Conic Sections in Math, CS and Game Programming
Kris Stewart, CS Professor
stewart [at] sdsu.edu

Updated: 21April2011

My colleague at SDSU, Janet Bowers, and I have collaborated in the past on an article that described the Supercomputer Teacher Enhancement Program (STEP), www.stewart.cs.sdsu.edu/step/step95.html. There are still some images available, online, www-rohan.sdsu.edu/~stewart/step/smithsonian/hires1.html, from when STEP was nominated for a Computerworld/Smithsonian Information Technology Award in 1996, www-rohan.sdsu.edu/~stewart/step/smithsonian/.

Courtesy of the WayBack Machine you can still access the curricula though not all links are avaiable in this Internet Archive. STEP 1995. Preparing for Supercomputing 97 in San Jose, celebrating the 50th anniversary of the invention of the first computer, Janet and I had a paper accepted to the SC97 Technical Paper Session, http://www.stewart.cs.sdsu.edu/SC97/, "STEP: A Case Study on Building a Bridge between HPC Technologies and the Secondary Classroom". This is also available from the CiteSeer, http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.41.5528, through their Download of http://www.supercomp.org/sc97/program/EDU/STEWART/, which is no longer available. pdf.

Background on conic sections is presented by the National Counciil of Teachers of Mathematics NCTM.

http://www.nctm.org/eresources/view_media.asp?article_id=7261
[Understanding Conic Sections - Using Alternate Graph Ppaer, MATHEMATICS TEACHER | Vol. 99, No. 5 December 2005/January 2006]
http://illuminations.nctm.org/Lessons/CuttingConics/CuttingConics-AS.pdf
http://illuminations.nctm.org/ActivityDetail.aspx?ID=195 [Conic Explorer]
http://illuminations.nctm.org/Lessons/CuttingConics/CuttingConics-AS.pdf [Cutting Conics activity]

Janet and I are collaborating on a CS Masters Thesis research project exploring conic sections through the XNA Game Framework by sathya narayan [sathyanarayan_chandrashekar]. We hope that the module developed will be useful for future high school teachers who enroll in Dr. Bower's Math 414 course at SDSU in Fall 2010. There is already a game interface that Stewart demonstrated to another group of high school teachers this summer during the http://www.biobridge.us/programs/cyberbridge/who-we-are CyberBridge program at SDSU. Stewart's participation involved highlighting the use of MIT's Scratch environment to motivate teaching programming, following the CSTA guidelines of the ACM. Within the variety of teaching modules of Scratch, we find http://scratch.mit.edu/projects/DrSuper/351810. The project notes scratch_conic.html, lead to the Wikipedia page for conics, http://en.wikipedia.org/wiki/Conic, providing another mental exercise in translating mathematics into practical usages.

Conic Sections

http://usiweb.usi.edu/students/gradstudents/j_k_l/kleinknecht_s/portfolio/Educ%20690_004%20ST/History%20of%20Conics.htm
This web page has a great figure illustrating what we wish Sathya to implement within a game environment. Draw the double-cone and allow the use to control passing a 2d plane through the double-cone at various angles to illustrate the family of curves defined. These 4 conics are the cirlce, elllipse, parabola and hyperbola.

http://jwilson.coe.uga.edu/EMT668/EMAT6680.F99/Erbas/emat6690/Insunit/conicsunit.html
This instructional unit by A. KURSAT ERBAS & GOOYEON KIM gives a wonderful, verbal description of the conics. "A conic (or conic section) is a plane curve that can be obtained by intersecting a cone with a plane that does not go through the vertex of the cone. There are three possibilities, depending on the relative position of the cone and the plane (Figure 1). If no line of the cone is parallel to the plane, the intersection is a closed curve, called an ellipse. If one line of the cone is parallel to the plane, the intersection is an open curve whose two ends are asymptotically parallel; this is called a parabola. Finally, there may be two lines in the cone parallel to the plane; the curve in this case has two open pieces, and is called a hyperbola."

Definition of the Parabola
"The parabola is the locus of a set of points equidistant from a fixed point, and a fixed line. The fixed point is called the focus of the parabola and the given line is called the directrix."
JavaSketchpad Exploring Parabolas http://mste.illinois.edu/dildine/sketches/parabola.htm


For a little frivolaty, I find these YouTube videos useful.

http://www.youtube.com/watch?v=OuQqXZhDtoo&feature=channel. I especially like Maldin's introduction and context on today's school violence.
http://www.youtube.com/watch?v=xky4fq8MVkw&NR=1 Teachers are People 1952, Disney