Anamorphic Drawings
Write Up Anamorphic is when an image portrays the appearance of a 3D object or shape, but when viewed at different angles, looks 2D. For example, an image will look 3D from one viewing point, and from the side, it will look elongated and identifiable.
The supplies my partner and I used to make our drawing, we used a picture frame to put our image on, sharpies to trace, poster board, beads to mark points on our poster board, a shoe box to put the picture frame into, and lastly, a laser pointer. The drawing we made was a result of projection from the image on the picture frame to the poster board. I sat and stared through the glass and marked points with the laser pointer. My partner would mark the points I pointed out. This four inch drawing turned into a large image on a poster board, and created a 3D effect because of the shading we used. The biggest challenge we faced was the points “moving”. We would sit at a slightly different height, and the points would be off by half an inch. So at one point, we had me sit down and power through the process of pointing certain edges and important points out. Without the usual breaks we would take, we were able to create a more accurate version of our picture by working through the challenge of heigh and inaccurate angles. |
Figuring out Size
Click here to see the math I did with my group!
For this, we used our knowledge of trigonometry and applied what we knew to guessing the size of tall objects. We measured angles the best we could from three different viewpoints and attempted to use our skills to get the height. In groups, we took a measuring tape and something to view the angle we are looking at through. We combined all of those numbers together and created our best estimate for the height.
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The Burning Tent Problem
With this lab, w had to figure out the shortest distance between the camper out for a hike, and the burning tent, so we can put out the tent. The shortest distance would be a straight line, but since we have to go to the river, too, we have to figure out to shortest distance possible.
The picture on the right doesn't meet the requirements because on this line, the shortest distance isn't actually the shortest. The distance from the camper to the river, to the river to the tent is the shortest it can be, but it's not the final answer because it can still be shorter. |
This picture, however, shows the shortest distance. If I wanted to walk over to someone across the room from me, I wouldn't turn around tables and make my way around obstacles in order to get to them, as that would naturally take longer. I'd want to talk in a straight line, right over to them. That'd take up less time. So by reflecting the tent over the the line AB, the distance between the camper and the tent fire is at the shortest is can be.
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I came to the first conclusion by comparing the two final results I got. As a class, we thought we got the final distance until Cathy told us that there was another way, and that's the last image. And now the last image is the only thing I see as accurate, because it simply makes sense. The reflection creates a straight line, instead of an adjacent line that point tentfire was.
Two Rivers Lab
There is a sewage treatment plant at the point where two rivers meet. You want to build a house near the two rivers (upstream from the sewage plant, naturally), but you want the house to be at least 5 miles from the sewage plant. You visit each of the rivers to go fishing about the same number of times but being lazy, you want to minimize the amount of walking you do. You want the sum of the distances from your house to the two rivers to be minimal, that is, the smallest distance.
This, however, would work because the house is right on the west river and the homeowner only has one distance to walk. Since they live right on the river, there is only one distance. In the picture, you can see that Using the same angles from the picture above, the distance is much much smaller. Due to not being able to get to exactly 0 on the river, the distance isn't at it's exact shortest, but the number, 2.08 is shorter, therefore, being correct.
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I came to the conclusion that the first image was wrong due to the fact that the distance just looked like it was longer than it could be. We didn't get the best line we could, and so it made sense to make the house right on one of the rivers so there's only one distance to measure. It makes less sense to measure two distances and see which way you could make it the shortest, so we put the house on the river and instantly our problem was solved.
Snail Trail Graffiti Lab
We went into a program called GeoGebra, and in that program we followed instructions to create a multicolored example of symmetry.
To clarify what this mass of colors is, they're all lines of symmetry centered around a circle and reflected by a single point outside of that circle. It sounds a little confusing, but what it did was create lines that are all reflections of each other in some way or another. The pink lines are identical to the purple lines. These shapes are based around a circular design.
What I learned about myself in this project is that I'm not so well at following wordy instructions without many examples. I messed up this lab on the first try, and this is the result of me doing it right the second time once I got some help and examples from others. These concepts and ideas are hard for me to wrap my mind around. |
Hexaflexagon
For this, we took a few days to create a design and folded and taped our designs into this strange paper apparatus called a hexaflexagon.
This uses line reflection because even though it's hard to see in the image given, the shapes in the triangles are reflections of the other triangles. The stars are in the same place as the stars across from them. Although they aren't exactly identical due to my own flaws, they are all examples of a line of reflection. The same goes for all of the other shapes and lines on the other triangles.
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Reflection
I really like how my hexaflexagon uses colors. The colors work together, and even though it's not exactly a good representation of linear reflection, it does play with colors and looks pretty nifty for a product I've created. Addressing my flaws, I only used a ruler every once and a while and kind of rushed it. I didn't think before I made the shapes, and I wish I could've refined it better to make a more beautiful hexafelxagon, but I did manage to understand the concept, so I have gained a better understanding of how reflections and rotational symmetry works. I will be able to use this in future projects and try harder to create beautiful work. I learned that I'm not someone who really sketches things out before I try them. I didn't think much before I did this, probably because it was the day before our Thanksgiving break, but either way, I didn't plan ahead. I'm someone who lets things come to me as I create, but this situation it probably wasn't the best idea.