Workshop on Geometry Software
Math 241
Spring 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, P. For each point A
on l we construct a point Z
that is equidistant from P and l ,
lying on the perpendicular to l at C.
You can animate C and have GeoGebra trace Z
. The result is a parabola. The line l is
called the directrix and the point P is called the
focus of the parabola.
We also started the construction of an ellipse from two foci P, Q
, and a
distance d. A point Z is on the
ellipse if the sum of the distance to P and the
distance to Q is d.
Dustin helped me figure out the problem about animating the ellipse.
You can't animate an arbitrary point; you can only animate a point on
a line (or on a circle). So, choose either an arbitrary line, or
any circle (I think I did it with the circle with center P
of radius d . Choose an arbitrary point on
this circle, call it A, construct the ray
PA and continue as we did in class.
Assignment:
 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.
 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?!
Second Day:
We worked with geometric transformations: dilations, translations,
rotations and reflections.
Assignment:
 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.
Upload your worksheets to GeoGebra and put them in two books:
Cool Conics and Pretty Picture.
Choose "Share with link" and send me the link via email.
(mosullivan@mail.sdsu.edu)
Due: Monday 2/16 at 5:00 am.
Comments:
Here are some observations that should be generally useful to all of
you for future assignments and revision of this one for the final portfolio.

For the parabola and ellipse: Most of you explained the steps in the
construction correctly. Only a few explained what property the points
on the parabola (or ellipse) satisfy. For the final version, please
do that, and *also* explain why the construction creates points that
satisfy the property.

For the final portfolio include a discussion of what happens in the
construction of the ellipse when the distance between the foci is
greater than the length of the string.
 Don't hide the steps in the construction, because we want to see
why it works. Use color or opacity to highlight or deepmphasize.

For the pretty picture, use the tools that we played with on Thursday
to create the figure; don't just draw a lot freehand. See if you can
make your figure work well even after I adjust it by moving points.
Explain your construction and think geometrically.
 For the pretty picture, try using animation, trace, or other
tools to make it more interesting.