In a couple of earlier posts (here and here), I wrote about how my school has acquired a couple of MakerBot Replicator2 3D printers. The students are getting very excited about using them. One of my Honors Precalculus students even designed and printed a “Menurkey” – a combination Menorah and turkey – because Hanukkah and Thanksgiving coincide this year. Here’s a picture of the small prototype she printed first:

Thingiverse recently had a competition for the best math manipulative, and there were some really useful entries. I especially liked a conic section one designed by Karl Crosby. We have purchased some different colored plastic, so I went with green this time:

Next, I printed it out in two stages, so I could use two different colors of plastic. It turned out really well!

These are great for showing students how slicing a cone at various angles results in a circle, an ellipse, a parabola, or half a hyperbola. Until now, all the math teachers in my department shared a wooden one that was very expensive. Now I can print out a classroom set for almost nothing.

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Hi, what is the difference between parabola & hyperbola?

Good question!

The definition of a parabola is “the set of points equidistant from a line (the directrix) and a point not on the line (the focus)”. A hyperbola is defined as “the set of points, the difference of whose distances from two distinct points (foci) is a constant”. That’s a lot of confusing jargon that really says a parabola has one focus, while a hyperbola has two. What you think is another parabola is just half of a hyperbola. Geometrically speaking, a parabola is formed when a plane intersects a cone at an angle parallel to the cone’s edge. A hyperbola is formed when a plane intersects two cones (balanced tip-to-tip) at an angle perpendicular to their bases.

Wow Thaddeus! So glad someone is putting that model to use : )

Doing my best, Karl! Thanks for sharing the printing file.