[GS] (20150418) Here is a method to visualize fraction thanks to its remainders in any base.

[http://wfr.tcl.tk/fichiers/images/fracdraw.jpg]

======
 # fracdraw.tcl
 # Author:      Gerard Sookahet
 # Date:        18 Apr 2015
 # Description: Fraction visualization
 # Reference: A Postmodern View of Fractions and the Reciprocals of Fermat Primes
 #            Mathematics Magazine, Vol. 73(2000), pp. 83-97

 package require Tk
  bind all <Escape> {exit}
  option add *Button.relief flat
  option add *Button.foreground white
  option add *Button.background blue
  option add *Button.width 6
  option add *Label.foreground white
  option add *Label.background black
  option add *Entry.background lightblue
  option add *Entry.relief flat
 
 proc FracDraw {{n 1} {d 13} {b 10} H} {
  .c delete all
  set r1 $n
  set d_1 [expr {$d-1}]
  for {set i 1} {$i <= $d_1} {incr i} {
     set r2 [expr {(1.0*$r1*$b/$d - $r1*$b/$d)*$d}]
     set r2r [expr {$r2 - int($r2)}]
     if {$r2r >= .5} {set r2 [expr {int($r2)+1}]}
     if {$r2r < .5}  {set r2 [expr {int($r2)}]}
     set s [expr {$H/($d-1)}]
     set x1  [expr {$r1*$s}]
     set x2  [expr {$r2*$s}]
     set y1 [expr {$H-$x1}]
     set y2 [expr {$H-$x2}]
     .c create line $x1 $y1 $x1 $y2 -width 2 -fill green
     .c create line $x1 $y2 $x2 $y2 -width 2 -fill green
     if {$r2 == $n} break
     set r1 $r2
  }
 }
 
 wm geometry . +100+1
 set H 400
 set num 1
 set den 37
 set base 35
 pack [canvas .c -width $H -height $H -bg black]
 set f1 [frame .f1 -relief flat -bg black]
 pack $f1 -fill x
 label $f1.l1 -text numerator
 entry $f1.e1 -width 4 -textvariable num
 label $f1.l2 -text denominator
 entry $f1.e2 -width 4 -textvariable den
 label $f1.l3 -text base
 entry $f1.e3 -width 4 -textvariable base
 button $f1.br -text Run -command {FracDraw $num $den $base $H}
 button $f1.bq -text Quit -command exit
 pack {*}[winfo children $f1] -side left -padx 2
======

----
[AMG]: Here's a version that uses [spinbox]es instead of [entry]s, automatically updates the screen, and has simpler rounding.  There are a few other minor tweaks.  I also added an arc visualization mode, and arcs and lines can be separately enabled or disabled.

======
# fracdraw.tcl
# Author:      Gerard Sookahet
# Date:        18 Apr 2015
# Description: Fraction visualization
# Reference: A Postmodern View of Fractions and the Reciprocals of Fermat Primes
#            Mathematics Magazine, Vol. 73(2000), pp. 83-97

package require Tk
bind all <Escape> {exit}
option add *Button.relief flat
option add *Button.foreground white
option add *Button.background blue
option add *Button.width 6
option add *Label.foreground white
option add *Label.background black
option add *Spinbox.background lightblue
option add *Spinbox.relief flat
option add *Checkbutton.foreground white
option add *Checkbutton.selectColor blue
option add *Checkbutton.background black
option add *Checkbutton.indicatorOn 0

proc FracDraw {n d b H arc line} {
   .c delete all
   set r1 $n
   set d_1 [expr {$d-1}]
   for {set i 1} {$i <= $d_1} {incr i} {
      set r2 [expr {int(($r1*$b/double($d) - $r1*$b/$d)*$d + 0.5)}]
      set s [expr {$H/($d-1)}]
      set x1 [expr {$r1*$s}]
      set x2 [expr {$r2*$s}]
      set y1 [expr {$H-$x1}]
      set y2 [expr {$H-$x2}]
      if {$line} {
         .c create line $x1 $y1 $x1 $y2 -width 2 -fill green
         .c create line $x1 $y2 $x2 $y2 -width 2 -fill green
      }
      if {$arc} {
         set xc [expr {($x1 + $x2) / 2}]
         set yc [expr {($y1 + $y2) / 2}]
         .c create arc\
               [expr {($x1 - $xc) * sqrt(2) + $xc}]\
               [expr {($y1 - $yc) * sqrt(2) + $yc}]\
               [expr {($x2 - $xc) * sqrt(2) + $xc}]\
               [expr {($y2 - $yc) * sqrt(2) + $yc}]\
               -start [expr {$r1 < $r2 ? 45 : -135}]\
               -outline blue -extent 180 -style arc -tag arc
      }
      if {$r2 == $n} break
      set r1 $r2
   }
   .c raise arc
}

wm geometry . +100+1
wm resizable . 0 0
wm title . "Fraction Visualization"
set H 400
pack [canvas .c -width $H -height $H -bg black]
set f1 [frame .f1 -relief flat -bg black]
pack $f1 -fill x
foreach {var val} {numerator 1 denominator 37 base 35} {
   set $var $val
   label $f1.$var-l -text $var
   spinbox $f1.$var-s -textvariable $var -from 1 -to 99 -width 4\
         -command {FracDraw $numerator $denominator $base $H $arc $line}
}
foreach {var val} {arc 1 line 1} {
   set $var $val
   checkbutton $f1.$var-c -text $var -variable $var\
         -command {FracDraw $numerator $denominator $base $H $arc $line}
}
FracDraw $numerator $denominator $base $H $arc $line
button $f1.quit-b -text Quit -command exit
pack {*}[winfo children $f1] -side left -padx 2
======

<<categories>>Mathematics | Graphics