Complex Origami

One of the things that appealed to me the most this week was when we practiced origami. I’ve never really been all that interested in origami so of course I thought it was probably really easy most of the time and didn’t require as much thought and precision as it really does. It’s so important and popular that during my research I found out that there is an origami competition held every two years in Japan. I did some research and found out that one of the three largest origami cranes in the world was constructed by Akita Japan residents and had a wingspan of 206.7 feet!

Obviously there is the lesser complex origami like what we did in class, but there are also super complex and incredibly complicated designs out there. The video I included the link to shows the top 10 most complex origami in the year 2014. I’m sure things have changed since then but while you watch I think it would be cool to just think about the precision and accuracy that has to go into this to make it look so realistic.

Here’s the link:¬†https://www.youtube.com/watch?v=uoBzal8hNFU

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.

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)

Traveling Salesperson Problem

I never find much use in math where I learn something that I’m going to ever actually use again in my life, but this is something that I know I will quite frequently. I actually use it a lot in real life and have for a long time without knowing it. Whether it’s going to town to do errands I figure what is the best route to stop at all the places I need to go, in the grocery store what isles I should go to in what order for the things I need, and even when I’m getting ready for the day trying to figure out the quickest most efficient way to do everything in the least amount of time.

What I connected this week to was a trip I’m taking this year. It’s for a 4 day trip with a group of friends to go car racing. To get to Florida using American Airlines directly it would be about $380 dollars. To stop at just one place along the way from Boston to Virginia would be $231 and then Virginia to where I will be flying into would be closer to $130. Of course these prices can and obviously will change, but for now I plan to use the theorem from the TSP to gauge although it could be a little longer time wise that it’ll be more cost effective to make a stop somewhere along the way.

Now that we do know these I feel like I am going to surprisingly find myself using this way more often in real life, especially now that I know it’s a real thing and not just something unnamed that everyone uses but no one actually has a real name for it. I’m looking forward to finding out some more useful things from class that I will actually use in my life, not just learn for a test, regurgitate the information, and forget it days later to never use again.

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.