Jack Tescher Unit 1 Portfolio 12/1/20 The Orchard Hide Out: Cover Letter: In the Orchard Hideout unit, we covered a lot of information. From the distance from a point to a point to the Pythagorean theorem when you are talking about the area of a circle. When we were starting this unit we worked on the distance from a point to a line and then when we had fully covered that we started to work on the best fit line or last line of sight. These directly correlate because how you prove that a line is the best fit is by proving the distance from that line to a point is the greatest out of all the possibilities that the line could be. I found that all the work that we did this unity was slowly building us up to because to answer the unit question.
Top start to find the unit question I need to first understand The Pythagorean theorem and Coordinate Geometry. One of the pieces of work we did this year that represents The Pythagorean Theorem and Coordinate Geometry is the In Or Out hand out that involved us trying to find if a point was inside our outside of a coordinate plane of 10. You had to be able to understand coordinate plains to complete this handout without having to completely write out every point. When I complete this assignment I had to ask myself first if the x or y coordinate was over 10 and then if it was then I would ask if it was close to the edge it could be off of the coordinate plane because of the curvature of the orchard. Using this technic answered most of the problems but for a few of them, I had to see if the math checked out by using the Pythagorean theorem using the coordinate Y value as the A value and the X value as the B. Then doing A^2 + B^2 to find C^2 and doing the square root of that number to find the distance from the center to the coordinate point. The other key concepts that we had to learn before I could answer the unit problem Circles and the square-cube law. These concepts were a bit easier for me to understand because they are concepts that are more easily visualized. The handout I chose for these concepts is the Square cube law because when I did this assignment it made the concept clear when I wasn’t getting it before. The square-cube law is when you increase the size of a shape and have to find the volume and area. To find the volume of the different sized shapes you must scale with the square of the length and when you are finding the volumearea of the new shape you have to scale with the cube of the length. The hardest part about this unit for me was the proof because most of the time I know how to complete the math concept I just have troupe proving why my answer is correct and show how I got there. Having this burden of always proving our answers was annoying to do at the moment but because able to back yourself up completely even in a subject like math. Having practice proving our work in this unit I feel I am much more efficient at proving my work.
Unit Problem: The Unit question Is “How soon after they planted the orchard would the center of the lot become a true “orchard hideout”?” How you first have to answer this question is by understanding the orchard as a coordinate plane and what the last line of the sign is. The last line of sight is a line that is drawn from the center of a coordinate plane and is the farthest away from any point. How you find that distance to prove that your line is the last line of sight. How you do this is by finding the distance from the cent to the point that is farthest out in the orchard but also closest to your line. This can be shown here. Then using the Pythagorean theorem and the square-cube law will help you find that distance from the last line of sight and the trees that close to that line. How you do this is by looking at the orchard as a coordinate plane and drawing a right triangle with the most acute side at the center and the right-angled side near the edge of the orchard. Shown below. After you have found this triangle and used the Pythagorean theorem to ding the lengths of all its sides you can use the square-cube law to scale down the triangle until the scaled downs triangle's side A is equidistant from the last line of sight to the tree its closest to. For the orchard hideout, this distance would be 2.4 inches. Next using the distance from the point to the line or how much the radius of the tree must grow to block out the line of sight you can find the area of the tree when it is the largest it needs to be. Using pie and the area of a circle equation you can find the area of the tree when it is blocking the line of sight then subtract the area of the tree when it is starting. Finally, you will divide the area of the new tree by 1.5 because that is the amount to which the area grows every year. The answer I came to is 11.7 years. All the math I did for this equation is on this document.
Reflection: The math concepts in this unit for me were mostly easy because they made sense to me and I could do the problems I just had trouble with coming up with proof and an explanation for my answers. I have never done this rigorous proof in math. When I would struggle with coming up with proof I would get very frustrated because I had already completed the math and got the correct answer it felt like coming up with proof was pointless. But as we got deeper and deeper into this unit I started to get better at coming up with the proof for the problems but also was able to see the benefit of being able to come up with proof. If you have a proof for something then no one can tell you that you are wrong because you have evidence to back up your claim. Even though I still have trouble coming up with proof and it can still be frustrating I can see how this will benefit me in not only future math classes but in all my classes and any time I have to back myself up. Have to create so much proof has made me think about how important it is especially in this day n age with how much fake or false information is shown to us. It makes me want to have more fact-checking in the work especially in the media. Too many media sources with thousands of followers will deliver them false information to sway them in a certain way and it does not allow people to look at the data that is real and then create their own opinions on it. People are also having ideas just be implemented in their brain without having to think “Is this real or are they lying?” You shouldn't have to ask yourself this question when you're watching a news channel or any kind of media is delivering you news or information and that is why we need to have more proof when we make claims.