# Engaging students: Deriving the Pythagorean Theorem

In my capstone class for future secondary math teachers, I ask my students to come up with ideas for engaging their students with different topics in the secondary mathematics curriculum. In other words, the point of the assignment was not to devise a full-blown lesson plan on this topic. Instead, I asked my students to think about three different ways of getting their students interested in the topic in the first place.

I plan to share some of the best of these ideas on this blog (after asking my students’ permission, of course).

This student submission comes from my former student Emma Sivado. Her topic, from Geometry: deriving the Pythagorean Theorem. How has this topic appeared in pop culture?

What if I told you that knowing the Pythagorean Theorem could help you become a millionaire? We’re all familiar with the popular game show “Who Wants to be a Millionaire” so let me take you back to 2007 when Ryan was playing for \$16,000. The question asks “which of these square numbers is the sum of two smaller square numbers.” We see the sweat immediately begin to accumulate on his brow as he struggles to find the right answer. He quickly goes to his life lines and asks the audience. The majority say the answer is 16. Ryan contemplates for a minute before going with the audience and selecting 16. Disappointment follows as we discover this is the wrong answer and Meredith explains that the answer is 25 or 42+32=52. How can this topic be used in your student’s future courses in mathematics or science?

The Pythagorean Theorem is first taught in Geometry, according to the TEKS, and is expected to be defined, proved, and executed by these students. However, many people say that the Pythagorean Theorem is the basis of trigonometry, which is studied in depth in the student’s pre-calculus course. Beyond pre-calculus applications, the Pythagorean Theorem is used in physics to calculate kinetic energy, in computer science to compute processing time, and in social media to prove Metcalfe’s Law. Beyond math and science, the theorem is used in architecture and construction to determine distances, heights, and angles, in video games to draw in 3-D, and in triangulation to locate cell phone signals.