The shape of any freehanging rope suspended from two points not necessarily at the same height. Basically a 'hyperbolic cos'.

Makes for interesting graphics as a 'family of curves'.

If you now understand about catenaries, try this poser. How far apart must the poles be to support a rope to match these four given dimensions??
nomainwin WindowWidth =600 WindowHeight =600 open "Catenaries" for graphics_nsb as #wg #wg "trapclose quit" #wg "size 2 ; fill lightgray" for a =0.4 to 8 step 0.1 #wg "up ; goto 0 0 ; down" s =int( a /8 *256) col$ =str$( s) +" 50 " +str$( 255 s) #wg "color "; col$ for x =6 to 6 step 0.05 y =a *cosh( x /a) #wg "goto "; 300 +50 *x; " "; 580 50 *y oldX =x oldY =y scan next x next a #wg "getbmp scr 0 0 600 600" bmpsave "scr", "catenaryFamily2.bmp" wait function cosh( x) cosh =( 1 +exp( 0 2 *x)) /( 2 * exp( 0 x)) end function sub quit h$ close #wg end end sub