunit=20truemm \PSpicture{2\PSunit}{2\PSunit}
\llcoords{-1 -1}
\setPSlinewidth{0.5\PSlinewidth}
\PScircle{0 0 1}\setPSlinewidth{2\PSlinewidth}
\PSline{% cos 22,5 = 0.9293
 0.9239  -0.3827
 0.9239   0.3827
 0.3827   0.9239
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 %9239*0,7071=6.532,89
 \PSline{0 0 0.6533 0.6533}
\PSline{0.6033 0.6033 0.5533 0.6533 0.6033 0.7033}
\PSmark{0 0}\CTX{$O$}{0 -0.2}\RTX{$d_m$}{0.3 0.25}
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\PSline{
 0.3827   0.9239
 0        0.9239
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\PSline{
 0.6533  -0.6533
 0.9239  -0.3827
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\endPSpicture

\Fig arkeryd1-1
\PSunit=1,25truemm
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%AT \PSpicture{107\PSunit}{10\PSunit}
\PSpicture{107\PSunit}{7\PSunit}
\def\markbox{\hss\vrule height 2\PSunit depth 2\PSunit
     width \PSlinewidth \hss}
\llcoords{0 -6}
\PSarrow{0 0 107 0}
\TeXmark{21 0 45 0 58 0 73 0 80 0}
\CTX{$0$}{21 -4}
\CTX{$x_1$}{45 -4}\CTX{$x_2$}{58 -4}\CTX{$x_3$}{73 -4}\CTX{$x_4$}{80
-4}
\endPSpicture

\Fig arkeryd1-2
\PSunit=1,25truemm
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\PSpicture{120\PSunit}{25\PSunit}
\llcoords{-1 -5}
\PSarrow{0 0 0 20}\RTX{$\,\rho$}{0 19}
\PSarrow{0 0 33 0}\RTX{$\,\,x$}{33 0}
\CTX{$X$}{24 -3}\CTX{$N$}{12 6}
\PSline{0 13 24 13 24 0}
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\llcoords{-42 -5}
\PSarrow{0 0 0 20}\RTX{$\,\rho$}{0 19}
\PSarrow{0 0 33 0}\RTX{$\,\,x$}{33 0}
\CTX{$X$}{24 -3}\CTX{$N$}{12 6}
\PSline{0 6 5 6 5 10 9 10 9 13 15 13 15 4 20 4 20 8 24 8 24 0}
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\PSarrow{0 0 0 20}\RTX{$\,\rho$}{0 19}
\PSarrow{0 0 33 0}\RTX{$\,\,x$}{33 0}
\CTX{$X$}{24 -3}\CTX{$N$}{12 6}
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\Fig arkeryd1-3
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%AT \PSpicture{45\PSunit}{16\PSunit}
\PSpicture{45\PSunit}{19\PSunit}
\llcoords{-1 -5}
\PSarrow{0 0 0 12}\RTX{$\,q$}{0 12}
\PSarrow{0 0 39 0}\RTX{$\rho$}{41 0}
\RTX{$\rho_{\max}$}{21 -3}
\dspline{-1 -3 0 0 10 8 22 0 24 -2}
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\Fig arkeryd1-4
\PSunit=1,25truemm
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%AT \PSpicture{45\PSunit}{20\PSunit}
\PSpicture{45\PSunit}{25\PSunit}
\llcoords{-1 -4}
\PSarrow{0 0 0 19}\RTX{$\,\frac{dq}{d\rho}$}{1 18}
\PSarrow{0 0 39 0}\RTX{$\rho$}{41 0}
\RTX{$\rho_{\max}$}{21 4}
\PSline{22 -1 22 1}
\spline{0 7 2 5 6 4.5 8 2.5 10 2 12 1.5 14 0.5 16 -1.5 18 -2 20 -3.5  22 -4}
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\Fig bjoerner-01
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%AT \PSpicture{30\PSunit}{43\PSunit}
\PSpicture{30\PSunit}{41\PSunit}
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\PSline{5 32 11.5 40 18 32} 
\PSline{14 24 18 32 25 24}  
\PSline{5 16 10 24 15 16}   
\PSline{20 16 25 24 30 16}  
\PSline{15 8 20 16 25 8}    
\PSline{20 0 25 8 30 0}     
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\whitemark{0 24 5 32 10 24}    
\whitemark{5 32 11.5 40 18 32} 
\whitemark{14 24 18 32 25 24}  
\whitemark{5 16 10 24 15 16}   
\whitemark{20 16 25 24 30 16}  
\whitemark{15 8 20 16 25 8}    
\whitemark{20 0 25 8 30 0}     
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\Fig bjoerner-02
\PSunit=1,25truemm
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\PSpicture{65\PSunit}{16\PSunit}
\PSmarkradius=1truemm
\putPSmarks
\PSline{0 0 6 8 12 0}
\PSline{6 8 12 16 18 8}
\whitemark{0 0 6 8 12 0}
\whitemark{6 8 12 16 18 8}
\llcoords{-47 0}
\PSline{0 8 6 16 12 8}
\PSline{6 0 12 8 18 0}
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 \whitemark{6 0 12 8 18 0}
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\endPSpicture

\Fig bjoerner-03
\PSunit=1,25truemm
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\PSpicture{82\PSunit}{30\PSunit}
\PSmarkradius=1truemm
\putPSmarks
\llcoords{0 -4}
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\whitemark{5 8 12 16 19 8}
\whitemark{14 0 19 8 24 0}\CTX{5}{14 -3}\CTX{7}{24 -3}
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\endPSpicture

\Fig bjoerner-04
\PSunit=1,25truemm
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\PSpicture{16\PSunit}{17\PSunit}
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\llcoords{-2 -6}
\putPSmarks
\PSline{0 0 6 8 12 0}\CTX{$w_1$}{0 -3}\CTX{$w_2$}{12 -3}
\whitemark{0 0 6 8 12 0}
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\Fig bjoerner-05
\PSunit=1,25truemm
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\PSpicture{50\PSunit}{7\PSunit}
\PSmarkradius=1truemm
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\Fig bjoerner-06
\PSunit=1,25truemm
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\PSpicture{50\PSunit}{14\PSunit}
\PSmarkradius=1truemm
\llcoords{-1 -6}
\putPSmarks\PSline{0 0 6 6 12 0}
\PSmark{24 0 36 0 48 0}
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\RTX{5}{7.5 6}
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\Fig bjoerner-07
\PSunit=1,25truemm
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\PSpicture{50\PSunit}{20\PSunit}
\PSmarkradius=1truemm
\llcoords{-1 -6}
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\whitemark{0 0 6 6 12 0 12 12 18 6 36 6 48 6}
\RTX{5}{18 3}
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\RTX{10}{14 12}
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\Fig bjoerner-08
\PSunit=1,25truemm
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\PSpicture{50\PSunit}{20\PSunit}
\PSmarkradius=1truemm
\llcoords{-1 -6}
\putPSmarks\PSline{0 0 6 6 12 0}\PSline{6 6 12 12 18 6}
\PSline{36 6 42 12 48 6}
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\RTX{5}{18 3}
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\RTX{10}{14 12}\RTX{14}{44 12}
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\Fig bjoerner-09
\PSunit=1,25truemm
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\PSpicture{50\PSunit}{24\PSunit}
\PSmarkradius=1truemm
\llcoords{-1 -6}
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\PSline{0 0 6 6 12 0}
\PSline{6 6 12 12 16 6}
\PSline{12 12 18 18 24 12}
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\RTX{5}{16 3}
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\Fig bjoerner-10
\PSunit=1,25truemm
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%AT \PSpicture{72\PSunit}{38\PSunit}
\PSpicture{72\PSunit}{40\PSunit}
\PSmarkradius=1truemm
\llcoords{-1 -6}
\putPSmarks
\PSline{0 0 6 6 12 0}
\PSline{6 6 12 12 24 0}
\PSline{12 12 28 28 56 0}
\PSline{28 28 34 34 50 18}
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\PSline{38 6 50 18 68 0}
%
\whitemark{0 0 6 6 12 0}
\whitemark{6 6 12 12 24 0}
\whitemark{12 12 28 28 56 0}
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\whitemark{32 0 38 6 44 0}
\whitemark{38 6 50 18 68 0}
%
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\Fig bjoerner-11
\PSunit=1,25truemm
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\PSpicture{20\PSunit}{20\PSunit}
\PSmarkradius=1truemm
\llcoords{-1 -1}
\putPSmarks
\PSline{0 6 6 12 12 6}
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\CTX{1}{12 9}\CTX{1}{18 3}\CTX{1}{18 15}
\endPSpicture

