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Pi, possibly one of the most famous mathematical constants out there. It tells us the ratio of a circle’s circumference to its diameter, and can be approximated to 3.14159. Mathematicians have been trying to calculate Pi to ever increasing accuracy, and with the computational power available to us today we are able to calculate Pi to trillions of digits.
So, why all the fuss about Pi? Apart from the excuse for mathematicians to share jokes around this constant, and the rest of us to break out the baking gear why should we celebrate Pi Day? Well, this magical number appears all around us and Pi Day gives educators a great opportunity to elevate this constant and showcase some ways Pi is utilized in the real world.
Pi and Orbital Period
One area in science where Pi is found is orbital period. Calculated by Kepler’s Third Law of Planetary Motion, orbital period tells us the time taken for one object to make a singular orbit around another object, for example a planet around the sun. This Core Interactive Text from Science Techbook, Earth and Space Science provides a useful recap of Kepler’s Third Law (as well as his other two laws of planetary motion).
By calculating orbital period, astronomers are able, for example, to determine the distance of a planet from its sun and determine whether the planet may have the correct conditions to support living organisms. NASA’s 2015 discovery of an earth-like planet is a recent example. (Discovery Education Streaming, Science Techbook | Canadian Link)
Closer to home, orbital period is also used in calculations to determine the speed of satellites that are orbiting the Earth or the weight a satellite should be to stay in orbit. Currently, thousands of satellites orbit the Earth, used for everything from transmitting television signals and approving credit card transactions, to tracking weather patterns and conducting research in space. (This STEM in Action overview from Science Techbook, Earth and Space Science provides a great look at tracking satellite movement in space including some of the related careers such as an aerospace engineer).
One area of technology we use daily that relies on this satellite technology is GPS. GPS uses a network of satellites to triangulate the position and elevation of almost anywhere on earth. This unit from Science Techbook, Earth and Space Science provides a good introduction to modeling the earth using GPS.
To give students a practical example of the use of Pi, have them research the history of GPS and how the system was developed. Using the resources available to you as part of your Discovery Education subscription (we’ve provided some suggestions below), ask students to research uses of GPS technology. How has this technology benefited humans? In what other ways do they think that GPS technology can benefit humans?
As an extension, guide students to understand that as Pi is used to calculate the area of spherical objects, Pi appears in many calculations to do with the Earth. Many of the technology applications they discuss above will likely revolve around line of sight triangulation. Encourage students to think through whether the curvature of the earth can be used to calculate beyond line of sight, and any potential applications this would have. For example, NASA has been experimenting with “out of sight” drones. Could research in this area be a first step towards more futuristic unmanned air traffic on earth? Your students could be the scientists working on such technology in the future.
Kepler’s Laws of Planetary Motion
For more information around Kepler’s Laws of Planetary Motion or for resources to start a discussion on how the third law can help determine whether there is life on other planets.
Problem Solving Worksheet – Putting Kepler’s Third Law into Practice (Canadian Link)
Science Techbook, Grades 9-12, Worksheet
Johannes Kepler Formulates Third Law of Motion: Mar 8, 1618 (Canadian Link)
Discovery Education Streaming, Event
The Habitable Zone
Discovery Education Streaming, Grades 6-8, 9-12, Video
For more resources around GPS and its applications in the world:
Stuff You Should Know Podcast: What is Geocaching? (Canadian Link)
Discovery Education Streaming, Grades 6-8, 9-12, Audio
GPS Technology: Helping Farms and Elephants Share Resources (Canadian Link)
Discovery Education Streaming, Science Techbook, Grades 6-8, Video