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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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