GeoGebra

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GeoGebra

• First International Conference of GeoGebra
• Linz - Austria

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A Suggestion of Using GeoGebra at College Level
The Case of Finding Arc-Length of a Curve
Dr. Tolga KABACA Dr. Mehmet BULUT
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The Relationship between programming algorithm
and mathematical thinking structure
Our task will be producing a visualization like
LowerSum and UpperSum commands of GeoGebra
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A Quick Algorithm For Constructing How to
Evaluate the Arclength of a Curve

• Plot the graph of the function f(x),
• Determine some points on the curve of f(x) for x
  a from x b if you want to evaluate the
  arc-length in the interval x ? a, b
• Constitute the line segments, attaching every
  successive point on the curve.
• Find the sum of the length of all line segments,
  which obtained at the previous step.
• When we increase the number of points on the
  curve, we will approach to the real value of
  arc-length of the curve.

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Math Language GeoGebra Language
?x (b-a)/n delta(b-a)/n
The points on curve obtained by the difference ?x pointlistSequence(a i delta, f(a i delta)), i, 0, n
Line segments attaching every successive points on the curve segmentlistSequenceSegmentElementpointlist, i, Elementpointlist, i 1, i, 1, n
arclengthSumsegmentlist,n
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Lets see the Visualization
Lets look at the mathematical perspective in
terms of GeoGebra
Lets consider on adding a module (or an easy
platform) to GeoGebra for producing quick
procedures to enrich GeoGebra Library!