Semester 1-
Hexaflexagon
My hexaflexagon uses rotational symmetry to create a mirror image of one design to make a complete hexagon. Rotational symmetry is used throughout the whole hexaflexagon to make an entire piece that rotates 4 times around, either inside or outside. Line symmetry is used to reflect the shape of the hexagon as well as the design drawn onto it. As you can see,both rotational symmetry and line-reflection are used throughout to make a whole body.
Reflection
A feature that I am most proud of are the range of colors I used in my designs. The colors bring out the hexaflexagon the most when it is rotating. If I could refine the piece I would probably create more complicated designs with more colors to reflect and challenge myself further. I would've taken more time on coloring, and really made my lines clean to make it look good. Something that I learned about myself includes how I discovered that I enjoy hands on learning, and have a better time when using this style of learning. This new knowledge that I have about myself I hope t use in my future math career.
Snail Trail Geogebra Lab (October 11th)
Geogebra is a downloaded program that my geometry class has been using for the majority of the first semester. We downloaded it off the internet and use the program almost everyday. Personally, I think Geogebra can be very useful for understanding basic geometric concepts. Our class has created many labs from labs using lines to labs using artistic ability.
The geometric concepts that are used in this lab include line reflection. I dragged one line that dragged the others along with it, causing a mirror reflection of the line I am dragging. The lines in this Geogebra can be dragged anywhere on the screen, as the other lines will just follow and create new reflection lines.
Reflection
During the process of creating this lab, I discovered more of my artistic ability. I also learned that I can be really apply myself to math in a creative and different way. Learning geometry through drawing and different non traditional ways makes the subject more fun to learn, as well as enjoyable.
Two Rivers Geogebra Lab (October 25th)
ORIGINAL SCENARIO: 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.
Location 1
Shown here is an unacceptable place for the house to be located. It is too far over by the West River, making the walk to the East River a lot longer. The two triangles that are inside are not even, causing the walks to be uneven.
Location 2
Shown here is an acceptable place for the house to be located. It is almost exactly in the middle of both rivers, and far enough away from the sewage plant. As you can see now, the two triangles on the inside are both equal, causing the walks to both rivers to be equal.
Conclusion
Geometry was used in many ways in the above lab. We were forced to look at how we can create lines and different shapes to create equal distances. Also, we used number sense to come up with the best solution to the sum of distances to create equal distances. All is all, geometry can be used in different ways to view different scenarios.
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.
Not an Acceptable Place
This picture shows an not an acceptable place for the camper to be to get to the river and put out the tent fire. It is not acceptable because the total distance is farther away from the river than it could be. Also, the angles are off and not close to eachother. The camper must move closer towards the river to the
Acceptable Place
Shown here is an acceptable place for the camper to be located. This is acceptable because the camper is closer to the river and the outward and inward angles are almost exactly the same. If the angles are the same, then it is easiest for the camper to get the water then to get to the tent fire.