\Fig bjoerner-12
\PSunit=1,25truemm
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\PSpicture{60\PSunit}{34\PSunit}
\PSmarkradius=1truemm
\llcoords{-1 -6}
\putPSmarks
\PSline{0 0 6 6 12 0}
\PSline{6 6 12 12 24 0}
\PSline{12 12 28 28 56 0}
%\PSline{28 28 34 34 50 18}
\PSline{12 12 22 22 38 6}
\PSline{32 0 38 6 44 0}
%\PSline{38 6 50 18 68 0}
%
\whitemark{0 0 6 6 12 0}
\whitemark{6 6 12 12 24 0}
\whitemark{12 12 28 28 56 0}
%\whitemark{28 28 34 34 50 18}
\whitemark{12 12 22 22 38 6}
\whitemark{32 0 38 6 44 0}
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%
\RTX{35}{40 6}
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\Fig carles1-1
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%TRUESIZE 
%AT \PSpicture{60\PSunit}{32\PSunit}
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\llcoords{-30 -13}
\PSline{-30 0 30 0}\PSline{0 -13 0 21}
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 15 -10 17.5 -20}
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\TeXmark{-16 1 16 1}
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\Fig carles1-2
\PSunit=1,4truemm
\def\markbox{\hss\vrule height 2\PSunit depth 0\PSunit
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 %TRUESIZE 
\PSpicture{76\PSunit}{52\PSunit}
% y=30-x^2/60
% x_0=12
% x_1=30-12*12/60=27,60
% x_2=30-27,6*27,6/60=17,30
% x_3=30-17,3*17,3/60=25,01 y=30-25,01*25,01/60=19,57
% xmax=35 y=30-35*35/60=9,58
% x=31, y=30-31*31/60=13,98
% x=21, y=30-21*21/60=22,65
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27.6 27.6
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35 9.58
31 13.98
27.60 17.3 
25.01 19.57
21 22.65
17.3 25.01
12 27.60
0 30 
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-21 22.65
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\RTX{$\,F$}{20 19.5}
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\Fig cegrell-1
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\llcoords{-35  -12}
\PSline{-35 0 44 0}\RTX{$\,x$}{44 0}
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\RTX{$y=f(x)$}{2 25}
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\RTX{$I={[}a,b{[}$}{3 -8}
\PSline{-16 36 -12 18 0 9 27 9}
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\endPSpicture

\Fig dunkels-1
\PSunit=1,25truemm
\PSpicture{6\PSunit}{10\PSunit}
\llcoords{60 32}
\putPSmarks
\PSline{60 32 66.2 42.5}
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\Fig dunkels-2
\PSunit=1,25truemm
\PSpicture{100\PSunit}{40\PSunit}
\llcoords{0 -8}
\CTX{Fig 2.}{50 -6}
\PScline{0 0 48 0 48 32 0 32}
\RTX{PYTHAGORAS' SATS}{3 29}
\RTX{$a^2+b^2=c^2$}{3 24}
\PScline{11 8 35 8 35 23}
\PSline{33.5 8 33.5 9.5 35 9.5}
\CTX{$a$}{23 6}\RTX{$\,b$}{35 15.5}\LTX{$c\,$}{23 17}
%
%
\llcoords{-52 -8}
\PScline{0 0 48 0 48 32 0 32}
\RTX{TAXI-PYTHAGORAS'}{3 29}
\RTX{SATS}{3 25}
\RTX{$a+b=c$}{3 21}
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\Fig dunkels-3
\PSunit=1,1truemm
\PSpicture{75\PSunit}{50\PSunit}
\llcoords{-14 -17}
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\putPSmarks
\PScline{0 0 24 6 12 18}
%
%
% sqrt 12^2+12^2=16.97
% sqrt 12^2+18^2=21,63    arctan 2/3=33.7 deg + 270 = 303.7
% sqrt 24^2+6^2=24.74     arctan 4/1=75.9 deg + 90 = 165.9
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%
%
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\llcoords{-20 -9}\PSline{0 0 0 40}
\llcoords{-26 -9}\PSline{0 0 0 40}
\llcoords{-32 -9}\PSline{0 0 0 40}
\llcoords{-38 -9}\PSline{0 0 0 40}
\llcoords{-44 -9}\PSline{0 0 0 40}
\llcoords{-50 -9}\PSline{0 0 0 40}
\llcoords{0 -11}\PSline{0 0 52 0}
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\llcoords{0 -35}\PSline{0 0 52 0}
\llcoords{0 -41}\PSline{0 0 52 0}
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\Fig dunkels-4
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\llcoords{0 -27}
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\PSmark{20 0}
\PScline{0 0 20 -20 40 0 20 20}
\PSline{5 5 20 0}\RTX{$A$}{20 -1}
\rotateRTX{18.45}{$\overbrace{\hskip15.81\PSunit}$\hss}{5 5}
\RTX{$5$}{12.5 7}
\RTX{Taxi-cirkel}{43 13}
\dspline{30 10 35 15 41 15 46 20}
\PSarrow{35 15 30 10}
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\Fig dunkels-5
\PSunit=1,25truemm
%AT \PSpicture{60\PSunit}{55\PSunit}
\PSpicture{60\PSunit}{50\PSunit}
\llcoords{-11 -15}
\CTX{Fig 5.}{30 -12}
\PSarrow{-11 0 45 0}\RTX{$\,x$}{45 0}
\PSarrow{0 -12 0 30}\RTX{$y$}{1 32}
\def\markbox{\hss\vrule height 2truemm\hss}
\TeXmark{5 0 10 0 15 0 20 0 25 0 30 0 35 0 40 0}
\def\markbox{\hss\vrule height 0.2pt width 2truemm\hss}
\TeXmark{0 5 0 10 0 15 0 20 0 25}
\PSline{-10 15 0 25 30 -5 45 10}
\PSmark{0 0 5 20 15 10 25 0 30 20}
\CTX{$P$}{5 17}\CTX{$G$}{15 13}\CTX{$Q$}{25 -3}
\RTX{$\,(0,0)$}{0 -2.5}\RTX{$(3,2)$}{17 10}
\RTX{$(6,4)$}{31 20}
\PSline{0 0 30 20}\PSline{5 20 17 32}\PSline{13 -12 25 0}
\endPSpicture

\Fig dunkels-6
\PSunit=1,25truemm
\PSpicture{75\PSunit}{50\PSunit}
\llcoords{-5 -15}
\CTX{Fig 6.}{40 -12}
\PSarrow{-5 0 38 0}\RTX{$\,x$}{38 0}
\PSarrow{0 -10 0 30}\LTX{$y$}{-1 32}
\def\markbox{\hss\vrule height 2truemm\hss}
\TeXmark{5 0 10 0 15 0 20 0 30 0}
\def\markbox{\hss\vrule height 0.2pt width 2truemm\hss}
\TeXmark{0 -5 0 5 0 10 0 15 0 20}
\PSline{5 25 5 20 25 0 25 -6}
\PSmark{0 0 30 20}\LTX{$O\,$}{0 -2}\RTX{$\,S$}{30 20}
\RTX{Taxi-mittpunktsnormalen}{42 25}
\RTX{till str\"ackan $OS$}{46 21}
\PSline{0 0 30 20}
\PSarrow{13 23 7 23}\dspline{7 23 13 23 15 25 21 25}
\PSline{15 25 40 25}
%\PSarrow{30 13 22 5}\dspline{22 5 30 13 25 13 33 21}
\PSarrow{34 10 26 2}\dspline{26 2 34 10 29 10 37 18}
\PSline{29 10 42 23}
\setdash{5\PSlinewidth}\PSline{5 25 5 32}\PSline{25 -6 25 -12}
\endPSpicture

\Fig dunkels-7
\PSunit=1,25truemm
\PSpicture{62\PSunit}{40\PSunit}
\llcoords{-6 -12}
\CTX{Fig 7.}{30 -9}
\PSarrow{-5 0 50 0}\RTX{$\,x$}{50 0}
\PSarrow{0 -3 0 25}\LTX{$y$}{-1 25}
\llcoords{-9 -15}
\putPSmarks\PSline{12 20 30 8}\nomarks
\RTX{$P_1=(x_1,y_1)$}{11 23}\RTX{$P_2=(x_2,y_2)$}{31 8}
\LTX{$\ssize|y_1-y_2|$}{9 14}
\LTX{$\left\{\vrule height 7\PSunit width 0pt\right.$}{12 14}
\CTX{$\ssize|x_1-x_2|$}{21 3}
\CTX{$\underbrace{\hskip18\PSunit}$}{21 6}
\RTX{$\ssize|x_1-x_2|+|y_1-y_2|$}{23 17}
%DOESN'T WORK:
%\rotateRTX{3 2 div atan}{$\overbrace{\hskip 21.63\PSunit}$}{13 21}
%
\rotateRTX{33.7}{$\overbrace{\hskip 21.63\PSunit}$}{13 21}
\setdash{5\PSlinewidth}\PSline{12 20 12 8 30 8}
\endPSpicture

