There is probably no number that has received more interest since ancient times that the number pi, symbolized by the Greek letter π. Originally defined as the ratio of the circumference of a circle to its diameter, it has been given approximate values including 3.14 and 22/7. Proven to be an irrational number, supercomputers have computed the value of pi to more than one trillion digits.
With this background in mind, what better number could there be to investigate with Voyager than the number pi? Mount Voyager to the top of an "intelino smart train" and you have the perfect combination for a math activity for 4th grade through junior high school students. What's an intelino smart train, you ask? Designed for all ages, the intelino smart train is intuitive with its app, has built-in sensors to provide an interactive experience for the user, and is easily programmed with color snaps that allow the user to control intelino's actions.
In this lesson, students will interface PocketLab Voyager and an intelino smart engine to determine an approximate value for pi. Students will also calculate the percent error in their value and use critical thinking to explain possible reasons for the error. Clearly, this activity supports STEM as well as NGSS practices.
The Voyager/Intelino Equation for Pi
An approximate value for pi will be determined from magnetic field data collected by the Voyager app, mounted to the top of an intelino smart engine, as they pass by magnets serving as timing gates. No meter sticks or other measuring devices are used. Your students will time two events:
Tc, the time for intelino/Voyager to travel one circumference around a circle of intelino curve tracks
Td, the time for intelino/Voyager to travel a length of one diameter of the circle on a series of straight tracks.
By definition, π is the ratio of the circumference C of a circle to its diameter D, π = C/D. If the speed of the intelino engine is kept the same for both the circle and the straight track, then the distance traveled would be proportional to the time, i.e., C/D = Tc/Td. Therefore, we can compute the value of π by finding the ratio Tc/Td of the two times!
Now with an experimental value for π, the percent error can be calculated by the usual method for computing percent error: