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27 July 1998 Vol. 3, No. 30 THE MATH FORUM INTERNET NEWS Project Interactivate | JavaSketchpad | Geometry Software/Theory PROJECT INTERACTIVATE - The Shodor Foundation http://www.shodor.org/interactivate/ 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: http://www.shodor.org/interactivate/lessons/ 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: http://www.shodor.org/interactivate/discussions/ Applets that provide computer simulations present opportunities for group work as well as individual investigation. http://www.shodor.org/interactivate/applets/ 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 http://www.keypress.com/sketchpad/java_gsp/ 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 contexts. See the JavaSketchpad demo gallery for some examples of JavaSketchpad in use. http://www.keypress.com/sketchpad/java_gsp/gallery.html \|/ JavaGSP! - Annie Fetter http://mathforum.org/workshops/sum98/java.gsp.explain.html 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. -|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|- GEOMETRY DISCUSSIONS: SOFTWARE AND THEORY GSP INTERSECTION OF A SEGMENT AND A LINE Dave Wilson and Nick Jackiw A geometry-software-dynamic discussion http://mathforum.org/epigone/geometry-software-dynamic/zouyybrel http://mathforum.org/epigone/geometry-software-dynamic/shunkunho http://mathforum.org/epigone/geometry-software-dynamic/smolstugou "... 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 questions: (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) http://www-cabri.imag.fr/Preuve/ "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. -|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|-\-/-|- CHECK OUT OUR WEB SITE: The Math Forum http://mathforum.org/ Ask Dr. Math http://mathforum.org/dr.math/ Problems of the Week http://mathforum.org/students/ Internet Resources http://mathforum.org/~steve/ Join the Math Forum http://mathforum.org/join.forum.html Send comments to the Math Forum Internet Newsletter editors _o \o_ __| \ / |__ o _ o/ \o/ __|- __/ \__/o \o | o/ o/__/ /\ /| | \ \ / \ / \ /o\ / \ / \ / | / \ / \ |

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