Catenaries of Constant Length

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  \put(0, 0){\vector(0, 1){1.15}}
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  % qbezier P1=(0.0/0.0) m1=0.0 
  %         P2=(0.2998/0.905) m2=10.0
  \qbezier(0.0,0.0)(0.2093,0.0)(0.2998,0.905)
  % qbezier P1=(0.0/0.0) m1=0.0 
  %         P2=(0.4625/0.8198) m2=5.0
  \qbezier(0.0,0.0)(0.2985,0.0)(0.4625,0.8198)
  % qbezier P1=(0.0/0.0) m1=0.0 
  %         P2=(0.5757/0.744) m2=3.3333
  \qbezier(0.0,0.0)(0.3525,0.0)(0.5757,0.744)
  % qbezier P1=(0.0/0.0) m1=0.0 
  %         P2=(0.6589/0.677) m2=2.5
  \qbezier(0.0,0.0)(0.3881,0.0)(0.6589,0.677)
  % qbezier P1=(0.0/0.0) m1=0.0 
  %         P2=(0.7218/0.618) m2=2.0
  \qbezier(0.0,0.0)(0.4128,0.0)(0.7218,0.618)
  % qbezier P1=(0.0/0.0) m1=0.0 
  %         P2=(0.7703/0.5662) m2=1.6667
  \qbezier(0.0,0.0)(0.4306,0.0)(0.7703,0.5662)
  % qbezier P1=(0.0/0.0) m1=0.0 
  %         P2=(0.8081/0.5207) m2=1.4286
  \qbezier(0.0,0.0)(0.4436,0.0)(0.8081,0.5207)
  % qbezier P1=(0.0/0.0) m1=0.0 
  %         P2=(0.8381/0.4806) m2=1.25
  \qbezier(0.0,0.0)(0.4536,0.0)(0.8381,0.4806)
  % qbezier P1=(0.0/0.0) m1=0.0 
  %         P2=(0.862/0.4454) m2=1.1111
  \qbezier(0.0,0.0)(0.4611,0.0)(0.862,0.4454)
  % qbezier P1=(0.0/0.0) m1=0.0 
  %         P2=(0.8814/0.4142) m2=1.0
  \qbezier(0.0,0.0)(0.4672,0.0)(0.8814,0.4142)
  % qbezier P1=(0.0/0.0) m1=0.0 
  %         P2=(0.8972/0.3866) m2=0.9091
  \qbezier(0.0,0.0)(0.4719,0.0)(0.8972,0.3866)
  % qbezier P1=(0.0/0.0) m1=0.0 
  %         P2=(0.9102/0.362) m2=0.8333
  \qbezier(0.0,0.0)(0.4758,0.0)(0.9102,0.362)
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  \put(0.6,    0.74){$(u,v)$}
  \put(0.5,    0.05){$L$}
  \put(0.18,    0.45){$L$}
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  \put(1, .06){\makebox(0, 0){$L$}}
  \put(-.02, 1){\line(1, 0){.04}}
  \put(.03, .98){$L$}
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