\Fig dunkels-8
\PSunit=1,25truemm
%AT \PSpicture{55\PSunit}{50\PSunit}
\PSpicture{57\PSunit}{56\PSunit}
\llcoords{-30 -30}
\CTX{Fig 8.}{0 -28}\LTX{$O\,$}{0 -2}\CTX{$P$}{8 15}
\PSarrow{-23 0 26 0}\PSarrow{0 -22 0 26}
\putPSmarks\PScline{-20 0 0 -20 20 0 0 20}\nomarks
\PSmark{0 0 8 12}
\LTX{$({-}1,0)$}{-18 -4}\RTX{$(1,0)$}{18 -4}
\RTX{$\,(0,1)$}{0 21}\RTX{$\,(0,{-}1)$}{1 -20}
\PSline{0 0 12 18}
\rotateRTX{45}{$\overbrace{\hskip 16.97\PSunit}$}{9 13}
\RTX{$x$}{6 4}\RTX{$x$}{17 10}
\PSarc{0 56.3}{0 0 6}
\setdash{5\PSlinewidth}\PSline{12 18 16 24}
\RTX{1 varv $=$ 8 rax}{24 9}
\RTX{1/2 varv $=$ 4 rax}{24 4}
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\Fig dunkels-9
\PSunit=1,1truemm
\PSpicture{46\PSunit}{42\PSunit}
\llcoords{-8  -16}
\CTX{Fig 9.}{18 -13}
\PScline{0 12 12 12 12 0}\PSline{10.5 12 10.5 10.5 12 10.5}
\PScline{24 0 24 12 30 6}\PSline{29.3 6.7 28.6 6 29.3 5.3}
\RTX{$\eightpoint\overbrace{\hskip12\PSunit}$}{0 13}
\rotateRTX{90}{$\eightpoint\overbrace{\hskip12\PSunit}$\hss}{12 12}
\rotateRTX{45}{$\eightpoint\overbrace{\hskip8.49\PSunit}$\hss}{24 12}
\rotateRTX{135}{$\eightpoint\overbrace{\hskip8.49\PSunit}$\hss}{30 6}
\RTX{$\ssize2$}{6 15}\RTX{$\ssize2$}{14.5 7}
\RTX{$\ssize2$}{28 -1.3}\RTX{$\ssize2$}{28 13}
\setPSlinewidth{0.3\PSlinewidth}
\llcoords{-2 -8}\PSline{0 0 0 34}
\llcoords{-8 -8}\PSline{0 0 0 34}
\llcoords{-14 -8}\PSline{0 0 0 34}
\llcoords{-20 -8}\PSline{0 0 0 34}
\llcoords{-26 -8}\PSline{0 0 0 34}
\llcoords{-32 -8}\PSline{0 0 0 34}
\llcoords{-38 -8}\PSline{0 0 0 34}
\llcoords{-44 -8}\PSline{0 0 0 34}
\llcoords{0 -10}\PSline{0 0 46 0}
\llcoords{0 -16}\PSline{0 0 46 0}
\llcoords{0 -22}\PSline{0 0 46 0}
\llcoords{0 -28}\PSline{0 0 46 0}
\llcoords{0 -34}\PSline{0 0 46 0}
\llcoords{0 -40}\PSline{0 0 46 0}
\endPSpicture

\Fig froeberg-1
\PSunit=1,25truemm
%AT \PSpicture{100\PSunit}{42\PSunit}
\PSpicture{100\PSunit}{36\PSunit}
\llcoords{0 -5}
\def\stroke{\PS{gsave 0.8 setgray fill grestore stroke}}
\PScline{14 2 30 10 20 25 2 20 1 5}
\PScline{45 0 100 0 76 21 79 14 65 16 74 27 50 24 55 10}
\def\stroke{\PS{stroke}}
\putPSmarks\PSline{65 24 81 15}\CTX{$P$}{65 29}\RTX{$Q$}{84 16}
\RTX{Konveks}{2 -3}\RTX{Ej konveks}{ 55 -3}
\endPSpicture

\Fig froeberg-2
\PSunit=6truemm
%cos 18=0.9511 sin 18=0.3090 cos 54=0.5878 sin 54=0.8090
\def\dodeci{\PScline{
0      %-05878+5878
0      %-08090+8090
1.1756 %05878+5878
0      %-08090+8090
1.5389 %09511+5878
1.1180 %03090+8090
0.5878 %0+5878
1.8090 %10000+8090
-0.3633 %-09511+5878
1.1180 %03090+8090
}}
%
\def\dodecii{\PScline{
0      		     
0      		     
1.1756 		     
0      		     
1.5389 		     
-1.1180 		     
0.5878 		     
-1.8090 		     
-0.3633		     
-1.1180 		     
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%AT \PSpicture{24\PSunit}{24\PSunit}
\PSpicture{24\PSunit}{22\PSunit}
\llcoords{-1 -18} 
\RTX{Tetrahedron $\{3,3\}$}{-0.5 -1}
\PScline{0 0 4 0 2 3.462}\PScline{1 1.732 2 0 3 1.732}
%
\llcoords{-13 -16}
\RTX{Dodecahedron $\{5,3\}$}{-0.5 -1}
  \dodeci
  %add  5878+03663=9.541,00   18090+11180=29.270,00
  \llcoords{-13.9541 -18.9270}
  \dodeci \dodecii
  %
  \llcoords{-12.4122 -17.8090}
  \dodeci
  \llcoords{-14.9182 -16}
  \dodeci
  %\rot{36}\dodec\endrot
  \llcoords{-15.4960 -17.8090}
  \dodeci
  %\llcoords{-40.319,00 -29270}
  \llcoords{-17.0319 -18.9270}
  \dodecii
  %\llcoords{-40.319,00-5878=-46.197,00 -29270-18090=-47.360,00}
  \llcoords{-17.6197 -20.7336}\dodecii
  %\llcoords{-46.197,00-19082=-65.279,00  -47.360,00}
  \llcoords{-19.5279 -20.7336}\dodecii
  %\llcoords{-24960-30778=-55.738,00 -18090}
  \llcoords{-18.5738 -17.8090}
  \dodeci \dodecii
  %\llcoords{-40319,00-30778=-71.097,00 -29270}
  \llcoords{-20.1097 -18.9270}
  \dodecii
 %
 %\dodeci
 %%add  5878+03663=9.541,00   18090+11180=29.270,00
 %\llcoords{-0.9541 -2.9270}
 %\dodeci \dodecii
 %%
 %\llcoords{0.5878 -1.8090}
 %\dodeci
 %\llcoords{-1.9182 0}
 %\dodeci
 %%\rot{36}\dodec\endrot
 %\llcoords{-2.4960 -1.8090}
 %\dodeci
 %%\llcoords{-40.319,00 -29270}
 %\llcoords{-4.0319 -2.9270}
 %\dodecii
 %%\llcoords{-40.319,00-5878=-46.197,00 -29270-18090=-47.360,00}
 %\llcoords{-4.6197 -4.7336}\dodecii
 %%\llcoords{-46.197,00-19082=-65.279,00  -47.360,00}
 %\llcoords{-6.5279 -4.7336}\dodecii
 %%\llcoords{-24960-30778=-55.738,00 -18090}
 %\llcoords{-5.5738 -1.8090}
 %\dodeci \dodecii
 %%\llcoords{-40319,00-30778=-71.097,00 -29270}
 %\llcoords{-7.1097 -2.9270}
 %\dodecii
 %
\llcoords{0 -9.5}
\RTX{Cube $\{4,3\}$}{1 -1}
\PScline{0 2 8 2 8 4 0 4}\PScline{2 0 4 0 4 6 2 6}\PSline{6 2 6 4}
 %
\llcoords{-13 -6}
\RTX{Icosahedron $\{3,5\}$}{1 -1}
\PSline{0 0 3 5.196}\PSline{0 0 -1 1.732}
\llcoords{-15 -6}
\PSline{0 0 3 5.196}\PSline{0 0 -2 3.468}
\llcoords{-17 -6}
\PSline{0 0 3 5.196}\PSline{0 0 -3 5.196}
\llcoords{-19 -6}
\PSline{0 0 3 5.196}\PSline{0 0 -3 5.196}
\llcoords{-21 -6}
\PSline{0 0 2 3.464}\PSline{0 0 -3 5.196}
\llcoords{-22 -7.732}\PSline{0 0 -2 3.468}
\llcoords{-23 -9.464}\PSline{0 0 -1 1.732}
\llcoords{-12 -7.732}\PSline{0 0 2 3.468}\PSline{0 0 10 0}
\llcoords{-13 -9.464}\PSline{0 0 10 0}
%
\llcoords{0 -4}
\RTX{Octahedron $\{3,4\}$}{1 -3}
\PScline{0 0 6 0 7 1.732 1 1.732}
\PSline{1 1.732 3 -1.732 5 1.732 4 3.464 2 0}
\PSline{3 1.732 4 0}
\endPSpicture

