### Dr. Sarah's Sketchpad 4 Classroom Activities and Explorations

Taking Full Advantage of Sketchpad 4 - Why You Can't Live Without It with Brian Felkel, the 15th International Conference on Technology in Collegiate Mathematics Proceedings

### Poincare Disk

From the Sketchpad 4 folder, open up Sketchpad/Samples/Sketches/Investigations/ Poincare Disk.gsp

Why Study Hyperbolic Geometry?

One could demo these to a class, or have students explore the Sketchpad files... What are the shortest distance paths in hyperbolic geometry?
Sketchpad Shortest Distance Paths
Image of Shortest Distance Paths

Is parallel the same as equidistant in hyperbolic geometry?
Image of Equidistant 1
Image of Equidistant 2

Given a hyperbolic line and a point off of the line, how many parallels can be formed? (Playfair's axiom) Sketchpad Playfair's
Image of Playfair's

What is the sum of the angles in a hyperbolic triangle? How large can the sum of the angles get? How small can the sum of the angles get?
Sketchpad Sum of Angles
Image of Sum of Angles

Is Euclid's 5th postulate ever, always or never true in hyperbolic space?
Sketchpad Euclid's 5th Postulate
Image of Euclid's 5th Postulate

Is the Pythagorean theorem ever, always or never true in hyperbolic space?
Image of Pythagorean Theorem

### Other Resources

Geometric Constructions

Euclidean, Spherical and Hyperbolic Geometries

Activities for a Geometry for Future High School Teachers Course

Geometry of the Earth and Universe - From the Classroom to Current Research

Taxicab Geometry Activities in Sketchpad

Dynamic Visualization Resources

Dynamic Geometry activities on the sphere
1) Brad Findell's Elliptic/Spherical Toolkit for Sketchpad
2) Walter Fendt's Java Applet