Real World Symmetry

I was thinking about what I could post about this week and decided to try and find some cool pictures of symmetry in photography. While I was looking I found this really interesting picture of a tower that has most of the types of symmetry in it.

While also just being a cool picture, this tower has both types of reflective symmetry, over the horizontal and vertical axis. It also has 180 degree rotational symmetry. The power lines at the top of the tower threw me off a little bit because I thought they broke the symmetry, but it seems like even they are symmetrical. I just thought this was a pretty cool picture and wanted to share it with you all.

Symmetry in Videogames

Hey all. I’d like to relate the topic of symmetry we talked about in class to videogames. Specifically, Overwatch.

Symmetry in videogames is extremely important to keeping certain game modes fair. In Overwatch, there is a mode called control point. IN this mode, the teams compete to get to and hold a control point. If one side had an advantage over the other, such as a shorter run to the control point, that side would have an incredible advantage over the other.

This is an overhead picture of the control map Nepal. As you can see, the overall shape of the map has reflective symmetry to it. While the details may not be exactly the same, the general layout of each side is.

Each side has health packs in the same place. Each side has the same 3 pathways to get to the point. Neither spawn point is closer than the other. This gives the map dihedral symmetry, and makes it fundamentally even for both teams.

There are more maps like this in Overwatch and plenty of other games that also have symmetrical maps. This kind of symmetry sits at the heart of map creation for any game with this type of game mode. It is the only way to guarantee that the maps are dead even for everyone. This makes symmetry one of the most important math topics in game and map creation.

Knights Path

I found our discussion in class about a knight’s path very interesting. What I like the most is how intricate the designs are if you trace the path completely. We looked at some of these in class, but I found some more online. Going into the class, it seemed like such a simple thing. I didn’t really think about how much the knight piece would have to move in order to land on every spot on the board. But, looking at the designs on this website just shows how intricate and complex it is. I used to play chess a lot with my mom, and so when I got home I was able to talk about all of this with her. This was probably my favorite topic so far.

Here is the website I’m talking about.

http://mathworld.wolfram.com/KnightGraph.html

First Blog Post

I found it very interesting that a popular vote counting method, Borda, has such a flaw in which it can’t be used with only two candidates. It isn’t possible to get two different winners with only two candidates. Whoever wins the “first place” vote just wins, and that defeats the entire purpose of the Borda method.