1 VS. 2 Point Perspectives
Visualizing 3D Objects in Different Perspectives
My Anamorphic 3-D Drawing Project
Calculating Heights of Objects
1)
tan 20=h/w tan15=h/(89+w) wtan20= tan15(89+w) wtan20= 89tan15+wtan15 wtan20-wtan15 = 89tan15 w(tan20-tan15) = 89tan15 w = 89tan15/(tan20-tan15) w = 248 h = tan20 x 248 h = 554 |
2)
tan18=h/w tan10=h/(87+w) wtan18=tan10(87+w) wtan18=87tan10+wtan10 wtan18-wtan10=87tan10 w(tan18-tan10)=87tan10 w=87tan10/(tan18-tan10) w = 103.2 h = tan18 x 103.2 h = 33.53 |
3)
tan15=h/w tan9=h/(126+w) wtan15=(126+w)tan9 wtan15=126tan9+wtan9 wtan15-wtan9=126tan9 w(tan15-tan9)=126tan9 w=126tan9/(tan15-tan9) w = 182.14 h = tan15 x 182.14 h = 48.8 |
PICTURE
Hexaflexagon
The designs on each section of the hexaflexagon used lines of reflection. It is reflected amongst the other sides of the hexaflexagon. What I liked about making this geometric shape is that you can't mess up with the designs, you just have to repeat that same design on the other faces. It was interesting to see how other students hexaflexagon designs ended up.
The first picture of my hexaflexagon is my favorite. As you can see it made a y-shape inscribed in that face. Whatever design you made on each face, you might be surprised yet intrigued by the abstract designs. This hexaflexagon was very fun to make but had a hard process. If you did not follow directions, it can end up being a disaster. This is what I have learned in this semester of Geometry. The parts I would refine about the hexaflexagon is how it maneuvers. In this picture above, it has a crease right in between the bottom two triangles. This happened when I was rushing the final part of this. It maneuvers and folds a bit unevenly, and I am quite unhappy with this because it actually made the hexaflexagon a mess.
Snail Trail
The snail trail was created in a program called GeoGebra. In GeoGebra you can create all different shapes and designs. This design above was formed when each line I drew was reflected in each portion of the circle. Each sixth of the circle is actually the same if you look hard enough, just different colors. This creates beautiful and slightly abstract drawings (like the hexaflexagon).
I learned in this mini-project that you can't mess up with this. Every design is very cool just the way it is. Follow directions exactly how they are told and nothing will go wrong.
Two Rivers
The objective for the two rivers geogebra lab was to discover the minimum sum of two distances from a point to two lines.
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.
The first picture is a representation where not to build your house. It has a 5 mile radius away from the sewage plant, but it is too far away from each of the rivers to fish in. It is unlikely that this house would be built here.
The second picture is a representation where you should build your house. It is a probable location of the house and it is right where a river is so you can fish in the west river. It is also in a 5 mile radius away from the sewage plant.
The Burning Tent
The objective for The Burning Tent lab was to determine the shortest two-part path to help a camper put out a fire based on the problem scenario described. 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.
The first image shows where to get the water to put out the tent fire. It is logical to fill up a bucket of water approximately the same distance from the camper to the river than the tent fire to the river. This is the fastest and most efficient way to put out a fire.
The second image shows where not to fill up your bucket of water. It is completely illogical to go past the tent fire to retrieve a bucket full of water then go back to the fire to put it out.