Quadric Surfaces in 3 dimensional Space

Student project for MA265

by Wilson Williams

12/16/2011

Ax^2+By^2+CZ^2+Dxy+Exz+Fyz+Gx+Hy+Iz+J=0


Ellipsoid – x^2/a^2+y^2/b^2+z^2/c^2=1

Hyperboloid of one sheet – x^2/a^2+y^2/b^2-z^2/c^2=1

Hyperboloid of 2 sheets – x^2/a^2+y^2/b^2-z^2/c^2=-1

Elliptic parabolic – x^2/a^2+y^2/b^2=z/c

Hyperbolic parabolic x^2/a^2-y^2/b^2=z/c

There is also a website that you can go to get a view of what quadric spaces look like. http://tutorial.math.lamar.edu/Classes/CalcIII/QuadricSurfaces.aspx

Here is table showing the relationship between physics and mathematics. Also how the graphs relate to one another conceptually speaking about the 2 topics.

Another Great tool to learn about Quadrics is to look up on the search engine Rhea page and type in the topic on Assimi search engine.

It is also helpful thttp://www.youtube.com/watch?v=uTUB_a-tyWI&feature=results_main&playnext=1&list=PLA1398719815F6BB0o look at these YouTube videos.

A fun activity and learning exercise is to go onto to Autodesk and create the quadric shapes. This is a great exercise for visual learners. Tip- If you would like to get a better understanding on the concept as a whole you can look up several things. One would be the idea of relativity and space in general. This topic can go on and on but relativity is one of the topics that can fit into this discussion

There are hundreds of ways to learn about Quadrics in 3D space. The most important thing is you should find which way is best for you to learn. If you are a more visual person, I would recommend taking a look at the graphs. If you are a more organized and structure learner, then I would recommend looking at tables and charts. If you are a conceptual learner, I would recommend reading the Essay and learning the philosophical aspect of it. Overall looking at all of the different ways to learn about quadrics is important, because it will make you a better-rounded learner.

## Alumni Liaison

Basic linear algebra uncovers and clarifies very important geometry and algebra.

Dr. Paul Garrett