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  1. Dynamic software--What is available? (David Boschetto) 11/04/96
    I am aware of Cabri Geometry, Geometer's Sketchpad, and Geometric Supposer. Are there any other affordable dynamic software programs appropriate for a high school geometry lab? [Geometry Expert, Calques2, Euklid]

  2. Poincare Disk Tools (Marlene Dwyer) 09/20/96
    Does Cabri have anything similar to GSP's Poincare tools? ["Explorations of the Poincare Disk Model and the Poincare Half-Plane Using Geometer's Sketchpad"]

  3. Dynamic Geometry and Algebra (Gilles G. Jobin) 08/29/96
    Is it possible to use a package like GSP to do algebra?

  4. 3D Dynamic Geometry Software (Safwan Qasem) 08/03/96
    Seeking information about 3D dynamic geometry software. [Surfaces]

  5. Let's get started - Dynamic Geometry Software (Mike Davidson) 07/29/96
    Seeking anyone's opinions on Geometer's Sketchpad, Cabri Geometry, or both.

  6. ICME 8 / TG19 Last Call (Nicolas Balacheff) 02/07/96
    8th International Congress on Mathematical Education (ICME) Sevilla (Spain), July 14 - 21, 1996. Presentation of Topic Group 19: "Computer-based interactive learning environments" and invitation for submission of short abstracts or relevant suggestions by e-mail.


  1. New Theorem related to Euler line? (Gilles G. Jobin) 11/30/95
    Let ABC be any triangle. Let H be the orthocenter of triangle ABC, let N be the centroid of triangle ABC, let T be the circumcenter O of triangle ABC. Then m(NH)/m(TH) = 2/3. This is an incredible result. Does anyone know if this is a discovery? Or was this theorem proved long ago? and by whom? Both the existence of the Euler segment (through H, N and T) and the ratio of distances are truly amazing results, though they are far from new...

  2. Curious triangle fact (Peter F. Ash) 10/29/95
    I saw the following problem posed on the math.sci newsgroup a while back: Given any triangle ABC, erect isosceles triangles (ABC', BCA', CAB') on each side of ABC, pointing outward and so that |A'| = |B'| = |C'| = 120 degrees. Then A'B'C' is an equilateral triangle. I had never seen this before, and wasn't sure I believed it, but after playing around with Geometer's Sketchpad for a while became less skeptical... I still have no idea WHY the proposition is true. Can anyone supply some geometric insight? [proof using three rotations / Napoleon triangle / M.C. Escher]

  3. abraCAdaBRI excerpts (Eric Sasson) 10/27/95
    The Geometry Forum has posted the first of what will be a monthly feature devoted to writing about dynamic geometry software. The publishers of the French journal "abraCAdaBRI" are allowing us to electronically distribute articles from their bimonthly magazine. These articles are written in the French language, and are focused on explorations with the software Cabri-Geometre.

  4. FunTiles (Doris Schattschneider) 09/26/95
    Daniel Huson has developed for systematically generating and interactively manipulating periodic 2-dimensional tilings of the plane, sphere, and hyperbolic plane, called FunTiles. In a way, FunTiles is similar to RepTiles, the Macintosh program he wrote with Olaf Delgado for doing 2-dimensional euclidean tilings. FunTiles takes as input a Delaney symbol and produces a picture of the encoded tiling, which one can then manipulate. The program comes with a number of files containing Delaney symbols of certain tilings, together with a number of programs for systematically generating Delaney symbols - e.g. the program orb2fund produces all possible fundamental tilings for a given 2-dimensional symmetry group.

  5. Probability/Geometry question (Nicholas R. Jackiw) 09/13/95
    Consider a robot arm composed of n rigid segments, each of length r, connected by (n-1) joints which can rotate 360 degrees in the plane. At one end of the arm is a shoulder joint (which can also rotate, but is at a fixed location in the plane---call it the origin), at the other, a hand. Fooling around in Sketchpad, Bill Finzer and I were examining the distribution of locations for the robot's hand, given random settings of each of the joints... Can anyone suggest ways of thinking about these problems geometrically?

  6. Can Sketchpad construct a pentacle? (Gary Tupper) 08/15/95
    A query for GSP masters: can a pentacle be constructed? (5-pointed star) with GSP?

  7. Non-Euclidean Geometer's Sketchpad? (Nicholas R. Jackiw) 08/15/95
    I'm thinking of a project I've been meaning to do ever since grad school, creating a "Non-Euclidean Geometer's Sketchpad." Am I out of my mind?

