Intro:
In the Measuring your World project, we were told to pick/make a group with up to two other people. I chose to be in a group with Matthew Mau and Diego Austin. After that we were instructed to take an object and measure the volume, area of an object, as well as using a trigonometric function in order to solve either an area and/or volume of the object. To make this convenient, we chose to measure my black water bottle. This bottle has 2 different cylinders to it. A primary cylinder where the majority of the water is held, a secondary cylinder which is a lot smaller in size compared to the primary cylinder. This means a lot less water is held in the secondary cylinder.
Since there were 3 of us, we decided we could split up the work somewhat evenly by tasking each of us with one mathematical process. Diego took on the process of finding the volume of the water bottle. Matthew decided to find the total area of the bottle. This left me with the trigonometric function option. Diego’s task was fairly simple. Since the formula to solve for volume is volume = height x length x width, he just needed to measure the height, length, and width of each cylinder of the water bottle. Then once he got the product for both cylinders, he added them up and got a total of 39.6 oz. For Mau, he had to take the dimensions of the bottle and transfer those dimensions to a 2D plane and find the area (which formula is area = base x height) by multiplying the base and the height of each cylinder one at a time, then adding the products together. His final answer is 37.92 inches. I was left to fulfill the task of using a trigonometric equation or process in order to find the volume/area of the object. I chose to find the volume of the water bottle if it had a hexagonal base. During the presentation I didn’t use an actual trigonometric formula/process to find this but however, Dr. Drew said I could redo it on the Dp update and use a trigonometric formula there. After going back through my notes and thinking and trying to figure out how to get the solution by applying trigonometry, I finally found a way. What you need to do is make the base of the object a regular hexagon with a total of 540 degrees. Then you want to split the hexagon into 6 equilateral triangles. From there you want to make a 30 60 triangle. You can do this by splitting one of the 6 equilateral triangles down the middle. From there we know the sides of the 30 60 triangle since we have the x that belongs with the 2x and 3x. We then go from there and solve the problem.
I think this was a fairly short project which isn’t a bad thing. I liked how it was simple and how we got the freedom to measure whatever we pleased to measure. I also enjoyed how the work could be split up evenly. I also enjoyed the group I was in and think I could work with them if we did a small and short project like this one we just wrapped up. Some habits of a mathematician my group and I have used throughout this project was starting small. We split the water bottle into different cylinders in order to solve the problem. We also used the habit of a mathematician, staying organized. We evenly split up the work evenly and made sure each one of us had things to do. We also stayed organized with our calculations and our diagrams. If we weren’t organized this project would have been a real hassle. I think something my group and I would do more differently would be to help each other with the math parts even though we have assigned each other since we each had trouble with something small or didn’t fully understand some things. If we were to do a project similar to this one, I think we would choose to do a more challenging and interesting object than a water bottle.
In the Measuring your World project, we were told to pick/make a group with up to two other people. I chose to be in a group with Matthew Mau and Diego Austin. After that we were instructed to take an object and measure the volume, area of an object, as well as using a trigonometric function in order to solve either an area and/or volume of the object. To make this convenient, we chose to measure my black water bottle. This bottle has 2 different cylinders to it. A primary cylinder where the majority of the water is held, a secondary cylinder which is a lot smaller in size compared to the primary cylinder. This means a lot less water is held in the secondary cylinder.
Since there were 3 of us, we decided we could split up the work somewhat evenly by tasking each of us with one mathematical process. Diego took on the process of finding the volume of the water bottle. Matthew decided to find the total area of the bottle. This left me with the trigonometric function option. Diego’s task was fairly simple. Since the formula to solve for volume is volume = height x length x width, he just needed to measure the height, length, and width of each cylinder of the water bottle. Then once he got the product for both cylinders, he added them up and got a total of 39.6 oz. For Mau, he had to take the dimensions of the bottle and transfer those dimensions to a 2D plane and find the area (which formula is area = base x height) by multiplying the base and the height of each cylinder one at a time, then adding the products together. His final answer is 37.92 inches. I was left to fulfill the task of using a trigonometric equation or process in order to find the volume/area of the object. I chose to find the volume of the water bottle if it had a hexagonal base. During the presentation I didn’t use an actual trigonometric formula/process to find this but however, Dr. Drew said I could redo it on the Dp update and use a trigonometric formula there. After going back through my notes and thinking and trying to figure out how to get the solution by applying trigonometry, I finally found a way. What you need to do is make the base of the object a regular hexagon with a total of 540 degrees. Then you want to split the hexagon into 6 equilateral triangles. From there you want to make a 30 60 triangle. You can do this by splitting one of the 6 equilateral triangles down the middle. From there we know the sides of the 30 60 triangle since we have the x that belongs with the 2x and 3x. We then go from there and solve the problem.
I think this was a fairly short project which isn’t a bad thing. I liked how it was simple and how we got the freedom to measure whatever we pleased to measure. I also enjoyed how the work could be split up evenly. I also enjoyed the group I was in and think I could work with them if we did a small and short project like this one we just wrapped up. Some habits of a mathematician my group and I have used throughout this project was starting small. We split the water bottle into different cylinders in order to solve the problem. We also used the habit of a mathematician, staying organized. We evenly split up the work evenly and made sure each one of us had things to do. We also stayed organized with our calculations and our diagrams. If we weren’t organized this project would have been a real hassle. I think something my group and I would do more differently would be to help each other with the math parts even though we have assigned each other since we each had trouble with something small or didn’t fully understand some things. If we were to do a project similar to this one, I think we would choose to do a more challenging and interesting object than a water bottle.