1- and 2- point perspectives
Exhibition Pictures
My Anamorphic 3-D Drawing Project
What Is Anamorphic?
"Anamorphosis is a distorted projection or perspective requiring the viewer to occupy a specific vantage point to reconstitute the image. The word "anamorphosis" is derived from the Greek prefix ana-, meaning back or again, and the word morphe, meaning shape or form." http://en.wikipedia.org/wiki/Anamorphosis
Things We Used
Ruler, for assistance with connecting the points; paint, to make coloring easier; marker, to connect the points; laser pointer, in order to mark the points; pennies, to make the points more visible; shoebox, to support the picture frame; picture frame, to use as a projector for the image; poster board, to draw on.
How We Used Them
The first task was to locate the desired image, which was traced onto the glass of the picture frame. The following task was to trace the points onto a large sheet of poster board. This was accomplished by taking a laser pointer, and marking the dots onto the sheet as per the picture showing the shape through the frame, in a process which consisted of aligning two points. Those points were marked with pennies, which we then drew over with markers. From there, it was a simple matter of connecting the dots, and filling in the right spaces.
Struggles And Adaptations
Initially, the laser pointer was put directly through the picture frame, however, this caused heavy refraction, which lead to the points being inconsistent. This dilemma was solved by shining the laser AROUND the frame.
"Anamorphosis is a distorted projection or perspective requiring the viewer to occupy a specific vantage point to reconstitute the image. The word "anamorphosis" is derived from the Greek prefix ana-, meaning back or again, and the word morphe, meaning shape or form." http://en.wikipedia.org/wiki/Anamorphosis
Things We Used
Ruler, for assistance with connecting the points; paint, to make coloring easier; marker, to connect the points; laser pointer, in order to mark the points; pennies, to make the points more visible; shoebox, to support the picture frame; picture frame, to use as a projector for the image; poster board, to draw on.
How We Used Them
The first task was to locate the desired image, which was traced onto the glass of the picture frame. The following task was to trace the points onto a large sheet of poster board. This was accomplished by taking a laser pointer, and marking the dots onto the sheet as per the picture showing the shape through the frame, in a process which consisted of aligning two points. Those points were marked with pennies, which we then drew over with markers. From there, it was a simple matter of connecting the dots, and filling in the right spaces.
Struggles And Adaptations
Initially, the laser pointer was put directly through the picture frame, however, this caused heavy refraction, which lead to the points being inconsistent. This dilemma was solved by shining the laser AROUND the frame.
Trigonometry Application
In geometry, we have started in class upon trigonometry, literally, "The measurement of triangles".
Pictured below are my solutions, in the program known as "Geogebra", which figures prominently into my education this year at Animas. Think "Software to digitally represent mathematical concepts precisely", and you'll have it down.
The images below showcase the process I used to determine the distance of various objects around the school away from myself.
Pictured below are my solutions, in the program known as "Geogebra", which figures prominently into my education this year at Animas. Think "Software to digitally represent mathematical concepts precisely", and you'll have it down.
The images below showcase the process I used to determine the distance of various objects around the school away from myself.
Hexaflexagon
This is my hexaflexagon. it's a hexagon that rotates through itself, cycling through different faces. When one face is rotated, it reveals the next. My project also uses lines of reflection. Each triangle is a reflection of its neighbor. The part of my hexaflexagon that pleases me most is the side shown in the picture. Notice the line reflection on each side. Pretty neat. I would definitely make the patterns that you see here a bit more congruous. I would also go for more complicated patterns, and have a bit more faith in my ability not to mess up symmetry.
Snail Trail Graffiti Lab
This design was based off the concept of reflection, and symmetry based off reflection. We made a circle, with a few line bisecting it. The cursor was then reflected over each of these lines, and it's properties were changed so it's path would be visible. This gives it the rather balanced look which appeals to me so much. For the precisely spaced points, I used the arrow keys to manipulate the cursor rather than the mouse.
This design taught me that my occasional pushing of seemingly useless buttons, both literally and metaphorically, can result in pretty patterns, both literally and metaphorically.
This design taught me that my occasional pushing of seemingly useless buttons, both literally and metaphorically, can result in pretty patterns, both literally and metaphorically.
Two Rivers Geogebra Lab
Yet another Geogebra lab. Our goal was to model in a Geogebra sketch this hypothetical: 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. I jokingly call this radius the dead zone. 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 version didn't work, as the distance is too far between the two points. Let's see what we can do about that.
This version did. The total distance between the two points is significantly shorter. It is also the perpendicular bisector of the east fork of the river.
Burning Tent Geogebra Lab
Another geogebra lab with a harrowing hypothetical harassment. 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?
First things first. Let's try that whole "Minimal distance to just one point leads to minimal distance to both points" thing again. Doesn't seem quite right. Maybe that line to the reflected point across the river can help me...
I think it did! The real focus here is perpendicular constructions create shorter paths. It would appear that it did in this case, upon examining the line that reflects the flaming tent across the river. Note the shorter total distance. The overall lesson here is that reflections can help one find perpendicularity, and thus the shortest path.