In this unit, we learned about the Pythagorean theorem and coordinate geometry. The Pythagorean theorem is the theory that goes with all right triangles. The main goal of this theorem is to find the hypotenuse of a right triangle. The formula for this is a²+b²=c². We used this formula a lot at the beginning of this problem. We used this a lot when finding the last line of sight in the orchard. Coordinate geometry is also a huge part of this. When I say this I’m talking mostly about the midpoint and the distance formula. These formulas were extremely important when solving the unit problem. The midpoint formula is (X1+X2)2, (Y1+Y2)2. This will help you find the midpoint between the two points. I used this when solving Proving Distance Part 2. I also used the distance formula. Which is, (X1-X2)²+(Y1-Y2)². Both of these formulas played a huge role in Proving the distance. At first, I didn’t understand these but when Julian drew it on a graph and showed why we do these equations and how we use them it clicked.

When talking about the square-cube law, there are many concepts that go along with it. For example, finding the circumference, finding the radius, finding the volume, and finding the surface area and the area. The equation for the circumference is C=2r. You can find the radius by calculating the midpoint of the circle and then using the distance formula to find the length of the radius. The volume equation is, V=h(r²). The equation for the area of a circle is A=2r. In this unit problem, we used all of these equations in order to find the radius of the trees and How to align all of the trees so that it would become a true orchard hideout. When understanding these equations and rules, the activity that helped me the most was when we put all of them together in order to find the size of the trees and how it becomes a true hideout and how long it takes.

Throughout the unit I learned a lot about geometric proofs. When solving a problem in this unit we always needed to make sure that the answer was true in order to make sure that it was accurate. When looking at different data in this unit we could conclude that some data may not be accurate based on certain variables. Some of those variables may include, lack of explanation, lack of research, or lack of information. We specifically looked at some graphs in order to prove whether they were accurate or not. I would say that about 50% of the time the graphs were not accurate. When learning about geometric proofs I first learned that some geometry and data may not be what it is supposed to. I then learned that there were certain equations that we could go through in order to prove things. As shown in the previous paragraphs. I finally learned how to look at data and figure out what was wrong and what I needed to prove. There were many activities that played an important role in finding geometric proofs. I would say that the major one for me was looking at graphs that we pulled from certain research and determining whether they were accurate or not. This made me understand that most math needs to be proved.