# Workshop on Geometry Software

Math 241
Fall 2015
Professor: Mike O'Sullivan

### Week 2: Beyond Euclidean Geometry

First Day:

We constructed a parabola. We start with a line, l and a point not on the line, F. For each point Q on l we construct a point Z that is equidistant from F and l , lying on the perpendicular to l at Q. You can animate Q and have GeoGebra trace Z . The result is a parabola. The line l is called the directrix and the point F is called the focus of the parabola.

We also did the construction of an ellipse from two foci F, G , and a distance d. A point Z is on the ellipse if the sum of the distance to F and the distance to G is d. Let Q be an arbitrary point on the circle with center F and radius d . Let Z be the intersection of theline FQ and the perpendicular bisector of QG. Animate the point Q and turn the trace option on for Z .

Assignment:

1. Pepare a Geogebra worksheet with the construction of the parabola. Explain the steps in the construction and give a short justification for the equidistance property. Remember to direct the worksheet to an audience of your students, not me!
2. Pepare a Geogebra worksheet with the construction of the ellipse. Explain the steps in the construction and give a short justification for the construction. What happens when d < b?!
3. Here is a challenge problem: Pepare a Geogebra worksheet with the construction of the hyperbola. Explain the steps in the construction and give a short justification for the construction. You might need to consult on line resources.

Second Day:

We worked with geometric transformations: dilations, translations, rotations and reflections.

Assignment:
1. Pepare a Pretty Picture, a Geogebra worksheet with a construction using the geometric transformation tools discussed in class. Describe precisely the steps you used in the construction. Make it so that varying the freely chosen points maintains the integrity of the figure. Use color, shading, animation, trace, or other tools to make it more interesting.
Upload your worksheets to GeoGebra. If you can figure out the "Book" feature put your work in a book: Beyond Euclid. Choose "Share with link" and send me the link via email. (mosullivan@mail.sdsu.edu)

Due: Thursday 9/17 at 5:00 pm.