This graph can be used to prove the Pythagorean Theorem. The equation for Pythagorean Theorem is a^2 + b^2 = c^2. The letters represent the length of the sides. In this diagram, we take the length of the sides (a = 3, b = 4, c = 5) and square them. When we do this, we can literally create squares. For example, squaring 3, we get an answer of 9. That means that we can create a square that's 3 by 3 on the length of the side. If you look at the squares, you see that the c square has the same number of units as the a and b squared combined. This proves that the equation a^2 + b^2 = c^2 is true.
During this project, we created a spiral shape using Pythagorean Triangles. Using the c side of the former triangle and one side length of 3, we were able to expand the triangles and create the shape. This is the art piece that I created after completing the spiral.
REFLECTION:
The process to create the spiral took a while. There are sixteen triangles, and each uses one side from the one before it to be completed. While creating the spiral, using a ruler worked well while creating the shapes. However, it was challenging to make sure that each triangle had a right angle. One habit of a mathematician that I practiced during this project was being patient and persistent, since it was frustrating trying to make everything perfect.
The process to create the spiral took a while. There are sixteen triangles, and each uses one side from the one before it to be completed. While creating the spiral, using a ruler worked well while creating the shapes. However, it was challenging to make sure that each triangle had a right angle. One habit of a mathematician that I practiced during this project was being patient and persistent, since it was frustrating trying to make everything perfect.