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Geometry and the Geometer's Sketchpad Links

101 Project Ideas for The Geometer's Sketchpad
This booklet from Key Curriculum Press is full of exciting project ideas for use in the classroom or at home. The projects are designed for users with varying degrees of Sketchpad experience and cover a wide range of subject areas (Art/Animation, Triangles, Real World Modeling, Calculus, Transformations and Tessellations, Trigonometry, Fractals, and many more).
http://www.keypress.com/sketchpad/projideas/projideas.html

Algebra and Calculus Sketches
Allows the user to explore equations for lines, parabolas, and tangents using Geometer's Sketchpad.
http://mathforum.org/sum95/ruth/sketches/algcalc.sketches.html

Betweenness Theorem
If point B lies between points A and C, the sum of the distances from A to B and from B to C will equal the distance from A to C. This site explores a geometric representation of this theorem.
http://www.wpunj.edu/icip/itm/Lessonpl/sketch/coutts/coutts.html

Buffon's Needle
Buffon’s Needle is a problem first posed by the French naturalist and mathematician, the Comte de Buffon (1707-1788). Consider a plane, ruled with equi-distant parallel lines, where the distance between the lines is D. A needle of length L is tossed onto the plane. What is the probability that the needle intersects one or more lines? The original problem had the condition that L < D, but in this version, we will also consider the probability where D > L.
http://www.nas.com/~kunkel/buffon/buffon.htm

Chase Four Sketches
Investigation: Each of four ants located in the plane crawls continuously towards the next ant. What paths do the ants describe?
http://mathforum.org/sketchpad/chase.html

Chinese Handcuffs
The sketch gets this name because it resembles a little bauble that used to be seen handed out as a prize at carnivals. It might be more interesting to let the students do their own investigations. There are applications for geometry, trigonometry, and probability.
http://www.nas.com/~kunkel/cuffs/cuffs.htm

Classification of Patterns
This site contains materials about symmetry and classification of repeating patterns for students in grades 7 - 10. The authors see them being used as either an introduction or as a review. It is meant to be a classroom-ready source of information.
http://www.geom.umn.edu/~demo5337/Group1/

Concurrency Points in a Triangle
This site contains explorations involving triangles. Start your journey with the section called Triangle Investigations, then pick one of the other topics the next time you visit this site.
http://www.geom.umn.edu/~demo5337/Group2/

Curves
When the first version of Sketchpad was released, you didn't see many constructions involving curves other than circles. With Version 2, people did a lot of curve stitching and curved locus tracing. With Version 3, you have arcs, and you have dynamic loci. These, combined with dynamic plotting, make for a lot of wonderful curve construction!
http://mathforum.org/sketchpad/gsp.gallery/curves/curves.html

The Dance of the Simson Lines
Dual to the notion of three lines coming together in one point is the notion of three points all lying on just one line. One of the most famous examples of such an occurrence is the Simson Line.
http://www.geom.umn.edu:80/~burgiel/Alan/outline/node3.html

Discovering Geometry Newsletter
Key Curriculum Discovering Geometry newsletter is published twice a year. In addition to providing lots of useful information and helpful teaching techniques for Discovering Geometry and The Geometer's Sketchpad®, it is an excellent resource of rich teaching ideas for anyone interested in geometry and technology education.
http://www.keypress.com/pdc/Cat_PDC_DGnews.html

Dueling Pinwheels
Dazzle your students with this animated introductory transformations exercise.
http://math.rice.edu/~lanius/misc/

Elliptic Geometry Drawing Tools
This web site explores an elliptic geometry sample sketch. The sketch shows a triangle drawn on the surface of a sphere. Use this simple sketch in conjunction with the posted scripts.
http://mathforum.org/sketchpad/maa96/findell/index.html

Escher’s World
Escher's World is a math studio where the student asks the questions and they use computer tools to answer them, while exploring important geometric and artistic ideas. The Escher's World project shows how people learn mathematics through computer-aided design.
http://el.www.media.mit.edu/groups/el/projects/EW/

Exponential Sketch
This is a dynamic model of the exponential function where the base of the exponential function is equal to the ratio of length of two line segments. The equation is also dynamically updated.
http://mathforum.org/sketchpad/exponential.html