\Fig hoermand-1
\PSunit=1,25truemm
\PSpicture{73\PSunit}{35\PSunit}
\PSline{0 0 73 0}\PSline{0 0 0 35}
\PSline{0 25 73 25}
\spline{0 0
6 16.5
17.5 30.5
34 23
52 26.5
65 24.3
73 23.7
}\endPSpicture

\Fig jonsson-1
\PSunit=1,25truemm
\def\markbox{\hss\vrule height 2truemm\hss}
%AT \PSpicture{105\PSunit}{30\PSunit}
\PSpicture{105\PSunit}{32\PSunit}
\llcoords{-3 -4}
\TeXmark{5 0 10 0 15 0 20 0 25 0 30 0}
\CTX{$1$}{5 -3}
\CTX{$2$}{10 -3}
\CTX{$3$}{15 -3}
\CTX{$4$}{20 -3}
\CTX{$5$}{25 -3}
\CTX{$6$}{30 -3}
\def\markbox{\hss\vrule height 0.2pt width 2truemm\hss}
\TeXmark{0 5 0 10 0 15}
\LTX{$1$}{-1 5}
\LTX{$2$}{-1 10}
\LTX{$3$}{-1 15}
\CTX{$P$}{4 7}\RTX{$R$}{31 10}
\putPSmarks\PSline{0 0 5 5 10 10 15 5 20 10 25 15 30 10}\nomarks
%
\llcoords{-63 -4}
\TeXmark{5 0 10 0 15 0 20 0 25 0 30 0}
\CTX{$1$}{5 -3}
\CTX{$2$}{10 -3}
\CTX{$3$}{15 -3}
\CTX{$4$}{20 -3}
\CTX{$5$}{25 -3}
\CTX{$6$}{30 -3}
\def\markbox{\hss\vrule height 0.2pt width 2truemm\hss}
\TeXmark{0 5 0 10 0 15}
\LTX{$1$}{-1 5}
\LTX{$2$}{-1 10}
\LTX{$3$}{-1 15}
\CTX{$P$}{4 7}\RTX{$R$}{31 10}
\putPSmarks\PSline{0 0 5 5 10 10 15 15 20 10 25 5 30 10}\nomarks
\setPSlinewidth{0.25\PSlinewidth}
\PSarrow{-3 0 38 0}\RTX{$\,x$}{38 0}
\PSarrow{0 -3 0 27}\RTX{$y$}{1 27}
\llcoords{-3 -4}
\PSarrow{-3 0 38 0}\RTX{$\,x$}{38 0}
\PSarrow{0 -3 0 27}\RTX{$y$}{1 27}
\endPSpicture

\Fig jonsson-2
\PSunit=1,25truemm
%AT \PSpicture{105\PSunit}{38\PSunit}
\PSpicture{105\PSunit}{42.5\PSunit}
\llcoords{-3 -14}
\CTX{$P$}{4 7}\RTX{$R$}{31 10}
\putPSmarks\PSline{0 0 5 5 10 10 15 5 20 0 25 5 30 10}\nomarks
%
\llcoords{-63 -14}
\CTX{$P$}{4 7}\RTX{$R$}{31 10}
\putPSmarks\PSline{0 0 5 5 10 0 15 -5 20 0 25 5 30 10}\nomarks
\setPSlinewidth{0.25\PSlinewidth}
\PSarrow{-3 0 38 0}\RTX{$\,x$}{38 0}
\PSarrow{0 -14 0 27}\RTX{$y$}{1 27}
\PSmark{5 -5}\CTX{$P'$}{4 -7.5}\RTX{$S$}{10 3}
\setdash{1truemm}\PSline{5 -5 10 0}\nodashes
\llcoords{-3 -14}
\PSarrow{-3 0 38 0}\RTX{$\,x$}{38 0}
\PSarrow{0 -14 0 27}\RTX{$y$}{1 27}
\PSmark{5 -5}\CTX{$P'$}{4 -7.5}\RTX{$S$}{20 -3}
\setdash{1truemm}\PSline{5 -5 10 -10 20 0}\nodashes
\endPSpicture

\Fig kjell-b-1
\PSunit=1,25truemm
\def\markbox{\hss\vrule height 2truemm\hss}
%AT \PSpicture{68\PSunit}{42\PSunit}
\PSpicture{68\PSunit}{40\PSunit}
\llcoords{-10 -6}
\PSarrow{-10 0 58 0}
\TeXmark{0 1 24 1 47.5 1}
\CTX{$\ln r-h$}{0 -4}\CTX{$\ln r$}{24 -4}\CTX{$\ln r+h$}{47.5 -4}
\PSmark{0 13 47.5 32.5}
\dspline{-8 15
0 13
%10 11.5
24 13.5
%40 25 
47.5 32.5
55 40}
\PSline{24 13.5 24 22.5}
\putPSmarks\PSline{0 13 47.5 32.5}
\endPSpicture

\Fig lindstr2-1
\PSunit=1,25truemm
\PSpicture{78\PSunit}{50\PSunit}
\llcoords{-1 0}
\LTX{$1\,$}{0 25}
\PSline{0 25 17 35}\RTX{1\ 2}{18 35}
   \PSline{26 35 41 43}\RTX{1\ 2\ 3}{42 43}
        \PSline{53 43 63 49}\RTX{1\ 2\ 3\ 4}{64 49}
        \PSline{53 43 63 45}\RTX{1\ 2\ 4\ 3}{64 45}
        \PSline{53 43 63 41}\RTX{1\ 4\ 2\ 3}{64 41}
        \PSline{53 43 63 37}\RTX{4\ 1\ 2\ 3}{64 37}
   \PSline{26 35 41 35}\RTX{1\ 3\ 2}{42 35}
   \PSline{26 35 41 27}\RTX{3\ 1\ 2}{42 27}
%
\PSline{0 25 17 15}\RTX{2\ 1}{18 15}
   \PSline{26 15 41 23}\RTX{2\ 1\ 3}{42 23}
   \PSline{26 15 41 15}\RTX{2\ 3\ 1}{42 15}
   \PSline{26 15 41 7}\RTX{3\ 2\ 1}{42 7}
\RTX{$1\ x\ 2$}{2 2}
\RTX{$x\ 3$}{31 2}
\RTX{$x\ 4$}{54 2}
\endPSpicture

\Fig philip-1
\PSunit=1,25truemm
%AT \PSpicture{98\PSunit}{50\PSunit}
\PSpicture{98\PSunit}{52\PSunit}
\RTX{Figur 1}{35 2}
\llcoords{-2 -20}
\PScline{0 0 40 20 22 28}
\CTX{$A$}{0 -3}\RTX{$C$}{40 18}\CTX{$B$}{22 30}
\setdash{5\PSlinewidth}
\PSline{0 0 50 0}\PSline{40 20 90 20}\PSline{22 28 72 28}
\nodashes\CTX{$T$}{25 -2}
\llcoords{-52 -20}
\PScline{0 0 40 20 22 28}
\CTX{$A'$}{0 -3}\RTX{$C'$}{40 18}\CTX{$B'$}{22 30}
\endPSpicture



\Fig philip-2
\PSunit=1,25truemm
%AT \PSpicture{115\PSunit}{90\PSunit}
\PSpicture{112\PSunit}{90\PSunit}
\RTX{Figur 2}{43 2}
\llcoords{-4 -23}
\PScline{58 0 0 54 99 65}\PScline{58 0 8 33 80 53}
\PScline{58 0 39 50 104 28}
% 14/60=0.233
%\PSline{58 0 51 60}\PSline{51.233 58 53.233 58.233 53 60.233}
\PSline{58 0 51 59.95}\PSline{51.233 57.95 53.233 58.183 53 60.1833}
%13/43,5=0.2989
\PSline{58 0 45 43.5}\PSline{45.2989 42 46.7989 42.2989 46.5 43.7989}
\PScline{8 33 39 50 0 54}
\LTX{$A\,$}{8 33}\LTX{$B\,$}{0 54}\RTX{$C$}{39 52}
\PScline{80 53 99 65 104 28}
\LTX{$A'\,$}{80 55}\RTX{$\,\,B'$}{99 65}\RTX{$\,C'$}{104 28}
\CTX{$O$}{58 -3}
\endPSpicture




