“How can we test the pythagorean theorem and the law of reflection?” was a question that had confused me to no end at the start of this project. After all, how can I test something when I didn’t even know what it was? However, after vigorous weeks of studying and learning, I had finally been able to answer that question.

The pythagorean theorem is a method to calculate the side lengths of a right triangle. According to our teacher, Mr. Gross, numerous fields of study have benefitted from this knowledge. As shown in the formula above, the square numbers of the legs of a right triangle, when added together, would equal the square number of the hypotenuse. This formula could also work in reverse (c² – b²).

The law of reflection explains that light travels and reflects at the same angle, as shown in the visual I made above. The “normal” is a line perpendicular to a reflective surface. The angle of incidence is where light first hits, and the angle of reflection is the light that reflects off of a surface. However, not all reflective surfaces are flat. Concave mirrors are mirrors that “cave in” somewhat like a spoon. A convex mirror is a mirror that curves out, somewhat like the back of a spoon. Although we learned about the law of reflection during this project, we hadn’t thoroughly covered the topic of reflection when it comes to curved mirrors.

It may be perplexing to some as to how both the pythagorean theorem and the law of reflection connect to one another. For this project, we used lasers and mirrors to form right triangles; which then combined both topics that were priorly mentioned. As a part of milestone 4, we were to individually write up a lab report that had answered our driving question. My hypothesis was “With the assistance of mirrors, light sources, protractors, and various other tools; we could test the pythagorean theorem and law of reflection by creating multiple laser displays.”

For milestone 5, our task was essentially the same as the previous milestone. The only difference was that were were to work together as a group. My group members for this milestone were Claire, Brooke, and Theryn. Similar to our last milestone, we had to write a lab report. However, this time we got to physically make our laser display, which was rather exciting. After we had set up our display, Mr. Gross used a smoke machine so that we would be able to see the lasers.

We had three curricular competencies for this project, the first of which was “Questioning and predicting: Demonstrate a sustained intellectual curiousity about a scientific topic or problem of personal interest.” I feel that as a group we did well on this competency since most of us were on task throughout the duration of class time. We demonstrated our curiousity of these topics through our understanding of the pythagorean theorem and law of reflection.

The second competency was “Communicating and Representing: Represent mathematical ideas in concrete, pictorial, and symbolic forms.” As mentioned prior, we had written up multiple lab reports for this project. They had clearly and thoroughly explained the law of reflection along with the pythagorean theorem using the required scientific method of writing out a lab report. We had made sure to write the correct measurements and thoroughly check them to ensure everything was correct.

Lastly, the third competency was “Applying and innovating: Co-operatively design projects.” Seeing as our laser triangle display that we had worked together on was proficiently built with precise measurements, I would say we have done well on this competency. Although it was challenging to correctly angle the laser, we had managed it in the end.

Now that we have completed this project, I am glad to be able to say that I have an answer to our driving question. There are a variety of ways to test both the pythagorean theorem and the law of reflection, but I had done so by creating a laser display in the shape of a right triangle. This project was challenging at times however, I had still thoroughly enjoyed it. I’m looking forward to being taught Scimatics again!