[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 {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. The arc mode seems to show interesting patterns with the perimeter of the "envelope" of the arcs, and these patterns are much harder to see with the lines alone. ====== # 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 {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 ====== Screenshot of the above: [Fraction visualization screenshot] ---- [Jeff Smith] Below is an online demo using [CloudTk] <> <> ---- <> Mathematics | Graphics | Visualization