Advanced Sketch Gallery
The Advanced Sketch Gallery is a collection of sketches featuring
advanced mathematical concepts, custom tools, and striking visualisations,
created by both Sketchpad developers and Sketchpad users
from around the world. They are loosely arranged by topic:
The sketches are all available for download for your personal or classroom
use, but are copyrighted by their authors; please contact the author
of a sketch if you are interested in using it in other contexts.
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Toolkits
Toolkit documents contain collections of related custom tools you
may find useful in your own explorations.
Knot Toolkit
This toolkit showcases several example knots, provides some
exercises for the reader, and supplies both a knot grid
and the tools for constructing your own knots.
Doris Schattschneider, 2002. |
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Graphing Toolkit
This set of tools and accompanying Instructional
Manual (16 page PDF file) add many capabilities of advanced
graphing calculators to Sketchpad, including finding
roots, plotting tangents, and calculating integrals.
Bjørn Felsager,
2004. |
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3D
Plotting Toolkit
This toolkit contains a template 3D coordinate system you
can reuse in other sketches, and tools and instructions for
plotting points (given 3D coordinates), segments, and curves.
Nick Jackiw, 2002. |
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3D
Invisibility Toolkit
The tools in this kit are designed for drawing dynamic models
of convex polyhedra whose faces, edges, and vertices correctly
change their appearance depending on their visibility: edges
become dashed and faces and vertices vanish when they appear
on the back side of the solid as its shape is changed by dragging
vertices or by spinning the entire image. (Tools like these
were used to construct the author's icosahedron.)
Vladimir Dubrovsky, 2004. |
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Advanced Tools
This set of advanced analytic tools from Sketchpad's
Samples collection includes calculations for tangents and
function sectors, definitions of piecewise functions, and
more.
Sketchpad Samples |
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Boolean Tools
This sketch provides a set of Boolean operators, comparison
tools, and Boolean functions, as well as detailed explanations
of how these tools were created and how you can make them
for yourself.
Scott Steketee, 2005. |
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3D Explorations
Although Sketchpad's native domain is the plane, rather than
three dimensions, many sketches construct the projection of higher-dimensional
mathematical models onto the two dimensions of the computer screen.
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3D Gallery
A collection of constructions in three dimensions, including
curves, surfaces, and various solids.
Nick Jackiw, Kate Mackrell, Paul Kunkel,
Yao Liu. |
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Icosahedron
A remarkable model of a regular icosahedron, with an
exercise page describing a construction of this Platonic
solid. The shape can be spun, lit from different angles,
and viewed from any reference point. (Constructions like
this can be made with the author's 3D
Invisibility Toolkit.)
Vladimir Dubrovsky, 2003. |
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Beyond Euclid
Sketchpad is based largely on a Euclidean view of geometry.
However, it is possible to both model other geometries within Euclidean
geometry, and to use non-Euclidean capabilities in Sketchpad (such
as the Calculator) to explore alternate geometries within Sketchpad.
This section offers some examples.
Minkowskian Geometry
This sketch and extensive documentation provide an introduction
to the Minkowski geometry, instructions for creating constructions
with the sketch provided, and notes for presenting a two-part Sketchpad workshop
introducing Minkwoskian geometry.
Bjørn Felsager,
2004. |
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Poincaré Disk
Model of Hyperbolic Geometry
This sketch from Sketchpad's Samples collection depicts
the hyperbolic plane using the Poincaré Disk model,
in which a line through two points is defined as the Euclidean
arc passing through the points and perpendicular to the circle.
Custom tools allow you to create constructions in the hyperbolic
plane.
Sketchpad Samples |
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Elliptic/Spherical
Toolkit
Tools for exploring elliptical geometry, in which the Euclidean
plane is replaced by the surface of a sphere, and lines in
the plane are replaced by great circles on the sphere.
Brad Findell, 2004. |
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Half Plane Model
of Hyperbolic Geometry
Tools for constructing in the half-plane model of hyperbolic
geometry, in which only points on one side of a horizontal
boundary line are considered. A "line" through
two p oints in this model is a semicircle whose center is
on the boundary line.
Judit Abardia Bochaca, 2004; Dan Bennett
2001. |
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Other Explorations
These sketches illustrate other unusual or advanced topics in Sketchpad.
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Statistics Collection
This set of statistics visualizations and questions includes
sketches of mean, least squares, r squared, the normal
curve, comparing two means, and chi square.
Bill Finzer, 1993/2003. |
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Rainbow Investigation
This explanatory sketch from Sketchpad's Samples collection
looks at the physics of rainbows: light traveling through
prisms and water droplets.
Sketchpad Samples |
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Dynamical
Systems
This sketch from Sketchpad's Samples contains sample
visualizations of several well-studied and potentially chaotic
dynamical systems.
Sketchpad Samples |
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Linkage Library
This anthology collects several famous mechanical linkages—Peaucellier
cell, a windshield wiper, and a sewing machine needle—in
demonstrations both of their outer kinematics and their inner
structure. An additional sketch on cam couplings allows you
to design your own cam, either by cam shape or by desired rotary
profile.
Nick Jackiw, 1994/2004. |
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Fractal Gallery
This sketch from Sketchpad's Samples illustrates a potpourri
of iterated geometric constructions, many of them producing
well-studied fractals.
Sketchpad Samples |
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©2005 KCP Technologies. All rights reserved. |
