Explore Math Reflection

I choose the Möbius Strip video. I choose this video because I already know a little bit about them, and they are very cool and wanted to know more about them. To understand how it works, it uses “abstract topological space.” I understand how it works and I remember a while back I was messing around and discovered it on my own and thought it was cool. I used a small strip of paper and traced along the surface and was amazed at how I had to do more than one circle to complete the loop. The content of the video makes a lot of sense and was easy to follow. The visuals showed exactly how it worked. I am curious what would happen if you did it with more shapes, like a triangle or square. Will you get more edges? More surfaces? What happens if you were to cut it.

I also watched a video on a cube fitting through a copy of itself. I chose this video because a while back, I would watch this show called brain games. One of the episodes included a box with another box inside of it. They then switched it so that the box that was on the outside was on the inside. The video reminded me of that series. To understand how this works, it uses geometry. This is a little hard for me to understand but after they showed how it works visually, I understood it. This really blew my mind because I would not have even thought about rotating the cube. They really thought outside of the box on that one. I wonder if you could do something similar using a pyramid or a hexagon as that is what the shadow of the rotated cube was.

Another video I watched was the chaos game. I choose this video because the concept of chaos seems really cool to me and I want to learn more and try to understand it better. Fractals are “infinitely complex” patterns that are similar. Since a few years ago I have known what fractals are and this definitely made me want to watch this video more as well. The math they use is called fractal mathematics although I may be wrong. I really do not understand what had to happen for it to become a fractal because in my mind, this should not be possible but once I try it for myself, it starts making sense. This is probably my favourite video out of the ones I have seen. I wonder what would happen if instead of it randomly choosing a point if it had to move in a circle so that it was not random. I think that it will not change at all, but I can be 100% sure.

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