\Fig philip-3
\PSunit=1,25truemm
%\PSpicture{125\PSunit}{50\PSunit}
\PSpicture{120\PSunit}{50\PSunit}
\RTX{Figur 3}{48 2}
\llcoords{-2 -25}
\PScline{0 0 45 0 32.5 15}
\CTX{$A$}{0 -3}\CTX{$B$}{32.5 18}\CTX{$C$}{45 -3}
\setdash{5\PSlinewidth}\PSline{57 -15 57 20}\nodashes
\PScline{67 0 116 0 82 16}
\CTX{$C'$}{67 -3}\CTX{$A'$}{116 -3}\CTX{$B'$}{82 19}
\endPSpicture



\Fig philip-4
\PSunit=1,25truemm
\PSpicture{125\PSunit}{70\PSunit}
\CTX{Figur 4}{63 2}
\llcoords{-2 -20}
\PScline{0 18 49 18 35 33}
\CTX{$A\,$}{0 16}\CTX{$B$}{35 36}\RTX{$C$}{49 20}
\PSline{0 18 120 0}\PSline{35 33 85 15}\PSline{49 18 71 0}
\PScline{71 0 120 0 85 15}
\CTX{$A'$}{120 -3}\CTX{$C'$}{71 -3}\RTX{$B'$}{86 17}
\PSmark{60 9 60 24}\LTX{$M_3\,$}{60 7}\RTX{$\,M_1$}{60 12}
\RTX{$\,M_2$}{60 26}\CTX{$m$}{60 40}
\setdash{5\PSlinewidth}\PSarrow{60 38 60 -10}
\PSline{35 33 85 33}\PSarrow{85 33 85 15.1}\nodashes
\PSline{84 33 84 32 85 32}
\endPSpicture






\Fig philip-5
\PSunit=1,1truemm
\def\D{\PScline{-5 0 5 0 0 -5}}\def\U{\PScline{-5 0 5 0 0 5}}
\PSpicture{47\PSunit}{192\PSunit}
\llcoords{-6 0}
\RTX{Figur 5}{55 2}
\LTX{$m_2\,$}{0 82.5}\LTX{$m_1\,$}{0 110}
\llcoords{-23 0}\PSline{0 0 0 190}
\setdash{5\PSlinewidth}
  \PSline{-15 82.5 15 82.5}\PSline{-15 110 15 110}\nodashes
\PSarrow{10 82.5 10 110}\PSarrow{10 110 10 82.5}
\RTX{$\,a$}{10 96.5}
\llcoords{-23 -8}\U\LTX{$R_2R_1R_2\,$}{-5 0}
\llcoords{-23 -49}\D\LTX{$R_2R_1\,$}{-5 0}
   \PSline{17 0 23 0}
   \PSarrow{20 0 20 54}\PSarrow{20 54 20 0}
   \PSline{17 54 23 54}\LTX{$2a\,\,$}{20 27}
\llcoords{-23 -62}\U\LTX{$R_2\,$}{-5 0}
\llcoords{-23 -103}\D\LTX{$I\,$}{-5 0}
   \PSarrow{20 0 20 54}\PSarrow{20 54 20 0}
   \PSline{17 54 23 54}\LTX{$2a\,\,$}{20 27}
\llcoords{-23 -116}\U\LTX{$R_1\,$}{-5 0}
\llcoords{-23 -157}\D\LTX{$R_1R_2\,$}{-5 0}
\llcoords{-23 -171}\U\LTX{$R_1R_2R_1\,$}{-5 0}
\endPSpicture





\Fig philip-6
\PSunit=1truemm
\PSpicture{102\PSunit}{95\PSunit}
\CTX{Figur 6}{50 2}
\llcoords{-53 -15}\CTX{$O$}{0 -3}\PSmark{0 0}
\PSline{0 0 -50 25}\PSmark{-40 20}\CTX{$A''$}{-40 24}
\PSline{0 0 25 75}\PSmark{15 45}\LTX{$A'\,$}{15 47}
\PSline{0 0 49 42}\PSmark{35 30}\RTX{$\,A$}{35 28}
\PSline{-40 20 15 45 35 30}
\setdash{5\PSlinewidth}
\PSline{0 0 -30 78}\LTX{$m_2\,$}{-30 78}
  \PSmark{-20 52}\RTX{$\,Q$}{-20 52}
\PSline{0 0 44 66}\RTX{$\,m_1$}{44 66}
  \PSmark{40  60}\RTX{$\,P$}{40 60}
\endPSpicture



\Fig philip-7
\PSunit=1truemm
\PSpicture{100\PSunit}{86\PSunit}
\CTX{Figur 7}{50 2}
\llcoords{-50 -25}
\CTX{$m$}{0 -13}\setdash{5\PSlinewidth}\PSarrow {0 60 0 -10}\nodashes
\PScline{-50 0 -16 0 -27 16}\CTX{$T$}{-20 14}
\PScline{50 0 16 0 27 16}\RTX{$G=TR=RT$}{37 14}
\llcoords{-50 -60}
\PScline{-50 0 -16 0 -27 16}\CTX{$I$}{-20 14}
\PScline{50 0 16 0 27 16}\RTX{$R$}{37 14}
\endPSpicture



\Fig philip-811
\PSunit=1,25truemm
\PSpicture{28\PSunit}{30\PSunit}
\llcoords{-14 -14}
\CTX{$C_1$}{0 -12}
\llcoords{-7 -10}
\LL
\endPSpicture

\Fig philip-812
\PSpicture{28\PSunit}{30\PSunit}
\llcoords{-14 -14}
\CTX{$C_2$}{0 -12}
\PSmark{0 0}\LL\PS{gsave 180 rotate}\LL\PS{grestore}
\PSline{0 -10  0 10}
\LL
\endPSpicture

\Fig philip-813
%
\PSpicture{28\PSunit}{30\PSunit}
\llcoords{-14 -14}
\CTX{$C_2$}{0 -12}
\PSline{-10 0 10 0}
\PSmark{0 0}
\llcoords{-6 -14}
\LL
\llcoords{-22 -14}\PS{gsave 180 rotate}\LL\PS{grestore}
\endPSpicture


\Fig philip-821
\PSunit=1,25truemm
\PSpicture{28\PSunit}{35\PSunit}
\llcoords{-14 -21}
\CTX{$C_3$}{0 -19}
\PSmark{0 0}
\PS{gsave}
  \PSline{0 -15 0 0}\PS{120 rotate}
  \PSline{0 -15 0 0}\PS{120 rotate}
  \PSline{0 -15 0 0}
\PS{grestore}
\llcoords{-14 -11}\PS{gsave 30 rotate}\LL\PS{grestore}
%Now add cos 30 sin 30 =(8.66 5) to default coords of origin
\llcoords{-22.66 -26}\PS{gsave 150 rotate}\LL\PS{grestore}
\llcoords{-5.34 -26}\PS{gsave 270 rotate}\LL\PS{grestore}
\endPSpicture

\Fig philip-822
\PSpicture{28\PSunit}{35\PSunit}
\llcoords{-14 -21}
\CTX{$C_3$}{0 -19}
\PSmark{0 0}
\PS{gsave}\PSline{0 0 15 0}
\PS{120 rotate}\PSline{0 0 15 0}
\PS{120 rotate}\PSline{0 0 15 0}
\PS{grestore}
%
\PS{gsave}\PS{30 rotate}\LL
\PS{120 rotate}\LL
\PS{120 rotate}\LL
\PS{grestore}
\endPSpicture


\Fig philip-831
\PSunit=1,25truemm
\PSpicture{35\PSunit}{40\PSunit}
\llcoords{-17 -22}\PSmark{0 0}
\CTX{$C_4$}{0 -20}
\PS{gsave}
 \PSline{0 0 17 0}\PS{30 rotate}\LL
 \PS{60 rotate}
 \PSline{0 0 17 0}\PS{30 rotate}\LL
 \PS{60 rotate}
 \PSline{0 0 17 0}\PS{30 rotate}\LL
 \PS{60 rotate}
 \PSline{0 0 17 0}\PS{30 rotate}\LL
\PS{grestore}
\endPSpicture

\Fig philip-832
\PSpicture{35\PSunit}{40\PSunit}
\llcoords{-17 -22}\PSmark{0 0}
\CTX{$C_5$}{0 -20}
\PS{gsave}
  \PS{180 rotate}
 \PSline{0 0 17 0}\PS{20 rotate}\LL
 \PS{52 rotate}
 \PSline{0 0 17 0}\PS{20 rotate}\LL
 \PS{52 rotate}
 \PSline{0 0 17 0}\PS{20 rotate}\LL
 \PS{52 rotate}
 \PSline{0 0 17 0}\PS{20 rotate}\LL
 \PS{52 rotate}
 \PSline{0 0 17 0}\PS{20 rotate}\LL
\PS{grestore}
\endPSpicture

