The Pattern of Fire Emblem

Since this week’s topic includes wallpaper patterns, of course I’m going to share the pattern from one of my favorite video games! This one is featured when you load into Fire Emblem: Awakening. For those who don’t know, Fire Emblem is a turn-based strategy game made by Nintendo.

Now I’ll take a look at this intricate design. There is a vertical reflection, but no horizontal or half-turn symmetry. I say f3 on this one.

Now for round 2: the FE: Fates Wallpaper that appears at the beginning of each map.

I really was lost on this one. There are some point where you clearly see a vertical reflection, and others where you can clearly see a glide reflection, but neither are continuing throughout the design on the outside. f1? What are your thoughts?





Symmetry You Can Eat

After searching through some different ideas for dihedral figures, I came across this cool concept in cookie making known as “Swedish Rosettes.” These cookies are made with a special iron that forms the dough into beautiful dihedral shapes that you can eat!

These look almost to perfect to be eaten. This image from Betty Crocker’s website features dihedral 8 cookies fresh out of the oven. They are extremely easy to make (short ingredient list) and the site even adds a chocolate glaze recipe to add on top! This is without a doubt my favorite new trend-math concepts in food!

If you’re interested in baking these (I most certainly am) I’ll place some links below as to where you can find the recipes to make them! The irons can be found just about anywhere, including Amazon and Walmart, and there are thousands of different dihedral shapes to choose from. Would anyone mind if I make a batch and bring it to a future class?

League of Steiner Trees

Though Pokemon once again stood out as a prime example of what a Steiner Tree looks like in the video game world (more specifically Kanto and Johto’s regions), I already made a post about that, so instead I focused on yet another video game I have seemingly been addicted to these days- League of Legends.

The above picture shows a place known as the Summoner’s Rift, where “summoners” channel these magical crystals and summon powerful characters to do battle against one another on teams of 5 v 5. The different vertices on this map signify the positions (except for blue, that’s the shop.) These also signify which “lane you are in.

The goal of the game is to destroy the other team’s base, run down your opponents and in some cases be as rude as possible while doing so! This being said, most professional players of the game actually take into account timing objectives (slaying the dragon, killing towers, etc.) and must have each player rotate back and forth from shop to upgrade their items and from lane to lane, capturing objectives and fighting the enemy. For the sake of our class, I thought it would be cool to showcase some trees within the rift!

In any case, the “jungler” character, who traverses the jungle defeating monsters, often must put this into practice the most. During the first fifteen minutes of the game, one or two characters are matched up against one another to collect as much gold from each others’ minions as possible.

The jungler’s job is to plan out their routes efficiently to both capture various jungle monsters and help their teammates in lane defeat enemy characters and capture turrets. This is much harder than it sounds, League is like a game of chess; every move you make has its benefits and drawbacks.

I just thought it would be cool to showcase some trees within yet another one of my favorite video games! If you’re more interested in what the game really is, and had a hard time understanding my vague description, feel free to visit or simply search the game on YouTube, tons of people stream it!

Source for Photo:

The Many Paths on a Pokemon Journey

As a kid, I shared the dreams of many: to become a Pokemon master. Although I can’t say I ever achieved this goal (because they keep making hundreds of new ones every year), one thought that came to mind after today’s class was the many routes in each region of the game that connect cities and towns to more cities and towns.

As the games have progressed, we’ve seen a drastic improvement in the overall layout of each region. Here below is the Kanto Region, in all of its glory:

And now, a map of the Kalos region, in a game released around twenty years later:

There are seven regions to choose from in the mainstream games, but personally I found that Kalos has a beautiful array of plots and lines to analyze.

Below is a more linear image of Kalos from, where you can see clear paths from one destination to the next. In math terms, a blue or orange dot represent the vertices here, and the white routes are edges:

Now for the big question: Is there a Euler’s Circuit or path in this Pokemon region? Unfortunately the answer is no, I found at least four or five odd degree vertices here. On another note, I couldn’t find a Pokemon region that was fully connected (that is, because there are often islands within the game for players to sail to).

The region which I believe does contain a Euler’s Path would be Generation V’s Unova, which as you can see below should have (if my counting is correct) exactly two odd vertices:

Did you guys find this post interesting? Am I off regarding how graphing theory works? Let me know in the comments below! Thought it’d be cool to reference one of the greatest series of RPGs out there.



The NBA All-Star Game: A Sporting Event Decided By the Fans

If there’s one aspect of my life I take pride in, it’s being a sports nerd. Whether you’re talking Danny Ainge’s Celtics or the GOAT himself looking for ring number six this weekend, I’m always following some form of professional sports at any given moment. One event that caught my attention after today’s class was the NBA All-Star game, where viewers can vote for their favorite players to start/substitute for the Eastern and Western Conference (teams on the eastern side of the U.S. vs. teams on the west side). Below, I’ve found a couple of preference schedules that highlight the results of this year’s All-Star voting in the Eastern and Western conferences of the NBA.

In the terms of voting theory, we can see that this system determines which players from their respective positions in the league (frontcourt and backcourt) will be starting in the game next month. The top two guards on each team as well as the top three forwards will start for each team in the All-Star game. We can say that these starters were determined by the Plurality method, because the top two guards and top three frontcourt players were determined by popular vote. 

I decided to find out how many possibly ways N players could be ranked by voters. With 10 total players in both guard and frontcourt categories on each team, this number can be found. I found there to be a grand total of 3,628,800 ways in which voters could rank the ten players for each position on each team. Why is this important? Well, in the end, the top two guards and top three frontcourt players from each category within a team are designated as starters (which is a pretty big deal to the players).

Please let me know if you have any basketball questions I can clarify for the above. In summation, I wanted to sort of show a realistic way in which the voting system we talked about today determines real life scenarios for real people. In this case, said event was the NBA All-Star game, the votes determining which players voted onto the All-Star teams will start and which will be on the bench.

Source: (The NBA official Twitter page)