In higher dimensions the Riemann curvature tensor is a more complicated object, but manifolds with constant sectional curvature are interesting objects of study, and have strikingly different properties, as discussed at sectional curvature. Indeed, by the uniformization theorem every surface can be taken to be globally (at every point) positively curved, flat, or negatively curved. Contact me if you would like any of the instructions or rubrics I have used for this project in the past.For conics in standard position, these parameters have the following values, taking a, b > 0. Giving each student 5 star stickers, I had students select their favorites. In some years, I have had students peer-assess their work by creating an art gallery of their work.

In the next example, Connor wanted to tilt his ellipses and researched on his own how to make that work using trig functions (did I mention that these kids haven’t had trig yet?). What I love most about this project is when students discover how the conics behave, and experiment with them without fear. Here are his graphs after the axes and grid were removed….Īny ideas what the finished product will be?

Then un-needed pieces are removed, and the final product emerges. Thanks to Kevin for working with his class to share their creations.įirst up is Kristin. Students this year could work on their equations at home, save work, and work with their teacher during time allotted in class. This year, the Desmos online calculator brought the project to a new level. The projects grew more intricate, and many kids took off with their creativity. Later, we started using Print Screen to grab the graphs and move them into MS Paint. The project grew new wings with a program called Math Toolkit, which allowed for finer graphing and the ability to save work. We were happy if we saw a tree made from a hyperbola and a parabola leaf line.

Back then, we used a DOS program which could only graph in black, cyan and magenta. I started with this project 12 years ago when a colleague, who has since retired, introduced me to his ideas. In the project, students are challenged to manipulate equations of conics and graph them using software to make pictures. One of my favorite math projects takes place during our unit on conic sections in Algebra II.

UPDATE – I recently posted more info about this project, with a rubric and more examples, at this post.

Conic art project with equations