  8. Can Sketchpad draw these figures? (gao s) 08/07/95
    I am not sure whether Sketch Pad can draw the following figures. I tried but failed. (1) Draw a square ABCD such that points A and B are on a given circle O1 and points C and D are on a given circle O2. We assume that circle O1 has different radius with circle O2. (2) Draw a line segment such that it has a fixed length, passes through a fixed point, and has its two endpoints on the two sides of a fixed angle respectively.

  9. No decimals in Translate boxes? (Gilles G. Jobin) 07/28/95
    Is it normal that the Translate dialog box (from the translate menu) does only accept integers (and NOT decimals numbers) as quantities in Horiz and Vertic. components? (I use Windows SkP v.3.0)

  10. Manufacturer of Sketchpad (Anonymous) 07/28/95
    Can someone tell me how to get in touch with the manufacturer of Sketchpad? [Key Curriculum Press - address, telephone, Web site]

  11. Conic sections (Stanley Rabinowitz) 07/27/95
    What is the latest version of Sketchpad on the Macintosh and does it support construction of conic sections? [Sketchpad 3 is able to produce graphics like parabolas, as it support analytic geometry / Cabri can do these things. I was just wondering when GSP will have this feature.]

  12. 2 Sketchpad Challenges (Gilles G. Jobin) 07/23/95
    Challenge no.1: Let XYZ be a given angle. Let A and B be two fixed points. Find, using Sketchpad) the locus of point P such that angle APB = angle XYZ. Challenge no.2: Is it possible, with Sketchpad, to solve this kind of problem: Given: A, B and C, three fixed points. <&t;>> a square number. Find the locus of point P such that dist(AP)^2 + dist(BP)^2 + dist(CP)^2 = x.

  13. Help Me: Intersecting line and Locus points (Mike Diamond) 07/13/95
    I was working on defining a line then developing an equation (cubic) based on variables points on the X-axis (A, B, C, and X). I then took the X- component of each variable to create a function f(x) such that Ax*Xx^3+Bx*Xx^2+Cx*Xx. I then constructed the locus of point X and the equation. The cubic line is formed. Since I teach calculus, how would I come up with a dynamic intersection point from the line and the generated locus. [general strategy]

  14. ICMI 8 / TG19 () 07/11/95
    8th International Congress on Mathematical Education (ICME), Sevilla (Spain), July 14 - 21, 1996. Presentation of Topic Group 19, "Computer-based interactive learning environments" - an invitation for submission of short abstracts or relevant suggestions by e-mail.

  15. Sketchpad 3.0 Gallery (Nicholas R. Jackiw) 06/27/95
    Sketches and scripts that show some of the new features of the new version of Sketchpad (3.0). The Geometry Forum hosts the gallery at: The collection includes investigations and models in physics, statistics, and architecture, as well as many in analytic geometry and algebra.

  16. Randomization in Sketchpad 3.0 (Nicholas R. Jackiw) 05/26/95
    By Nick Jackiw, author of Sketchpad. New feature: Using the command-line interface in Sketchpad 3.0, you can have the program automatically choose "new" random values for the randomly-determined components of an existing construction you've made. Also a binary post with a sketch example of using randomization to animate a construction.

  17. Cabri & Sketchpad compared; tool then object (Dave Wilson) 05/19/95
    A discussion of the relative merits of Sketchpad and Cabri, questioning whether and how students learn best, using a program that forces the choice of tool, then object, or vice versa. Explanation by the author of Sketchpad, Nick Jackiw, of the relation between the program and Mac or Windows conventional computer design.

  18. GSP scripts, Scripting in Sketchpad (Michael Thwaites) 04/19/95
    I want to make scripts that work like computer subroutines and that can be applied with the same effect under all circumstances. However, when I make scripts for GSP I often have trouble making the right intermediaries hidden. If the intermediaries coincide with other objects that existed before the script executed, sometimes the original objects get hidden. [This behavior has changed in Sketchpad 3.0.] One way to 'edit' a completed script.

  19. Measuring Arcs (Don Versteeg) 04/18/95
    How can you measure the length of the major arc on a circle created by two secant segments drawn from the same external point? I can measure the minor arc, but can't measure the major arc. [In Sketchpad, to measure a major arc, select a circle and three points and select Angle from the Measure menu.]

