Here are my mathematical and personal statements:
Personal Statement
The reason I chose to create a replica of a Cardioid graph using various colors of string on a cardboard background was simply because it is fairly simple way to represent a form of graphs we had focused on this year. This appealed to me because it gave me the opportunity to be creative as well as incorporate arts and crafts into making a great and educational final product. Making this graph out of string was surprisingly easier than I thought it was originally going to be. It consisted of a pattern involving just straight lines and these lines all were methodically figured out to be doubles. So if you started at point 4, you would thread into point 8. This cardioid got me interested in if all other graphs could be recreated using needle and thread or if a Cardioid was just a unique type that I was able to do this with. It got me more interested in Cardioid graphing and why it is the shape it is, and how just using string got me to that shape. It made me think of how someone came up with how to do string graphing, and how long it had taken them to come up with how to recreate so many different types of mathematical aspects in such creative and fun ways. At first I just pulled out the cardioid graph to try to make out of string because I recognized it as something that we had studied this year making for a good connection, but as it turns out this was one of the more interesting graphs in general as well as to make myself.
Math Statement
Cardioid's are a type of polar graphs that we had worked with this year along with other types of rose graphs. More specifically, a cardioid is a type of limaçon. Limaçons are another type of polar graphs that incorporate the radius turning around a set circle creating a loop, dented circle or heart-shaped graph. Cardioid’s stuck out to me because they had the familiar shape of a heart, and I remembered that they were one of the more complex graphs to get a hang of graphing during this part of trigonometry. The string graph that I created depicts a standard Cardioid. Even though there are many strings going through the graph (which is inevitable due to the full length of string needed to make the graph successfully) but it is still clear to see the basic curvature of a Cardioid graph with the string design.
The reason I chose to create a replica of a Cardioid graph using various colors of string on a cardboard background was simply because it is fairly simple way to represent a form of graphs we had focused on this year. This appealed to me because it gave me the opportunity to be creative as well as incorporate arts and crafts into making a great and educational final product. Making this graph out of string was surprisingly easier than I thought it was originally going to be. It consisted of a pattern involving just straight lines and these lines all were methodically figured out to be doubles. So if you started at point 4, you would thread into point 8. This cardioid got me interested in if all other graphs could be recreated using needle and thread or if a Cardioid was just a unique type that I was able to do this with. It got me more interested in Cardioid graphing and why it is the shape it is, and how just using string got me to that shape. It made me think of how someone came up with how to do string graphing, and how long it had taken them to come up with how to recreate so many different types of mathematical aspects in such creative and fun ways. At first I just pulled out the cardioid graph to try to make out of string because I recognized it as something that we had studied this year making for a good connection, but as it turns out this was one of the more interesting graphs in general as well as to make myself.
Math Statement
Cardioid's are a type of polar graphs that we had worked with this year along with other types of rose graphs. More specifically, a cardioid is a type of limaçon. Limaçons are another type of polar graphs that incorporate the radius turning around a set circle creating a loop, dented circle or heart-shaped graph. Cardioid’s stuck out to me because they had the familiar shape of a heart, and I remembered that they were one of the more complex graphs to get a hang of graphing during this part of trigonometry. The string graph that I created depicts a standard Cardioid. Even though there are many strings going through the graph (which is inevitable due to the full length of string needed to make the graph successfully) but it is still clear to see the basic curvature of a Cardioid graph with the string design.
In this math class so far this year I think the thing that I am most proud of would be my ability to do my homework. In most of my other classes I tend to get overwhelmed and don't always do my homework, but I noticed that in Mrs. Eagen's class I did all of my homework. Each couple of weeks we would receive a new assignment packet for the next homework to be completed and for each of these packets I got one-hundred percent. This I am proud of and feel that my hard work with completing my homework helped me work out a lot of the problems that I may have been having with the chapter.
A topic that I particularly enjoyed learning this year was learning to graph polar graphs, roses, cardioids, limaçons and other graphs of that nature. These graphs were appealing to me because of the shape they all portrayed. From flowers to hearts they were the prettiest graphs I had ever had experience with and in that sense the most fun too. I never knew that typing in one equation could lead to such an interesting graph that, without analyzing it, you would never expect to turn out the way it did. Some of the graphs we worked with are below.
