1-Point and 2-Point Perspective
Visualizing 3-D Objects from Different Perspectives
Anamorphic Drawing of the Impossible Cube
An Anamorphic drawing is typically a 3-D image that is distorted unless looked upon at a specific angle. To create the anamorphic drawing, a glass frame,
box, laser pointer, poster board, and pennies were used.
The anamorphic drawing is a projection because the original drawing was placed vertically in the box while the poster board laid flat on a table some distance away. If the drawing was a tracing then the end product would be the same size as the beginning project, but since it was projected the end product was significantly larger than the beginning product. To create the anamorphic drawing, a glass frame with the selected drawing was placed on a box. A laser pointer was used to show the partner where the points were to be. Pennies were placed at the points to allow for the movement of points to get the correct image. Once all points were placed, lines were drawn connecting the dots. We then used paint to shade the shape
A challenge for my group was getting started and finding the correct process to use when creating the drawing. At first we used pencil marks instead of pennies but we kept messing up and was constantly erasing our mistakes so we switched to pennies. The pennies allowed us to get an approximation of where the point was but still be able to adjust the point if necessary without the need to erase.
Finding the Height of Objects Using Trigonometry
Hexaflexagon
Hexaflexagons are 3-D objects that can be rotated revealing different designs.
For my Hexaflexagon I focused mainly on rotational symmetry, for each side the centers match up. When we first colored the hexaflexagon each side was a single horizontal strip. To create the rotational symmetry the corners had to be drawn to match. This was not easy because the corners were not next to each other, making the reference points harder to create.
For my Hexaflexagon I focused mainly on rotational symmetry, for each side the centers match up. When we first colored the hexaflexagon each side was a single horizontal strip. To create the rotational symmetry the corners had to be drawn to match. This was not easy because the corners were not next to each other, making the reference points harder to create.
I enjoyed coloring the most. Creating the designs was difficult yet fun. Making sure the designs matched each other was really difficult. If I could recreate the hexaflexagon I would take more time to ensure that the designs matched up better once I actually constructed the hexaflexagon. I learned that at times I can forget to think further into a project which would ensure that I make less mistakes, but at times I can forget that and my projects don't turn out as well.
Snail-Trail Graffiti Geogebra Lab
This was a very entertaining
lab. We created art using reflections and rotations. We took a circle and
divided it into 6 parts. In a single section of the circle we place a random
point. Then we reflected the point over each line of the circle. Since each dot
was a reflection of the first, however we manipulated the first dot, the rest
would follow.
I learned that I can create interesting
designs using simple geometric concepts. Not all things about geometry are
numbers or shapes. There are many designs that can be created using geometry.
Two Rivers Geogebra 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.
Even though this point (Green House) would seem like the ideal point for the person to live it is not. This is because even though tchically it is the shortest distance to each river, the problem is asking for the shrotest distance total.
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This actually would be the place you would like to build your house (or on the other river). This is because it does achieve the goal of having the smallest possible distance to travel.
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The Burning Tent Lab
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? In this exploration you will investigate the minimal two-part path that goes from a point to a line and then to another point.
This scenario does not satisfy the requirements because the angles from the Tent fire to the river and from the Camper to the river are not equal. When the tent fire is reflected over the line the line to the Camper is not the same as the line from the camper to the river.
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This scenario does satisfy the requirements because the in going and out going angle of the river are equal and the reflected Tent fire is along the same line as the Camper to the river.
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