Thursday, November 10, 2016

How Are Hyperbolas Used In Real Life?

Dulles, Airport, Building  When we teach conic sections, we include hyperbolas but have you ever wondered how they are used outside of the classroom?  I have but this is the first time I've really looked at the topic.  The ellipse activity went well so I want to an activity I can have students use for hyperbolas.

The picture above is found at the Dulles Airport.  The building is a hyperbola if viewed from one location but a parabola if viewed from another so we can see hyperbolas in architecture.  The shadow from a cylindrical lampshade or flashlight forms a hyperbola if you look carefully at the wall.

The open orbit of a comet as it goes around the sun forms a hyperbolic shape along with the area of interference between two circular waves.  Did you know the property of hyperbolas is used in radar tracking stations where they locate an object by sending out sound waves from two sources?  The circular sound waves intersect in a hyperbolic shape.

If you roll a steel ball by a strong magnet, the ball's path is changed from a straight path to a hyperbolic path.  This is easy to explore, just borrow a few things from the science department and you have an experiment.

I found this hyperbolic paper folding activity on line.  The activity uses wax paper and something circular .  The students form the hyperbola from the folds they create.  In addition, this You Tube video shows how to do the folding.  I think I'm going to try this activity as an introduction on hyperbolas with my students on Friday.

Illuminations from NCTM has a nice applet to explore the graph and conic sections of hyperbolas by playing around with various factors such as height, slant, m and b so students can explore to see what happens as each one is changed.

Another site is Learning with a gizmos app students can use to play around with the a, b, h and k to see how each term effects the hyperbola.  You can get 5 minutes use without signing up for the service.

I think my students are going to have fun later in the week with the paper folding activity.  Let me know what you think.