Presentations and materials from the Sketchpad User Group, held at the 2009 NCTM Annual Meeting in Washington, D.C.

The Ultimate Geometry Course
Abstract: Why use a textbook? Why give class notes to students? Why not let students create their own geometry textbook and, through the experience, learn all the geometry in the textbook?
Presenter: Michael J. Bosse, East Carolina University, Greenville, NC

Pictures in Sketchpad 5
Abstract: Iterating Digital Pictures into Fractals in GSP5. Sketchpad's new capabilities with pictures have motivated Kendra to find ways to enliven mathematical exploration by introducing digital images into the mix. When she started putting pictures into fractals, she found a new artistic possibility that doesn't exist in any other software. Kendra showed at the User Group how she's been combining her love of photography with her love of mathematics by creating fractals with pictures.
Presenter: Kendra Lockman, Oakland, CA
Presentation Materials:

You, My Dear, Are Beautiful
Abstract: Starting with Fibonacci's bunnies, we will explore the Golden Ratio in a quest to uncover why, oh why, is Mrs. Mona Lisa so darned pretty.
Presenter: Karim Kai Logue,
Presentation Materials:

Realistic Motion Animations in Sketchpad
Abstract: To share how teachers can create realistic motion problems that take in account gravity, for example, to be used in both physics and mathematics.
Presenter: Irina Lyublinskaya, The City University of New York, Staten Island, NY
Presentation Materials:

Projective Transformations Using Sketchpad
Abstract: Not only can we build custom tools for transformations of similarities, shear, and affine transformations, we can create projective transformations on a plane with Sketchpad. We can display that an ellipse can be transformed into a hyperbola and parabola.
Presenter: Dr. Subhash C. Saxena, Emeritus Coastal Carolina University, Conway, SC
Presentation Materials: projective_transformation_non_ideal_pts.gsp

Geometric Inversion with Sketchpad 5
Abstract: Using the new custom transformation feature of Sketchpad 5, it is now possible to explore the mathematics of inversion through a circle more easily than ever before. With mathematics that is accessible to most high school students, this presentation explores what happens to circles, lines, grids, and digital photos when they are inverted through a circle.
Presenter: Daniel Scher, KCP Technologies, Emeryville, CA
Presentation Materials: Circle_Inversion.gsp

They're More Picturesque Than You Think
Abstract: This presentation explores several kinds of functions, based on the idea that the elements of the ordered pair need not be numbers - they can be locations in the plane, positions, sizes, and orientations of geometric objects, and even a mapping that does an anamorphic transformation of a picture. It includes a geometric construction of a pinhole camera as a function machine, using the resulting custom transformation to project a scene onto film, and then running it in reverse to generate an anamorphic image similar to the sidewalk paintings of Julian Beever. Finally, it includes an image generated directly from numbers, using BarnsleyÍs iterated function system to produce a fractal fern.
Presenter: Scott Steketee, Key Curriculum Press, Emeryville, CA
Presentation Materials: Picturesque_Functions.gsp

Simple Linkages Using Geometer's Sketchpad
Abstract: Upon uncovering an antique pantograph in the science lab at my school, I have been intrigued by linkages and the possibilities for studying them through the use of The Geometer's Sketchpad. See both expected and unexpected results that develop from a dynamic exploration of linkages.
Presenter: John Threlkeld, Graland Country Day School, Denver, CO
Presentation Materials: NCTM_Pantographs_043009.gsp, NCTM_Linkages_2_042409.gsp