\Fig philip-833
\PSpicture{35\PSunit}{40\PSunit}
\llcoords{-17 -22}\PSmark{0 0}
\CTX{$C_6$}{0 -20}
\PS{gsave}
 \PSline{0 0 17 0}\PS{15 rotate}\LL
 \PS{45 rotate}
 \PSline{0 0 17 0}\PS{15 rotate}\LL
 \PS{45 rotate}
 \PSline{0 0 17 0}\PS{15 rotate}\LL
 \PS{45 rotate}
 \PSline{0 0 17 0}\PS{15 rotate}\LL
 \PS{45 rotate}
 \PSline{0 0 17 0}\PS{15 rotate}\LL
 \PS{45 rotate}
 \PSline{0 0 17 0}\PS{15 rotate}\LL
\PS{grestore}
\endPSpicture



\Fig philip-911
\PSunit=1,25truemm
\PSpicture{35\PSunit}{40\PSunit}
\llcoords{-17 -22}
\CTX{$D_1$}{0 -20}
\PSline{0 -10 0 10}
\LL
\PS{gsave}
 \PS{180 rotate}\GG
\PS{grestore}
\endPSpicture

\Fig philip-912
\PSpicture{35\PSunit}{40\PSunit}
\llcoords{-17 -22}
\CTX{$D_1$}{0 -20}
\PSline{0 -10 0 10}
\llcoords{-17 -17}
\PS{gsave}
  \PS{90 rotate}\GG\LL
\PS{grestore}
\endPSpicture

\Fig philip-913
\PSpicture{35\PSunit}{40\PSunit}
\llcoords{-17 -22}
\CTX{$D_1$}{0 -20}
\PSline{0 -10 0 10}\PSline{-17 0 17 0}
\LL\GG
\PS{gsave}
 \PS{180 rotate}\GG\LL
\PS{grestore}
\endPSpicture


\Fig philip-921
\PSunit=1,25truemm
\PSpicture{40\PSunit}{45\PSunit}
\llcoords{-20 -27}
\CTX{$D_3$}{0 -25}
\PS{gsave}
 \PS{-30 rotate}
 \PSline{-20 0 20 0}\PS{3 rotate}\LL\PS{-6 rotate}\GG\PS{3 rotate}
 \PS{120 rotate}
 \PSline{-20 0 20 0}\PS{3 rotate}\LL\PS{-6 rotate}\GG\PS{3 rotate}
 \PS{120 rotate}
 \PSline{-20 0 20 0}\PS{3 rotate}\LL\PS{-6 rotate}\GG\PS{3 rotate}
\PS{grestore}
\endPSpicture

\Fig philip-922
\PSpicture{40\PSunit}{45\PSunit}
\llcoords{-20 -27}
\CTX{$D_4$}{0 -25}
\PS{gsave}
 \PSline{0 0 20 0}\PS{2 rotate}\LL\PS{-4 rotate}\GG\PS{2 rotate}
 \PS{45 rotate}\PSline{0 0 20 0}\PS{45 rotate}
 \PSline{0 0 20 0}\PS{2 rotate}\LL\PS{-4 rotate}\GG\PS{2 rotate}
 \PS{45 rotate}\PSline{0 0 20 0}\PS{45 rotate}
 \PSline{0 0 20 0}\PS{2 rotate}\LL\PS{-4 rotate}\GG\PS{2 rotate}
 \PS{45 rotate}\PSline{0 0 20 0}\PS{45 rotate}
 \PSline{0 0 20 0}\PS{2 rotate}\LL\PS{-4 rotate}\GG\PS{3 rotate}
 \PS{45 rotate}\PSline{0 0 20 0}
\PS{grestore}
\endPSpicture

\Fig philip-931
\PSunit=1,25truemm
\PSpicture{40\PSunit}{45\PSunit}
\llcoords{-20 -27}
\CTX{$D_5$}{0 -25}
\PS{gsave}
 \PS{90 rotate}
 \PSline{0 0 20 0}\PS{1 rotate}\LL\PS{-2 rotate}\GG\PS{1 rotate}
 \PS{36 rotate}\PSline{0 0 20 0}\PS{36 rotate}
 \PSline{0 0 20 0}\PS{1 rotate}\LL\PS{-2 rotate}\GG\PS{1 rotate}
 \PS{36 rotate}\PSline{0 0 20 0}\PS{36 rotate}
 \PSline{0 0 20 0}\PS{1 rotate}\LL\PS{-2 rotate}\GG\PS{1 rotate}
 \PS{36 rotate}\PSline{0 0 20 0}\PS{36 rotate}
 \PSline{0 0 20 0}\PS{1 rotate}\LL\PS{-2 rotate}\GG\PS{1 rotate}
 \PS{36 rotate}\PSline{0 0 20 0}\PS{36 rotate}
 \PSline{0 0 20 0}\PS{1 rotate}\LL\PS{-2 rotate}\GG\PS{1 rotate}
 \PS{36 rotate}\PSline{0 0 20 0}\PS{36 rotate}
\PS{grestore}
\endPSpicture


\Fig philip-932
\PSpicture{40\PSunit}{45\PSunit}
\llcoords{-20 -27}
\CTX{$D_6$}{0 -25}
\PS{gsave}
 \PS{90 rotate}
 \PSline{0 0 20 0}\LL\GG
 \PS{30 rotate}\PSline{0 0 20 0}\PS{30 rotate}  
 \PSline{0 0 20 0}\LL\GG
 \PS{30 rotate}\PSline{0 0 20 0}\PS{30 rotate}  
 \PSline{0 0 20 0}\LL\GG
 \PS{30 rotate}\PSline{0 0 20 0}\PS{30 rotate}  
 \PSline{0 0 20 0}\LL\GG
 \PS{30 rotate}\PSline{0 0 20 0}\PS{30 rotate}  
 \PSline{0 0 20 0}\LL\GG
 \PS{30 rotate}\PSline{0 0 20 0}\PS{30 rotate}  
 \PSline{0 0 20 0}\LL\GG
 \PS{30 rotate}\PSline{0 0 20 0}\PS{30 rotate}  
\PS{grestore}
\endPSpicture

\Fig philip-10
\PSunit=1,25truemm
\PSpicture{80\PSunit}{40\PSunit}
\llcoords{-35  -28}
\CTX{$F_1$}{0 -15}\CTX{Figur 10}{0 -23}
\llcoords{0 -28}\PSline{0 -10 0 10}\LL
\llcoords{-16 -28}\PSline{0 -10 0 10}\LL
\llcoords{-32 -28}\PSline{0 -10 0 10}\LL
\llcoords{-48 -28}\PSline{0 -10 0 10}\LL
\llcoords{-64 -28}\PSline{0 -10 0 10}\LL
\llcoords{-80 -28}\PSline{0 -10 0 10}
\endPSpicture

\Fig philip-11
\PSunit=1,25truemm
\PSpicture{96\PSunit}{40\PSunit}
\llcoords{-48  -28}
\CTX{$F_2$}{0 -15}\CTX{Figur 11}{0 -23}
\llcoords{0 -28}\PSmark{0 0 16 0 32 0 48 0 64 0 80 0 96 0}
\PSline{0 -10 0 10}
\llcoords{-16 -28}\PSline{0 -10 0 10}\LL\PS{gsave 180 rotate}\LL\PS{grestore}
\llcoords{-32 -28}\PSline{0 -10 0 10}
\llcoords{-48 -28}\PSline{0 -10 0 10}\LL\PS{gsave 180 rotate}\LL\PS{grestore}
\llcoords{-64 -28}\PSline{0 -10 0 10}
\llcoords{-80 -28}\PSline{0 -10 0 10}\LL\PS{gsave 180 rotate}\LL\PS{grestore}
\llcoords{-96 -28}\PSline{0 -10 0 10}
\endPSpicture


\Fig philip-12
\PSunit=1,25truemm
\PSpicture{68\PSunit}{40\PSunit}
\llcoords{-34  -28}
\CTX{$F_1^{\,1}$}{0 -15}\CTX{Figur 12}{0 -23}
\PSline{-34 0 34 0}
\llcoords{-2 -28}
\PSline{0 -10 0 10}\LL\GG
\llcoords{-18 -28}\PSline{0 -10 0 10}\LL\GG
\llcoords{-34 -28}\PSline{0 -10 0 10}\LL\GG
\llcoords{-50 -28}\PSline{0 -10 0 10}\LL\GG
\llcoords{-66 -28}\PSline{0 -10 0 10}
\endPSpicture


\Fig philip-13
\PSunit=1,25truemm
\PSpicture{68\PSunit}{40\PSunit}
\llcoords{-34  -28}
\CTX{$F_2^{\,1}$}{0 -15}\CTX{Figur 13}{0 -23}
\PSline{-34 0 34 0}
\llcoords{-2 -28}\PSmark{0 0 16 0 32 0 48 0 64 0}
\PSline{0 -10 0 10}
\llcoords{-18 -28}
 \PSline{0 -10 0 10}
 \PS{gsave 180 rotate}\LL\GG\PS{grestore}\LL\GG
  \PSline{16 -10 16 10}
\llcoords{-50 -28}
 \PSline{0 -10 0 10}
 \PS{gsave 180 rotate}\LL\GG\PS{grestore}\LL\GG
 \PSline{16 -10 16 10}
\endPSpicture