  20. Geometry software (Linda Reichenbach) 03/16/95
    Request for recommendations about geometry software. [Geometer's Sketchpad, Cabri / comments from Nick Jackiw, designer of Sketchpad / hyperbolic Geometer's Sketchpad]

  21. 3-D software for Windows? (Robin McLeod) 02/24/95
    Can anyone can point me towards where I might get some Windows software for sketching and moving (rotating and more general transformations)simple three-dimensional shapes? [3dScheme]

  22. Hyperbolic Sketchpad (Robin Mc Leod) 02/21/95
    Interactive mathematics and geometry. What is really needed in grades 9-12? In the first two years of college and down to about grade 6? The ultimate goal is to have a "complete" mathematical environment on a PDA. [hyperbolic Sketchpad / hyperbolic geometry / spherical Sketchpad / What would be the advantages and disadvantages, when teaching hyperbolic geometry, to having a ready-made "hyperbolic sketchpad" versus having the students building many of the tools themselves as Sketchpad scripts (or Cabri macros)? / hyperbolic geometry program SnapPea (Mac), spherical geometry package Cinderella (NeXT, developed in France]

  23. Dynamic verification (was Re: Sketchpad & Triangle Congruence) (James R. King) 01/31/95
    Another example of the limitations of calculators and computers, drawn from dynamical systems. [I think that this is an excellent example of the limitations of using computed numerical evidence, and I have no doubt that Michael used it as a springboard for a stimulating class discussion. If we are going to teach using calculators or computers, it is important to spend some time helping students understand the limits of such tools. However, I would disagree a bit from the interpretation that "Here is an example where examples betray truth."]


  1. Dirichlet polygons (F. Alexander Norman) 12/14/94
    I've been trying, without success, to use GSP to produce a grid of Dirichlet polygons, which might be described as follows: Imagine a plane upon which a number of discrete points have been scattered. Using these points as centers of circles, begin expanding the circles at a uniform rate. As two neighboring circles intersect, the points of intersection trace out a segment which becomes a side of a Dirichlet polygon. The endpoints of these segments are obtained at the common intersection of three neighboring circles. More mathematically, the Dirichlet polygon associated with one of the centers, say C, is the boundary of the region formed by points of the plane closer to C than to any other. [for three points, it is relatively easy to construct a sketch for the Dirichlet regions / sketches are in Forum archives]

  2. GSP worksheets for 9th-10th grade (Doug Sly) 12/10/94
    I am looking for someone who has rewritten some of the Geometry Sketchpad worksheets that come with the teacher package so that especially younger students (say grade 9 and grade 10) have more structure for their answers. [Some teachers have had good luck introducing Sketchpad to students through the tours that come with _Exploring Geometry_.]

  3. Modeling (Bill Finzer) 11/23/94
    What examples do you have or know about where dynamic geometry is being used outside of the geometry classroom? Is there yet any substantive support for the claim that dynamic geometry can be used for general mathematical modeling beyond the numerous sketches that have been created to show that it *could* be so used? [abstract concepts in group theory / isometries (and similarities) / symmetry and tiling]

  4. Trisecting angles in Sketchpad (J. A. Lester) 11/09/94
    Is there any way to trisect angles dynamically using Sketchpad? I am investigating Morley's theorem, and it would be useful to be able to divide an angle into ANY ratio. Something like "rotate by _Calculated_ angle" in the Transform menu would do the trick, if it existed. Is there any way to do this? [constructing an angle and tripling it? / is there some way to trisect an angle using dilations? / Sketchpad Euclidean / Mira reflection tool / directions for dividing an angle into n equal angles / trisected angle not dynamic]

  5. Most effective way to teach w/DG software? (James King) 11/08/94
    What are the topics and most successful ways you have taught using dynamic geometry software? [relationship between tessellations and isometries of the plane / hands-on from the beginning or using written instructions? / most involved and seemingly valuable learning going on when learners are constructing a sketch from scratch--solving the ``construction puzzle'' / ``Work with a partner and come up with three different ways to construct a rhombus that will stay a rhombus now matter how you drag it.'']

  6. College course on conics and inversion (Dave Wilson) 11/02/94
    Request for suggestions for a one-term course on Conics and Inversion (the students are in the 3rd year of a 4-year BEd specialising in mathematics and training to teach maths in UK secondary schools age 11-16. [paper folding by patty paper followed by reproducing using Sketchpad / exploration of inversion in a circle with accompanying GSP sketch in Forum archive]

  7. Dynamics of a point on a line and interesting triangle behavior (James King) 11/01/94
    A clump of questions surrounding the Desargues Theorem. [Lengthy response by Nick Jackiw, author of Sketchpad / . . . at its heart, "dynamic geometry" is not a well-formulated mathematical model of change, but rather a set of heuristic solutions provided by software developers and human-interface designers to the question "how would people like geometry to behave in a dynamic universe?" / circle intersection / segments and lines / random points / Activity: _The Hot Zone_ - outbreak of Ebola virus]

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The Math Forum
11 June 1997