Differences between revisions 2 and 10 (spanning 8 versions)

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   1 def syntax(highlight):
   2     print "on"
   3     return None

   1   public void main(String[] args]){
   2      System.out.println("Hello world!");
   3   }

Linking

HelpOnEditing InterWiki

http://moinmoin.wikiwikiweb.de/ [http://www.python.org/ Python]

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Glossary

Term: Definition

Drawing

drawing:mytest

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A graphical illustration

x=var('x') @interact def _(x = slider(-7/10,7/10,1/20,1/2)):

html('<h3>A graphical illustration of $\lim_{x -> 0} \sin(x)/x =1$</h3>') html('Below is a unit circle, so the length of the <font color=red>red line</font> is |sin(x)|') html('and the length of the <font color=blue>blue line</font> is |tan(x)| where x is the length of the arc.') html('is |sin(x)| and |tan(x)|, respectively where x is length of the arc.') html('From the picture, we see that |sin(x)| $\le$ |x| $\le$ |tan(x)|') html('and it follows easily from this that') html('cos(x) $\le$ sin(x)/x $\le$ 1 when x is near 0.') html('As $\lim_{x ->0} \cos(x) =1$, we conclude that $\lim_{x -> 0} \sin(x)/x =1$.') if not (x == 0):
- pretty_print("sin(x)/x = "+str(sin(float(x))/float(x)))
elif x == 0:
- pretty_print("The limit of sin(x)/x as x tends to 0 is 1")
C=circle((0,0),1, rgbcolor='black') mvp = (cos(x),sin(x));tpt = (1, tan(x)) p1 = point(mvp, pointsize=30, rgbcolor='red'); p2 = point((1,0), pointsize=30, rgbcolor='red') line1 = line([(0,0),tpt], rgbcolor='black'); line2 = line([(cos(x),0),mvp], rgbcolor='red') line3 = line([(0,0),(1,0)], rgbcolor='black'); line4 = line([(1,0),tpt], rgbcolor='blue') result = C+p1+p2+line1+line2+line3+line4 result.show(aspect_ratio=1, figsize=[3,3], axes=False)

-  ⇤ ← Revision 2 as of 2007-10-12 22:35:12 → 
  Size: 1408
  Editor: SandorKovacs
  Comment:
+   ← Revision 10 as of 2008-09-28 20:42:21 → ⇥
  Size: 2717
  Editor: pong
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+== A graphical illustration ==

x=var('x')
@interact
def _(x = slider(-7/10,7/10,1/20,1/2)):
    html('<h3>A graphical illustration of $\lim_{x -> 0} \sin(x)/x =1$</h3>')
    html('Below is a unit circle, so the length of the <font color=red>red line</font> is |sin(x)|')
    html('and the length of the <font color=blue>blue line</font> is |tan(x)| where x is the length of the arc.') 
    html('is |sin(x)| and |tan(x)|, respectively where x is length of the arc.')
    html('From the picture, we see that |sin(x)| $\le$ |x| $\le$ |tan(x)|')
    html('and it follows easily from this that')
    html('cos(x) $\le$ sin(x)/x $\le$ 1 when x is near 0.')
    html('As $\lim_{x ->0} \cos(x) =1$, we conclude that $\lim_{x -> 0} \sin(x)/x =1$.')
    if not (x == 0):
        pretty_print("sin(x)/x = "+str(sin(float(x))/float(x)))
    elif x == 0:
        pretty_print("The limit of sin(x)/x as x tends to 0 is 1")
    C=circle((0,0),1, rgbcolor='black')
    mvp = (cos(x),sin(x));tpt = (1, tan(x))
    p1 = point(mvp, pointsize=30, rgbcolor='red'); p2 = point((1,0), pointsize=30, rgbcolor='red')
    line1 = line([(0,0),tpt], rgbcolor='black'); line2 = line([(cos(x),0),mvp], rgbcolor='red') 
    line3 = line([(0,0),(1,0)], rgbcolor='black'); line4 = line([(1,0),tpt], rgbcolor='blue')
    result = C+p1+p2+line1+line2+line3+line4
    result.show(aspect_ratio=1, figsize=[3,3], axes=False)

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