\Fig philip-14
\PSunit=1,25truemm
\PSpicture{96\PSunit}{36\PSunit}
\llcoords{-48  -28}
\CTX{$F_1^2$}{0 -15}\CTX{Figur 14}{0 -21}
\llcoords{0 -28}
\PSline{0 -10 0 10}
\llcoords{-16 -28}
    \PSline{0 -10 0 10}\LL
    \PS{gsave 180 rotate}\GG\PS{grestore}
    \PSline{16 -10 16 10}
\llcoords{-48 -28}
    \PSline{0 -10 0 10}\LL
    \PS{gsave 180 rotate}\GG\PS{grestore}
    \PSline{16 -10 16 10}
\llcoords{-80 -28}
    \PSline{0 -10 0 10}\LL
    \PS{gsave 180 rotate}\GG\PS{grestore}
    \PSline{16 -10 16 10}
\endPSpicture


\Fig philip-15
\PSunit=1,25truemm
\PSpicture{68\PSunit}{36\PSunit}
\llcoords{-34  -28}
\CTX{$F_2^{\,2}$}{0 -15}\CTX{Figur 15}{0 -21}
\PSline{-34 0 34 0}
\llcoords{-2 -28}\PSmark{8 0 24 0 40 0 56 0}
 \PSline{0 -10 0 10}\GG
\llcoords{-18 -28}
 \PSline{0 -10 0 10}
 \PS{gsave 180 rotate}\GG\PS{grestore}\LL
\llcoords{-34 -28}
 \PSline{0 -10 0 10}
 \PS{gsave 180 rotate}\LL\PS{grestore}\GG
\llcoords{-50 -28}
 \PSline{0 -10 0 10}
 \PS{gsave 180 rotate}\GG\PS{grestore}\LL
\llcoords{-66 -28}
 \PSline{0 -10 0 10}
 \PS{gsave 180 rotate}\LL\PS{grestore}
\endPSpicture


\Fig philip-16
\PSunit=1,25truemm
\PSpicture{64\PSunit}{36\PSunit}
\llcoords{-32  -28}
\CTX{$F_1^{\,3}$}{0 -15}\CTX{Figur 16}{0 -21}
\llcoords{0 -28}
 \PSline{0 -10 0 10}\LL
\llcoords{-16 -28}
 \PSline{0 -10 0 10}\GG
\llcoords{-32 -28}
 \PSline{0 -10 0 10}\LL
\llcoords{-48 -28}
 \PSline{0 -10 0 10}\GG\PSline{16 -10 16 10}
\endPSpicture



\Fig philip-17
\PSunit=1,25truemm
%AT \PSpicture{74\PSunit}{50\PSunit}
\PSpicture{74\PSunit}{53\PSunit}
\def\rLL{\PS{gsave 10 rotate}\LL\PS{grestore}}
\llcoords{-37  -18}
\CTX{$W_1$}{0 -10}\CTX{Figur 17}{0 -15}
\llcoords{1 -16}
\PSline{0 0 72 0}\PSline{0 12 72 12}
     \PSline{0 24 72 24}\PSline{2 36 74 36}
\PSline{0 -2 20 38}\PSline{18 -2 38 38}
    \PSline{36 -2 56 38}\PSline{54  -2 74 38}
\llcoords{-5 -18}\rLL  
\llcoords{-23 -18}\rLL
\llcoords{-41 -18}\rLL
\llcoords{-59 -18}\rLL
%
\llcoords{ 7  -30}\rLL
\llcoords{-11 -30}\rLL
\llcoords{-29 -30}\rLL
\llcoords{-47 -30}\rLL
%
\llcoords{ 1  -42}\rLL
\llcoords{-17 -42}\rLL
\llcoords{-35 -42}\rLL
\llcoords{-53 -42}\rLL
\endPSpicture



\Fig philip-18
\PSunit=1,15truemm\PSmarkradius=1truemm
\PSpicture{64\PSunit}{180\PSunit}
\LTX{Figur 18}{70 0}
\llcoords{-3 -100}
\putPSmarks\PSline{0 0 0 60}\PSmark{0 22 0 40}
\whitemark{0 0 0 22 0 40 0 60}
\LTX{$P\,\,$}{0 0}\LTX{$Q\,\,$}{0 22}
\LTX{$P'\,\,$}{0 40}\LTX{$Q'\,\,$}{0 60}
%
\llcoords{-25 -22.7}
\PSline{17.3 -10 17.3 10 0 20 -17.3 10}\setdash{5\PSlinewidth}
\PSline{-17.3 10 -17.3 -10 0 -20 17.3 -10}\nodashes
\whitemark
{17.3 -10
17.3 10
0 20
-17.3 10
-17.3 -10
0 -20
}
\RTX{$\,\,P$}{17.3 -10}
\RTX{$\,\,Q$}{17.3 10}
\CTX{$P'$}{0 22}
\LTX{$Q'\,\,$}{-17.3 10}
\RTX{$n=3$}{30 0}
%
\llcoords{-20 -55}
\PSline{20 0 20 20 0 20 0 0}\setdash{5\PSlinewidth}
\PSline{0 0 20 0}\nodashes
\whitemark{0 0
20 0
20 20
0 20}
\RTX{$\,\,P$}{20 0}
\RTX{$\,\,Q$}{20 20}
\LTX{$P'\,\,$}{0 20}
\LTX{$Q'\,\,$}{0 0}
\RTX{$n=4$}{30 10}
%
\llcoords{-20 -90}
\PSline{20 0 20 20 0 15 13 -2}\setdash{5\PSlinewidth}
\PSline{13 -2 20 0}\nodashes
\whitemark{13 -2
20 0
20 20
0 15}
\RTX{$\,\,P$}{20 0}
\RTX{$\,\,Q$}{20 20}
\LTX{$P'\,\,$}{0 15}
\LTX{$Q'\,\,$}{13 -3}
\RTX{$n=5$}{30 10}
%
\llcoords{-20 -125}
\PScline{20 0 20 20 2.7 10}
\whitemark{20 0
20 20 
2.7 10}
\RTX{$\,\,P$}{20 0}
\RTX{$\,\,Q$}{20 20}
\LTX{$P'\,\,$}{2.7 10}
\LTX{$Q'\,\,$}{20 -1}
\RTX{$n=6$}{30 10}
%
\llcoords{-20 -160}
\PSline{20 0 20 20 12 3 25 10}\setdash{5\PSlinewidth}
\PSline{25 10 20 0}\nodashes
\whitemark{20 0
20 20 
12 3 25 10}
\RTX{$\,\,P$}{20 -1}
\RTX{$\,\,Q$}{20 20}
\LTX{$P'\,\,$}{12 3}
\RTX{$\,Q'$}{25 13}
\RTX{$n>6$}{30 10}
\endPSpicture


\Fig philip-19
\PSunit=1,25truemm
%AT \PSpicture{68\PSunit}{46\PSunit}
\PSpicture{68\PSunit}{48\PSunit}
\def\rLL{\PS{gsave 8 rotate}\LL\PS{180 rotate}\LL\PS{grestore}}
\llcoords{-34  -11}
\CTX{$W_2$}{0 -2}\CTX{Figur 19}{0 -7}
\llcoords{-14 -24}\rLL
  \PSline{-18 -8 12 -8}\PSline{-12 8 18 8}
  \PSline{-17.3 -8.8 -10.7  8.8}
  \PSline{-3.3 -8.8 3.3  8.8}
  \PSline{10.7 -8.8 17.3  8.8}
\PSmark{-17 -8 -14 0 -11 8 -3 -8 0 0 3 8 11 -8 14 0 17 8}
%Add (28 0)
\llcoords{-42 -24}\rLL
  \PSline{-18 -8 12 -8}\PSline{-12 8 18 8}
  \PSline{-17.3 -8.8 -10.7  8.8}
  \PSline{-3.3 -8.8 3.3  8.8}
  \PSline{10.7 -8.8 17.3  8.8}
\PSmark{-17 -8 -14 0 -11 8 -3 -8 0 0 3 8 11 -8 14 0 17 8}
%Add (6 16)
\llcoords{-20 -40}\rLL
  \PSline{-18 -8 12 -8}\PSline{-12 8 18 8}
  \PSline{-17.3 -8.8 -10.7  8.8}
  \PSline{-3.3 -8.8 3.3  8.8}
  \PSline{10.7 -8.8 17.3  8.8}
\PSmark{-17 -8 -14 0 -11 8 -3 -8 0 0 3 8 11 -8 14 0 17 8}
%Add (34 16)
\llcoords{-48 -40}\rLL
  \PSline{-18 -8 12 -8}\PSline{-12 8 18 8}
  \PSline{-17.3 -8.8 -10.7  8.8}
  \PSline{-3.3 -8.8 3.3  8.8}
  \PSline{10.7 -8.8 17.3  8.8}
\PSmark{-17 -8 -14 0 -11 8 -3 -8 0 0 3 8 11 -8 14 0 17 8}
\endPSpicture


