1. Anamorphic is a form of perspective. The image that is represented is distorted in some way, creating an illusion of being stretched. Anamorphic art is not stretched, however, since it will look correct if you look at it from the right place. It is not an illusion if size, it is an illusion of perspective.
2. To create our drawing, we used several tools. We needed a box, a clear surface, a large piece of poster board, and a laser pointer. The box held the image, which was traced onto the transparent surface. The laser pointer was used to mark points, and the points were actually drawn on the posterboard.
3. Our final image is the result of projection. For the project, we projected a 3D image onto a larger piece of paper using perspective, making the image anamorphic in the process. To start, we traced our image into the clear surface, and then mounted it on the box. Then, one of the partners in the group sat behind the drawing, and the other partner drew on the poster board. The person sitting behind the image would use the laser to mark points, and the other person would mark them. When all the points were connected, an anamorphic projection drawing was created.
4. The biggest challenge for our group was making the projection look “right.” We would use the laser pointer technique, and it would look right from each of our perspectives, but when we looked at the final image, all the lines and points seemed off. We eventually figured out that the shape we chose was too complex. We got around this by choosing a different shape to project, and our project turned out much better the second time.
Tan16 = H Tan21 = H
1 x+20 1 x
Tan20= H Tan24 = H
1 x+15 1 x
Tan8 = H Tan 9 = H
1 x+41 1 x
For this project, we had to create our own circle designs. We were required to include arcs and segments, reflectional symmetry and rotational symmetry, and 3 out of 4 geometrical components. The components were:
A) construct perpendicular bisector
B) construct angle bisector
C) construct congruent angles
D) construct congruent segments
I used all of these in my drawing. In order to get the inner circle, I had to construct the perpendicular bisector of the outward lines. To double the outward lines, I had to construct an angle bisector. For the rest of the lines and arcs, I had to construct congruent angles and congruent segments. When I was done, A photocopy was made and I colored it in
A camper out for a hike is returning to her campsite. The shortest distance between her and her campsite is along a straight line, but as she approaches her campsite, she sees that her tent is on fire! She must run to the river to fill her canteen, and then run to her tent to put out the fire. What is the shortest path she can take?
Where not to fill the bucket.
This is not the best place to fill the bucket. This is because the angle the camper is coming to the river is too large compared to the angle of her going to the tent fire. Therefore, the total distance is not the smallest it can be, and the requirements of the problem are not fulfilled.
Where to fill the bucket.
This is the best place on the river to fill the bucket. The incoming and outgoing angles of the camper are almost exactly the same. Therefore, the total distance is minimized, satisfying the requirements of the problem.
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.
Where not to build a house.
This location may be outside of the "danger zone" but that is the only part of the problem that this situation satisfies. The total distance to each river is not the least, and therefore does not satisfy all of the requirements.
Where to build a house.
This location satisfies all of the requirements of the problem. The house (green dot) is outside of the "danger zone" and the total distance sum to each river is the lowest it can be.
In order to construct the designs, we had to use different geometry concepts in order for the faces to line up. As you can see, the faces line up with each other to create a pattern. We had to use geometrical concepts like rotational symmetry and line-reflection symmetry in order to make the faces line up like this.
Describe one feature of your hexaflexagon that pleases you most and explain why.
One feature in my hexaflexagon that pleases me is the way that the edges line up with each other, because it looks very clean and the colors line up, for the most part.
Describe the symmetry refinements you would make to your design now that you better understand the geometrical concepts used.
I would refine my hexaflexagon by taking more precise measurements and making sure the colors lined up. I got a little bit lazy towards the end of the project and as you can see, the lines do not line up perfectly.
Describe something you learned about yourself during this activity.
I learned that sometimes I can get lazy and distracted. I was getting tired of coloring, since that was all we did for the whole class, and I messed up the lines a little bit, as I talked about before.
This is a Geogebra lab we did in Geometry. We were instructed to create points and reflect them around the circle. Once we were done, we were able to select all the points and drag them around to create this picture. Some concepts in this picture are reflections and rotational symmetry. We divided the circles into 60 degree chunks, and when the points are dragged around, they act as reflections of each other.