[Arjen Markus] (19 december 2003) I intend this page for collecting a few examples to show with my "mathematical notebook". 

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'''Example: Constructing a cycloid'''
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 # Explain the construction of a cycloid
 #
 # Note:
 # We use a simple animation technique here
 #
 # Initialisation: define the procedure that takes care of drawing
 #
 @init {

    # Notes:
    # - Time must start at zero!
    # - The first time we do not want the animation
    #
    set stop 1

    proc drawCycloid {time deltt} {
       variable CNV
       variable width
       variable height
       variable radius
       variable stop

       $CNV delete all

       #
       # Draw the circle at the right position
       #
       set xcentre [expr {$time+$radius}]
       set ycentre [expr {$height-1-$radius}]
       set xleft   [expr {$xcentre-$radius}]
       set xright  [expr {$xcentre+$radius}]
       set ytop    [expr {$ycentre-$radius}] ;# Signs are correct!
       set ybottom [expr {$ycentre+$radius}]

       $CNV create oval $xleft $ytop $xright $ybottom -outline gray -width 2

       #
       # Draw the spoke
       #
       set angle [expr {$time/$radius}]
       set xend  [expr {$xcentre-$radius*sin($angle)}]
       set yend  [expr {$ycentre+$radius*cos($angle)}]

       $CNV create line $xcentre $ycentre $xend $yend -fill black

       #
       # Draw the cycloid
       #
       set t     0.0
       set xend  $radius
       set yend  [expr {$height-1}]
       while { $t <= $time } {
          set angle  [expr {$t/$radius}]
          set xbegin $xend
          set ybegin $yend
          set xend   [expr {$t+$radius-$radius*sin($angle)}]
          set yend   [expr {$ycentre+$radius*cos($angle)}]

          $CNV create line $xbegin $ybegin $xend $yend -fill black

          set t      [expr {$t+$deltt}]
       }

       #
       # Careful: we need to call this procedure from the global namespace
       #
       set time [expr {$time+$deltt}]
       if { $time < $width && $stop == 0 } {
          after 100 [list [namespace current]::drawCycloid $time $deltt]
       } else {
          set stop 0
       }
    }
 }
 <h1>Constructing a cycloid</h1>
 <p>
 (Press the Refresh button to see the construction at work)
 <p>
 @canvas 500 100 {
    set width  [$CNV cget -width]
    set height [$CNV cget -height]
    set radius [expr {$height*0.4}]
    set deltt  [expr {$width/50}]
    set time   0

    drawCycloid $time $deltt
 }
 <p>
 If you take a circle and roll it along a straight line, just as with a
 bicycle, then a fixed point on the circle (or wheel, if you like),
 follows a curve called the cycloid (see the picture)
 <p>
 The points on the cycloid can be described via these formulae:
 <pre>
    x  =  r * (t - sin(t))
    y  =  r * (1 - cos(t))

    r = radius of the circle
    t = time parameter
 </pre>
 <h1>Exercise</h1>
 Proof these equations
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'''Example: Pythagorean triples'''
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TODO

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[[
[Category Mathematics]
| [Category Education]
]]