\Fig philip-20
%the drawing is not centered:
\PSunit=1,25truemm
%AT \PSpicture{60\PSunit}{56\PSunit}
\PSpicture{56\PSunit}{54\PSunit}
\def\rLL#1{\PS{gsave #1 rotate}%
   \PSline{0 0 10 0}\PS{15 rotate}\nomarks
  \PS{gsave 0.8 0.8 scale}\LL\PS{grestore}\putPSmarks
   \PS{45 rotate}\PSline{0 0 10 0}\PS{grestore}} 
\llcoords{-35  -15}
\CTX{$W_3$}{-6 -5}\CTX{Figur 20}{-6 -10}
\llcoords{-20 -25}
  \rLL{60}\rLL{180}\rLL{300}
% Add (15 8.66)
\llcoords{-35 -33.66}
  \rLL{60}\rLL{180}\rLL{300}
% Add (15 -8.66)
\llcoords{-35 -16.34}
  \rLL{60}
% Add (30 0):
\llcoords{-50 -25}
  \rLL{60}\rLL{180}
% Add (0 17.3205
\llcoords{-20 -42.3205}
  \rLL{60}\rLL{180}\rLL{300}
   %Erase part of it:
   {\def\stroke{\PS{gsave 1 setgray fill grestore}}
    \nomarks\PScline{-4 8.66 4 8.66 4 15 -4 15}}
% Add (15 25.9807)
\llcoords{-35 -50.9807}
  \rLL{180}\rLL{300}
% Add (-15 8.66)
\llcoords{-5 -33.66}
  \rLL{300}\rLL{60}\PSline{-5 8.66 0 17.3205}
% Add (30 17.3205
\llcoords{-50 -42.3205}
  \rLL{180}\PSline{-5 8.66 5 -8.66}
% Add (0 -17.3205)
\llcoords{-20 -7.6795}
  \rLL{60}
   %Erase part of it:
   {\def\stroke{\PS{gsave 1 setgray fill grestore}}
    \nomarks\PScline{-5 8 5 8 5 -1 -5 -1}}
%
\llcoords{-5 -50.9807}
  \rLL{300}
% Add (-15 -8.66)
\llcoords{-5 -16.34}
\rLL{60}\PSline{-5 8.66 0 17.3205}
\PSline{0 0 5 8.66}\PSline{0 0 10 0}\PSline{20 0 40 0}
\endPSpicture


\Fig philip-21
\PSunit=1,25truemm
\PSpicture{50\PSunit}{65\PSunit}
\def\rLL{\PS{gsave 30 rotate}\LL
  \PS{90 rotate}\LL
\PS{90 rotate}\LL
\PS{90 rotate}\LL\PS{grestore}}
\llcoords{-25  -15}
\CTX{$W_4$}{0 -8}\CTX{Figur 21}{0 -13}
\llcoords{-13 -27}\rLL
  \PSline{-13 -12 13 -12}
  \PSline{-13 -0 13 -0}
  \PSline{-13 12 13 12}
  \PSline{-12 -13 -12 13}
  \PSline{0 -13 -0 13}
  \PSline{12 -13 12 13}
\PSmark{-12 -12 0 -12 12 -12 -12 0 0 0 12 0 -12 12 0 12 12 12}
\llcoords{-37 -27}\rLL
  \PSline{-13 -12 13 -12}
  \PSline{-13 -0 13 -0}
  \PSline{-13 12 13 12}
  \PSline{-12 -13 -12 13}
  \PSline{0 -13 -0 13}
  \PSline{12 -13 12 13}
\PSmark{-12 -12 0 -12 12 -12 -12 0 0 0 12 0 -12 12 0 12 12 12}
\llcoords{-13 -51}\rLL
  \PSline{-13 -12 13 -12}
  \PSline{-13 -0 13 -0}
  \PSline{-13 12 13 12}
  \PSline{-12 -13 -12 13}
  \PSline{0 -13 -0 13}
  \PSline{12 -13 12 13}
\PSmark{-12 -12 0 -12 12 -12 -12 0 0 0 12 0 -12 12 0 12 12 12}
\llcoords{-37 -51}\rLL
  \PSline{-13 -12 13 -12}
  \PSline{-13 -0 13 -0}
  \PSline{-13 12 13 12}
  \PSline{-12 -13 -12 13}
  \PSline{0 -13 -0 13}
  \PSline{12 -13 12 13}
\PSmark{-12 -12 0 -12 12 -12 -12 0 0 0 12 0 -12 12 0 12 12 12}
\endPSpicture



\Fig philip-22
\PSunit=2truemm
\PSpicture{35\PSunit}{38\PSunit}
\def\rLL#1{\PS{gsave #1 rotate}% 
%    \PSline{0 0 17.3205 0}\PSmark{8.66 0}
\PSline{0 0 8.66 0}
   \PS{30 rotate}\PSline{0 0 10 0}\nomarks
   \Gg
   \PS{grestore}\putPSmarks} 
\putPSmarks
\llcoords{-17.3205 0}\CTX{$W_6$}{0 4}\CTX{Figur 22}{0 1}
\llcoords{-8.66 -7}
  \rLL{0}\rLL{60}\rLL{120}
%Add (17.3205 0)
\llcoords{-25.9805 -7}
  \rLL{0}\rLL{60}\rLL{120}
%Add 8.66 15
\llcoords{-17.3205 -22}
  \rLL{0}\rLL{60}\rLL{120}\rLL{180}\rLL{240}\rLL{300}
\llcoords{-34.641 -22}
  \rLL{120}\rLL{180}\rLL{240}
\llcoords{-25.9805 -37}
   \rLL{180}\rLL{240}\rLL{300}
\llcoords{-8.66 -37}
  \rLL{240}\rLL{300}
\llcoords{0 -22}
  \rLL{0}\rLL{60}\rLL{300}
\llcoords{0 -7}
\PSline{0 0 34.641 0}\PSline{0 5 0 15}
\PSline{0 25 8.66 30}\PSline{0 30 34.641 30}
\PSline{34.641 25 34.641 15}
\endPSpicture

\Fig philip-23
%Drawing not centered
\PSunit=1,25truemm
\PSpicture{95\PSunit}{55\PSunit}
\def\rLL{\PScline{-2 0 12 7 26 0 12 -7}\PSline{-2 0 26 0}\LL\GG}
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%
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\llcoords{-49 -15}\LL\PS{gsave 180 rotate}\GG\PS{grestore}
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%
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\Fig philip-25
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\Fig philip-26
%Not quit centered:
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\llcoords{-1 -16}\rLL{0}
\llcoords{-21 -16}\rLL{0}
\llcoords{-41 -16}\rLL{0}
%Add 20(cos 2v, sin 2v)=20(0.28 0.96) = 5.6 19.2
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\Fig philip-27
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%
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\llcoords{-32 -43}\rLL{180}
\llcoords{-64 -27}\rLL{180}
\llcoords{-64 -43}\rLL{180}
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\Fig philip-28
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\CTX{Figur 28}{24 4}\CTX{$W_2^{\,3}$}{24 12}
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\llcoords{-16 -43}\rGG{180} %13
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\Fig philip-29
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\llcoords{-16 -43}\rGG{180} %13
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\llcoords{-16 -37}\rGG{0}   %22
\llcoords{-32 -49}\rLL{180} %23
\llcoords{-48 -19}\rGG{180} %31
\llcoords{-32 -31}\rLL{0}     %32
\llcoords{-48 -43}\rGG{180} %33
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\Fig roedseth-1
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%15\sqrt 2=1500*1,41421=21.2131
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%vect1
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%vect2:  2560,66-2*2121,32=-1.681,98
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\Fig roedseth-2
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\PSarc{165 195}{0 0 1}\PSarc{250 320}{0 0 1}
%36000/17=21,177:  0.933 0.361	  
%7200/17=42,353    0.739 0.6736	  
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%4*360/17=84,71    0.0923 0.9957  
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%6*360/17-90=37,06   -0.6025 0.7980
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%
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%%0.0923 -0.9957   009,23+(100-9,23)/5 -99.57+99,57/5
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%
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\Fig sjoegren-1
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%cos 20=2000*0,9397=1.879,40 sin 20=2000*0,3420=684,00
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\Fig svensson-3
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\bye
\enddocument