Math Forum Internet News

Volume 3, Number 30

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27 July 1998                                   Vol. 3, No. 30


Project Interactivate | JavaSketchpad | Geometry Software/Theory

        PROJECT INTERACTIVATE - The Shodor Foundation


Project Interactivate is part of the Presidential Technology 
Initiative. The materials it develops are designed to be 
adapted easily to any NCTM Standards-based middle school 
mathematics text.

Middle school lessons cover probability, statistics, 
functions, and fractals:

Discussions on these subjects range from the probability 
of simultaneous events and introducing elementary set 
operations through Internet search, to histograms vs. bar 
graphs and recursion in fractals:

Applets that provide computer simulations present 
opportunities for group work as well as individual 
   Explorations offered by Project Interactivate include:

     - Monty Hall, three doors 
     - Stock Exchange
     - Linear Regression
     - Normal Distribution
     - Gnuplot
     - Random Function Machine
     - Hilbert Curve Generator
     - Sierpinski Carpet Generator
     - Pascal's Triangle - Multiples, Remainders
     - Fire!!
          ... and many more.

            JAVASKETCHPAD - Key Curriculum Press

JavaSketchpad is software that lets you interact with or 
publish sketches from The Geometer's Sketchpad on the Internet. 
(The Geometer's Sketchpad is a dynamic geometry exploration 
environment available for Macintosh and PC computers from 
Key Curriculum Press.) 

JavaSketchpad can be used to share geometry work with people 
who may not have desktop Sketchpad or who use computers 
(like most Unix machines) that can't access it; or to 
distribute interactive dynamic geometry activities and 
curriculum over the Internet. Advanced users, programmers, 
and mathematical researchers can use the program to add 
dynamic geometry visualization to other software or problem 

See the JavaSketchpad demo gallery for some examples of 
JavaSketchpad in use.


                  JavaGSP! - Annie Fetter

A short tutorial: everything you need to know to make your 
first JavaSketchpad page. A quick reference is followed by
other features, details, and considerations: what you need, 
what you do, what works, and what doesn't. 

Examples include Drawing a Solid and Its Net; Investigating 
Parallelograms; and Identifying Polygons.


                 Dave Wilson and Nick Jackiw

            A geometry-software-dynamic discussion

    "... GSP shows this point on the screen when
     the lines are visually not parallel... a quick 
     measurement of the angle shows that the lines 
     are 3 to 5 degrees out. GSP measures the 
     distance from the constructed midpoint to the
     the parallel line through B and reports a 
     non zero distance whilst displaying the point 
     of intersection. A bit of a contradiction."
                                            - Dave Wilson

    "Dave has put together a construction that reveals 
     an inherent limitation in floating point number 
     representation, and even... conflicts with special 
     purpose code embedded in Sketchpad that attempts 
     to circumvent these limitations in typical cases. 
     As Dave writes, the result is that, under this
     construction, Sketchpad incorrectly displays a 
     point at intersection when none theoretically 
     exists...."                          - Nick Jackiw

A discussion of floating point representation and exact
arithmetic as these affect Sketchpad construction issues. 
Nick Jackiw also poses and explores some interesting 

 (1) What is the desirability of a proving system 
     integrated with a dynamic geometry program?

 (2) Lacking proof-integrated systems, how do you handle 
     the inevitable problems of rounding in construction 
     and metric inaccuracies in the classroom?

 (3) What sort of workarounds are available?


                  The Theme of the Letter: 
             PROOF AND PERCEPTION II - Michael Otte 

         (From PREUVE PROOF PRUEBA, the Web Newsletter)


   "In the July/August issue of the Proof Newsletter,
    Michael Otte from Bielefeld offers some thoughts 
    on Geometry and mathematical proof. The newsletter 
    is open to reactions and comments."
                               - Nicolas Balacheff, Editor   

"Mathematics as a form of relational thinking is not 
 concerned with objects or their properties as such, and 
 neither with relations between objects in themselves, 
 but rather with relations between possible objects of 
 activity.... Mathematics, and in particular axiomatized 
 mathematics, considers objects only with regard to the
 consequences they might have for the process of 
 mathematical reasoning...."                - Michael Otte                  

   The goal of "The Theme of the Letter" is the stimulation
   of exchanges on current questions about the learning
   and teaching of mathematical proof. This contribution
   by Michael Otte is a continuation of text published in
   the Jan./Feb. 1998 issue of the Proof Newsletter.   


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