We're learning conic sections in precalculus, and so far it's just been 2 days on each (circles, ellipses, parabolas, hyperbolas). We've covered the first 3. That was the bulk of how I was going to present it: create the conics with either paper folding or strings and pencils, and then get to the equation and then "work them to death". THEN. I kept reading about these elliptical pool tables where if a ball is at one focus, then any where you hit it, it will bounce off the wall and pass through the other focus. I think that's the coolest thing. I mentioned it to my 3 classes, and they got excited, so I think we're going to try and make one for each class to test this thing out. I told them that then we could be pool sharks and place bets with nonsuspecting non-mathies.
My latest idea is a thick wood piece left over from shelves, the inside part hollowed out in an ellipse shape, and then the thickness can be the "walls" of the table and we can use a marble as a pool ball. I'm so curious to see if this will work out.
On a funny side note. When I started the conic sections, I mentioned the properties of a parabola where if you put a microphone at the focus or a light bulb at the focus it has special "powers" because everthing "bounces" through there. Then on Friday one of my students had mentioned that he was at an electronics store and he saw this music contraption where it had a dome (I guess in the shape of a paraboloid) and a person would be the only one to hear the music. He said he was then thinking about what we talked about in class, and he joked that he called people over and gave them a lesson on parabolas.
One thing that my kids thought were cool when we were talking about parabolas was that some cultures put kettles at the focus and use parabolic mirrors to heat up the water. They were pretty impressed that people would think of that. (We also talked about statelite dishes with parabolic cross sections and where to put the reciever to get the best reception--that's a good quiz/test question.) :)
ReplyDelete-KH
Flashlights also have parabolic (or nearly so) reflectors to get the thrown light to provided the brightest "bundle" of light.
ReplyDeleteWill you discuss hyperbolic paraboloids? Will you eat some out of the tall red cylinder?
Please report your results on the oval pool table.
I built a parabolic and an elliptical pool table to use in my math classes. I posted the instructions on my web site
ReplyDeletehttp://staff.jccc.net/coneil/
It only cost about 35 dollars per table, but it was quite time consuming. Has anyone else tried this? Bumper materials seem to be the big problem.
My friend and I are building an elliptical pool table for our "Senior Project." For bumpers we are using replacement cushions made specifically for a pool table. I think the main focus should be put on using a surface that is completely flat. We are using 3/4" MDF (Medium Density Fiberboard) which is very stable in hot/humid conditions and will stay flat. It's the next best solution to slate (which is really expensive). I think the rails will also prove to be challenging. We're planning on cutting them from mahogany; the main problem is getting them to be in a perfect ellipse and also to mount the cushions.
ReplyDeleteWish us luck!
If I can remember, I'll post a picture here when we finish
I am a math teacher - 34.5 years and now subbing. We are about to do parabolas and ellipses and it reminded me that I had made an elliptical pool table in the late 60's. The inspiration was that a student at Union collegeg made and was involved with a professionally manufactured elliptical pool table. Some of the local pool parlors bought them and Montgomery Wards sold them. The one that I made was of plywood with the top layer being made of 1/4" plywood with a bumper made from some rubber tubing from the chem lab and split to fit over the 1/4" plywood. Balls were from a little set a toy company was selling. The cues were dowels drilled out to receive a smaller diameter dowel in the hole driven by rubber bands.
ReplyDeleteSmall and cheap but demonstrated the principle. The professionally made tables never made it. The balls eventually hugged the rails. Are you still teaching? Year #17?