Frieze Patterns in Real Life

Above is a picture of shelf that I’ve had in my room since I was little, although it doesn’t have rainbow fish on it anymore. The bottom of the shelf where the wave looking things are, theres no vertical symmetry because when you fold the “waves” over they don’t match up to the other one. In fact, they’re the opposite. Horizontal symmetry is not evident either because when you split it horizontally in half it also will not match up exactly because the waves all are oriented counter clockwise. I also don’t see half turn symmetry because if you were to turn this then if would just be backwards and not the same, in the reflection.

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.

Illusions

I thought what we talked about in class the other day was pretty cool considering I had never really associated math with fun optical illusions. As we studied different ones I would have to say that the music videos were probably my favorite because it incorporated music, which I love, as well as the fun music video with tons of different things going on including illusions, various colors, and patterns. I’ve always found myself interested in colors and patterns, as I work at a daycare I find myself almost always accidentally pushing my kids to create some sort of color pattern for my own pleasure. So I did some further research about illusions and some popular one’s that you all may or may not have seen.

This one was interesting to me because it was all about trying to decide if the horizontal lines were sloped or parallel to each other. We are so focused on if the black and white lines are parallel to each other in terms of being vertical together that it would appear that the horizontal lines are crooked, which they really aren’t.

This is a more simple one. Because our eyes automatically focus on the black dot in the center and it makes it seem as though the black lines are curved,  it therefore makes the two purple lines curved. The illusion it plays on us begins with the black dot in the center, do you think it’s curved or straight? I feel that some people will see it differently but I think that they are in fact straight.

This last one is an old yet effective one. I remember seeing this back when I was way younger in some of the Nintendo DS games, it was part of a series of games. The object is to try and focus on saying the actual color you see not the color the word says. For example, green, red, blue, yellow, blue, black, etc. It may seem easy at first but after a couple times try to speed it up a little to add more difficulty.

 

Overall I find optical illusions really interesting. Honestly, sometimes some of the hardest ones are the most simple and not that difficult to solve we just end up getting into our own heads too much and convince ourself that it’s more complicated than it really seems. I’m excited to see what the rest of the semester holds with colors, shapes, and illusions like these because I actually think they’re much more interesting and fun than taxes stuff we did. (Nothing personal, I just like hands on stuff more than notes and quizzes)

“Crowdsensing” and Trees

I have personally only experienced the hustle and bustle of the subway station a handful of times in my life. With this being said, it it quite apparent that the system is messy and often times chaotic.

When I heard about UrbanEngines, a company that uses math, specifically the trees we have beendiscussing this past week, to infer the real-time state of a transit system, I wanted to read more. It was founded by led former Googler Shiva Shivakumar and Balaji Prabhakar, a Stanford computer science professor.

Users of the subway simply enter and exit the system, and the company then produces a digital replica of the city’s transportation network.

By tapping at the station when a commuter arrives and tapping out upon exiting…

“An individual’s commuting history has limited information,” Prabhakar said. “But if you have the trips of everybody, you can now reconstruct.” It just takes some math: algorithms that can compare all those trips and figure out how long it took for the buses to run or the trains to arrive. It is no surprise that Prabhakar’s background is in traffic routing for computer networks. I’m going to give the algorithm category a name: we call it crowdsensing.

This system doesn’t rely on seriously complex data- they just need to know where people tapped in and out. The really interesting thing is, if they bundle enough of the trips together, they can piece together what’s happening in the system into a real-time visualizations with astute accuracy.

“Urban Engines’ work offers potentially revolutionary solutions for addressing the complex issue of commuter congestion through incentives and data­-driven insights,” said Shomik Mehndiratta, the World Bank’s Lead Transport Specialist for Latin America.

It’s a pretty fascinating way to simply solve such a monumental problem-congestion especially in big cities- and all with a couple of “taps”.

To learn more:

https://www.theatlantic.com/technology/archive/2014/05/the-new-math-of-subways/371029/

 

Inheritance

Brad wall

2/8/18

Excursions in Mathematics

Inheritance

After today’s class I have become super interested in the idea of fair and equal giving. I did some research and found a Huffington Post article that has much different approach than the method we used today. The post outlines a few different apps that claim to make diving inheritance easier. A person using these apps can take a picture of the items they inherited and these apps will value them. There still needs to be a discussion about who gets what but it puts everything on an even playing field. The issue that I have with valuing an item based on its worth is that it doesn’t add in the sentimental value. I think our method best outlines this aspect of inheritance. I would love to know if there is any other methods people use.

Link: https://www.huffingtonpost.com/2012/04/25/inheritance-planning-relative-dies_n_1452183.html

 

Voting That Will Never Be Fair

What got me thinking after yesterdays class and even during is when we applied the criterion to each method and made the chart of what criterion satisfied each method and what didn’t, no voting method satisfied every single criteria across the board. Some satisfied more than others and vice versa but none of them worked for every single method. We also talked about how there is no true method out there that will ever satisfy all categories of criteria. Is this to say that no method in the world is truly 100% fair for voting when it comes to real life? Our presidential election, mayoral elections, elections in different countries even, are none of these satisfied by all of the criterion so no election is ever actually 100% fair? In thinking more about this I wondered if there was a way to come up with a method of voting that would satisfy all of the criteria but soon realized that if it hadn’t been thought up yet by some genius mathematician then it’s probably not all that likely. If no voting system is ever truly fair I find it somewhat amusing to think that we all just settle for the “closest to fair” so to speak and were all okay with it. Sure there are some people that get angry because it’s not fair that their candidate didn’t win and the system is “rigged” but you don’t see people rioting over it or taking it to some high up people to do something about it. Not that I’m saying anything can really be done, I just think it’s interesting that we are all just willing to settle.