Extended Concurrencies of a Triangle
Exploration: Take any triangle ABC. Construct equilateral triangles externally on each side and locate the center of each equilateral triangle. Label these centers A', B', and C' for the triangle centers opposite angles A, B, and C. Construct lines AA', BB', and CC'. (Note: Use lines rather than segments.) Observe.
http://jwilson.coe.uga.edu/emt669/essays/concurrent.html

Finding the Triangle of Smallest Perimeter
Find the inscribed triangle of minimum perimeter for a given triangle ABC. This problem is ideal for demonstrating the power of a dynamic geometry program like the Geometer's Sketchpad. The solution utilizes an "unfolding" technique by taking reflections about the sides of the given triangle ABC.
http://mathforum.org/sketchpad/maa96/parks/index.html

First Steps
If three points determine a triangle, then four points determine four triangles! This web site describes some discovery exercises (thanks to Allan L. Edmonds and Charles Livingston of Indiana University) using four such points, all lying on a circle.
http://www.geom.umn.edu:80/~burgiel/Alan/outline/node2.html

Fractal Tree
An activity whose goal is a construction of a fractal tree whose branching angle and ratio of dilation can be dynamically changed. http://mathforum.org/sketchpad/gsp.activities/fractal1.html

The Geometer's Sketchpad Activity Center
Here you will find exciting interactive lessons for The Geometer's Sketchpad.
http://mathforum.org/sketchpad/gsp.activities/home.html

Geometry In Art
This project presents four areas in which geometry and art are tied together. The purpose of the project is to demonstrate some applications of technology in the geometry classroom. It is intended to be used by teachers but was also written for use by students in grades 7 - Ph.D.
http://www.geom.umn.edu/~demo5337/Group4/

The Golden Ratio
The purpose of this web page is to provide an introduction to the Golden Ratio and Fibonacci Sequence. Instead of simply supplying definitions and asking the student to engage in mindless practice, our idea is to have the student work through several activities to discover the applications of the Golden Ratio and Fibonacci Sequence.
http://www.geom.umn.edu/~demo5337/s97b/

Introductory Questions for Geometer's Sketchpad
A set of geometry problems using Sketchpad. Although not difficult, the problems are not just a set of instructions leading you to the answer.
http://www.geom.umn.edu/~math5337/gsp/

Introduction to Symmetries
These materials were developed at the Geometry Center and are used for teaching pre- and in-service teachers of high-school geometry who are interested in using technology in their classrooms.
http://www.geom.umn.edu/~math5337/Symmetry/

Lesson Plans Using GSP for Grades 6-8
This site contains overviews of units and objectives by grade, lesson plans by grade, and GSP performance based unit tests for each grade.
http://www.math.byu.edu/~lfrancis/readings302/GSP/GSPLessonPl.html

Mark Dabbs' Geometer's Sketchpad Files and Scripts
Here you will find a large collection of interactive sketches and scripts using The Geometer's Sketchpad. All of the files are downloadable, and need Sketchpad to be opened.
Mark Dabbs' Geometer's Sketchpad Files and Scripts

Maximum Volume & Area with the Geometer's Sketchpad
Common in calculus and advanced algebra texts for years, these well known optimization problems now appear in several high school geometry texts, as interesting explorations that integrate measurement, model building, polynomial functions and use of the graphing calculator. The sketches listed provide another facet through which to dynamically view and explore this rich genre of problems.
http://mathforum.org/sketchpad/maxvol/index.html

Modeling a Ferris Wheel
Physical devices can be modeled using dynamic geometry. A vital tool for moving objects around in the model is the isometries, or distance-preserving transformations. This model of a Ferris wheel provides a good example.
http://mathforum.org/dynamic/jrk/ferris_dir/

Monge's Theorem
This lab uses Sketchpad to explore the geometry of circles, culminating in the discovery of a famous result of the nineteenth century called Monge's Theorem. It then proceeds to outline a proof of the theorem using dilations.
http://www.geom.umn.edu/~math5337/monge/

Morphing in Sketchpad
In this activity, we're going to turn an ordinary polygon into a circle. Doesn't sound very interesting when it's described like that, but what we're really going to do is "morph" a polygon onto a circle, which means create an image that at one point is a polygon, then becomes a circle.
http://mathforum.org/~annie/gsp.handouts/morphing/

