Hexaflexagon
My hexaflexagon uses rotational symmetry to create a mirror image of a certain design to construct an impeccable hexagon. Throughout the whole hexaflexagon, the rotational symmetry is used to make a whole piece that can rotate four times with ends that all match up. For example, on picture number four (see below) you can see how all faces are the same and each corner connects.
REFLECTION:
A feature of my hexaflexagon that I particularly like most is the how the structure is infinite. No matter how many times you spin the hexaflexagon, it will never loose its order and will continue to interest you. A symmetry refinement that I would make to my hexaflexagon is on design number 2. I messed this up and forgot to build something that would have all ends connecting. If I would've done this simple step, my structure would be more attractive. Something that I learned about myself from this project is how impatient I am when it comes to time consuming projects. Especially when it involves coloring!
A feature of my hexaflexagon that I particularly like most is the how the structure is infinite. No matter how many times you spin the hexaflexagon, it will never loose its order and will continue to interest you. A symmetry refinement that I would make to my hexaflexagon is on design number 2. I messed this up and forgot to build something that would have all ends connecting. If I would've done this simple step, my structure would be more attractive. Something that I learned about myself from this project is how impatient I am when it comes to time consuming projects. Especially when it involves coloring!
Snail-trail graffiti ggb lab
To create this Geogebra design, we used reflections and symmetry. The geometric transformation of a reflection can be displayed by the lines being a opposite of each other in the image. Symmetry is shown by the equal spacing between each line and the consistent shape throughout the figure.
REFLECTION:
Something I learned about myself throughout this project is how creative I can be if I apply myself to math. Also, I learned that my partner Easton and I work very well together when we are put to the challenge of geometry, but I will start working alone due to lack of individual research and learning. I will be more confident and understand more if I work individually. To me, this lab was very interesting and I had a lot of fun because there were so many challenging steps that lead up to a playful and amusing outcome.
Something I learned about myself throughout this project is how creative I can be if I apply myself to math. Also, I learned that my partner Easton and I work very well together when we are put to the challenge of geometry, but I will start working alone due to lack of individual research and learning. I will be more confident and understand more if I work individually. To me, this lab was very interesting and I had a lot of fun because there were so many challenging steps that lead up to a playful and amusing outcome.
two rivers ggb lab
For this construction, there were certain requirements that had to happen in order for there to be a successful outcome. The problem was: "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.
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 location does not satisfy the requirements needed to solve this problem. The problem asks for the house to be close to the West river but also to be five miles walking distance of the East river. In the picture above, the house is very close to the East River and certainly not 5 miles away from the East River.
This image shows the correct requirements of this Geogebra lab. The sum of the river's distance from the house is the smallest it can be. Also, the distance from the house to the sewage plant is 5 or more miles.
As you can see from the first picture the sum of the two distance was not at it's minimum number. It was out of proportion and that is why it isn't correct.
In the second picture, both of distances add up to the minimum number and that is why it is correct.
Buning tent lab
Scenario:
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.
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 mage is not correct because her path (the dashed line) isn't going to the river as fast as she could've. The distance of this path is not at its minimal because its number is a lot higher than it could be.
This image shows that correct requirements specified by the problem. The dashed line (the path) is at it's minimum distance which makes it the shortest path.