Description
This is a project we did in school called scaling your world. During this project we looked at many different consents. For me I knew most of the concepts already however I did learn some new things. In this project we were tasked to make a model of something that was either scaled up or scaled down. We started off brainstorming what each person (or group) wants to scale up or down. After that we needed to draw some diagrams of what we were scaling and write down the scale factor that each group or person are doing. The scale factors do not have to be the same as everyone. after that we had to build our scaled models. if your model was too big to fit into the room or if it was temporary then you had to make a video about it.
Concepts we looked at Congruence and Triangle Congruence. When a shape is congruent to another shape that means it shares every trait the first shape has. It must have the same perimeter as the first and it must have the same angles as the first shape. That goes for triangles to. something else about consultancy is that a shape can be mirrored, moved, or rotated and it will still be congruent. it is called rigid motion.
Definition of Similarity. The definition of similarity means that two shapes are proportional to each other. What that means is that if a shape has the same angles and the side lengths grow or shrink proportionally, all at the same time and by the same amount. now this adds another way to add motion to an object. Dilation. Dilation is not a rigid motion because rigid motion moves all the points the same direction the same amount. What dilation does is move all the points inward towards the center of dilation or away from the center of dilation. When you dilate a shape that shape is similar to the first shape but not congruent. A shape can be congruent and similar though. Ratios and Proportions, including solving proportions. Ratios and Proportions are used to tell if an object is similar. lets suppose there is a right triangle that has a base of ten and a height of fourteen. Now is a right triangle with a base of five and a height of seven similar to the first shape? well if we take the two sides and arrange them into something like this 10/14=5/7 you can see they are similar. This is how proportions work. Proportions are used when doing dilation. Proving Similarity: Congruent Angles + Proportional Sides. As I stated in the definition of similarity the way to tell if something is similar is to see if the angles are the same and see if the side lengths are proportional. I also think I have mad it clear that this connects to dilation and how using ratios and proportions are a part of solving for similarity. Dilation, including scale factors and centers of dilation. As like I stated Dilation is a motion in which it shrinks or enlarges a shape. The amount it enlarges or shrinks by is the scale factor. Now the center of dilation is the point in which the dilation happens. the center can be anywhere on the same plain as the shape. Dilation: Affect on distance and area. Dilation as the title suggests can affect the perimeter and area. It affects it because the shape is getting bigger. There are some linear equations that work for perimeter and area. In the worksheet that we did called billy bear. The growth of the perimeter grew by the scale factor multiplied by the first/orig anal perimeter. The Area grew by the scale factor squared multiplied by the first/original area. |
ExibitionThe 1st benchmark was the basic info about what you are doing. Who you are working with, what you are scaling, how will you come up with your scale factor, and how will your model be constructed and exhibited. I worked by myself. I chose to do the large hadron collider. I would figure out the scale factor when I got the materials and I thought it would be created with tubing and exhibited in the classroom on a table. I do not have my benchmark 1#. Benchmark #2 was asking us to draw out what our model will be with a diagram. What our scale factor were. Mine had two circles that represented the real collider and two that were my models. I found the diameter of the large hadron collider and the tube of the lhc. I found out the scale factor by dividing the tub diameter by the material diameter. the final scale factor was 1,196.8. Benchmark #3 was all about building the model. I did a video because it was huge. It had a final diameter of 232.5 ft. I made it out of yarn and also added the border between Switzerland and France.
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Reflection
This was a really fun project. I had a lot of fun making my model. I did have a hard time at first trying to find a good object to scale. I wanted something big and part of the science community. I first thought of the mars rover. However, I chose the LHC because I thought it would be better and I was just reading about it when I was deciding. Working alone I think was best for what I did. It would have been hard for each of us to do an equal share. Anyway, I think I was very organized when writing down my calculations in the second benchmark. I think I could have done some different things than what I did for this. I felt it was pretty easy so I think I should have tried to find my Lego wheels and make the rover. I also think if I stayed with the LHC I would have loved to have enough money for an actual tube instead of yarn. However with what I actually did It was pretty good. I also could have measured out the border instead of eyeing it but it does look like the picture I based it off of. All and all It was a good project and I enjoyed it.