Napoleon's Theorem Explorations
Draw a triangle. On the edges of the triangle, construct equilateral triangles. Find the centroids of the equilateral triangles and connect them to form a new triangle.
http://mathforum.org/ces95/napoleon.html

Peaucellier's Linkage
Peaucellier's Linkage is a simple toy that could be constructed using straight rods attached together. The lab gives instructions for constructing and studying the linkage in Sketchpad. It then uses Sketchpad to explore the geometric properties of inversion, allowing the reader to discover how the linkage works.
http://www.geom.umn.edu/~math5337/linkage/

Physics Simulations
This site explores Sketchpad as a powerful tool for modeling situations from physics, including motion, optics, vectors, electrostatics, simple harmonic motion, and waves.
http://mathforum.org/sketchpad/gsp.gallery/physics/physics.html

The Poincaré disk
This directory contains a base sketch and tools for interactive investigation of hyperbolic geometry using the Poincaré disk model. For example, one can easily discover that the construction of the incircle of a triangle that works in the Euclidean plane also works in the hyperbolic plane.
http://mathforum.org/sketchpad/gsp.gallery/poincare/poincare.html

Random Walk
A robot's processor has gone haywire so that the robot cannot walk in a straight line. Each time the robot goes to take a step, it chooses a direction completely at random. Each step it takes has the same length. We are interested in a model that will show how far the robot gets on the average after a given number of steps.
http://mathforum.org/sketchpad/gsp.activities/random1.html

Reuleaux Triangle
It is not a circle, but it has constant width. Study the properties of this figure with interactive animated sketches.
http://www.nas.com/~kunkel/reuleaux/reuleaux.htm

The Simple But Amazing Triangle
If you were to throw a handful of pick-up sticks down onto the floor, you might notice that no three of them intersected each other in exactly one point. So if we were to construct three lines in the plane, only to find out that these lines all came together in one spot, then that would be somewhat remarkable!
http://www.geom.umn.edu:80/~burgiel/Alan/outline/node1.html

Sketchpad for Little Ones
This website has geometry activities that can be used with elementary school students. Topics span several mathematics concepts such as: lines, rays, segments, angles, area, perimeter, circles, etc.
http://mathforum.org/sketchpad/littleones/

Sketchpad Gallery
Many physics and calculus related sketches (e.g., Trapezoidal Rule, Simpson’s Rule, Law of Cosines, etc.)
http://www.nas.com/~kunkel/math.htm

A Slice of Pi
This project studies how pi has been computed throughout history, including current connections between pi and geometry. A first-time viewer should start with the "Historical Overview", which ties the project together as a timeline about pi.
http://www.geom.umn.edu/~huberty/math5337/groupe/

Symmetry
This site is designed for students and teachers interested in exploring symmetry (grades 7-12). It contains lesson plans, definitions, examples, activities, and links to other web sites. There is also some extension activities for those who would like a challenge.
http://www.geom.umn.edu/~demo5337/s97a/

Tessellations
A tutorial to create Escher-like tessellations using The Geometer’s Sketchpad.
http://mathforum.org/sum95/suzanne/tess.gsp.tutorial.html

Triangles and Evolutes
The Geometer's Sketchpad provides an excellent tool to study Plane Geometry by studying geometric objects rather than the point. Polygons, and triangles in particular, reveal much structure. After delving into the above constructions it is natural to ask if there are other revealing families of lines associated to such objects. Perhaps one of the most famous lines of all is Pascal's Line.
http://www.geom.umn.edu:80/~burgiel/Alan/outline/node4.html

Vectors
The sketches and pictures are intended as supplementary material to help students in their first encounter with vectors.
http://mathforum.org/~klotz/Vectors/vectors.html

A Visual Dictionary of Special Plane Curves
The goal of the project is to produce materials that demonstrate interesting properties of plane curves visually. Many concepts or properties of plane curves such as cusp, tangent, evolute, involute, envelope, are more readily explained by an illustration or animation. Overall, this project is designed to educate and entertain.
http://xahlee.org/SpecialPlaneCurves_dir/specialPlaneCurves.html

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Last modified on February 19, 2004