Where in The World Are Conic Sections?

 

I am beginning conic sections in the pre-calculus class.  I’m used to teaching it using the basic equations but I seldom take time out from instruction to have students apply what they’ve learned to provide more of a context to their learning. I knew of only two applications of conic sections but I’ve discovered there are more.

1.  The paths of planets circling the sun.  One can use the formula for ellipses to calculate the equation for orbits of all the planets.  All that is required is to find the length of the major and minor axis.  I did this one time in class and the students had fun calculating the equations for each planet’s orbits.

2. Satellite dishes and parabolic mirrors and microphones.  With just a few measurements, students can calculate the equation for each one.  In fact, they could even research these to learn more about the sizes for each one. Since solar ovens and cookers use parabolic mirrors, have students design their own solar oven.

3. For bridges, both suspended and the ones on the ground, are parabolic in nature.  It would be easy to find measurements and using those measurements, students can calculate the equation for the arch part of the bridge.

4. There is a long range navigation system referred to as LORAN uses hyperbolic conic sections.  This particular system was developed during World War II and was especially popular in the 1950’s.

5. Of course, there are all those video games such as Angry Birds where the object that is shot ends up traveling in a parabolic trajectory.  In addition, many rides such as roller coasters rely on a series of parabolic shapes to create a wonderful ride.

6.  Did you know that the sides of a guitar form a hyperbolic shape?  Image having the students calculate the equation of the hyperbola used on the sides of a guitar?  In addition, the Kobe Port Tower gets its hourglass shape from a pair of hyperbolas.

These are just a few ways conic sections are used in real life.  This makes a nice Padlet activity where students can research each shape or only one and find several examples and calculate the equation associated with the object or trajectory.  Remember earlier when I commented that things that are shot such as angry birds, follow a parabolic trajectory?  Introduce students to the National Pumpkin Chunkin contest via youtube so they can see the pumpkin fly.

It is always nice for students to find real life applications for conic sections rather than situations that work out neatly and seem contrived.  Let me know what you think, I’d love to hear. Have a great day.