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.

Frieze Pattern In Real Life

Frieze patterns are patterns that repeat in a straight vertical or horizontal line. Frieze patterns are found in architecture, fabrics, and wallpaper borders. As we learned in class, there are only seven types of frieze patterns. 

As I was looking for frieze patterns around the house, I found that the headboard of my bed has a frieze pattern. Using the reflection chart, I figured out that this frieze pattern is “F1”. It has no vertical or horizontal reflection and it also has no half turn symmetry. 

 

Frieze Pattern

As it turns out, my house has very little patterns.  The closest thing I could find to resemble a Frieze pattern was this pattern on some old piece of clothing.

Taking just a line section of the repeating pattern, I went down the reflection chart.  I figured out there was a vertical reflection, so I followed the chart to figure out that there was also a horizontal reflection.  Having both vertical and horizontal reflections make this pattern a Frieze 7, or F7 pattern.  The picture is crooked so the lines aren’t exactly straight, but I made the vertical and horizontal lines of reflection on the pattern below.

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?

 

https://www.bettycrocker.com/recipes/rosettes/75a92005-db32-411b-a9cc-e4efa438d121

http://www.geniuskitchen.com/recipe/rosette-cookies-swedish-rosettes-396389

Symmetry Gives Things Beauty

I know a lot of people don’t like spiders, but with the most recent conversation of symmetry we had in class, I can finally talk about them, and even show a picture of one! I specifically picked a very large species, shown below, which is the Giant Huntsman Spider, so called because they can reach a leg span of 12 inches, and they don’t make webs, but chase down (hunt) their prey. Aside from the incredible importance spiders have in keeping pest insect populations down, they are also symmetrical, as can be seen below.

Not only are they symmetrical, but they are also not chiral; their reflections would look exactly the same, and their original images could be superimposed on the mirror ones.  This perspective gives the spider a kind of beauty, in my eyes. So, in conclusion, it’s amazing how many cases of natural symmetry can be found, and yay, for something finally giving me a reason to post and talk about the Giant Huntsman Spider!

Symmetrical Mehndi Hand Designs

Similar to Mandalas, Mehndi hand designs are meant to be symmetrical in one way or another. For those who don’t know, Mehndi is a form of body art from Ancient India. The designs are made from a paste using dried powder from a Henna plant. Each Mehndi design has a significant meaning, much like mandalas. Many Indian women cover themselves on Mehndi for special events, such as weddings. The designs last from one to four weeks, depending on where you get the design. Here are some cool pictures some designs.

 

Here is a link to a website about Mehndi: http://www.mehndimama.com/info.html

Nature Mandalas

If you know me, you know that I’m a nature freak.  I always strive to be one with the Earth and feel the energies radiating off of its surface and all that stuff, I just find it so calming and interesting and it keeps me in the present. So obviously, I had to incorporate this into my blog post this week.

Natural mandalas can occur in so many places in nature, whether its in flowers, shells, spiderwebs, or even fruits.

Fruits hide a natural mandala in their core.  When it comes to citrus fruits, there are mandalas all throughout, but when it comes to fruits like apples, a perfect mandala is always formed right at the center.

Flowers can have a circular center blooming out to colorful outer rings that have layers of color.  Ferns can also be considered nature mandalas as well because the dewdrops on the leaves create symmetrical patterns.

Shells contain multicolored spirals throughout their entirety.  Spiderwebs, which I find the most intriguing and beautiful, create mandalas with a circular pattern beginning in the middle and working its way outward.  What makes them extra eye-catching is when the dewdrops (I don’t know why I’m focusing on dewdrops here but I guess I am) are glistening in the sunlight.  It just adds something extra to the whole image.

I could go on and on about this but instead, you can check out this link:

http://www.mandalasforthesoul.com/nature-mandalas/

If you’re as into this stuff as I am, I recommend checking out the rest of the website while you’re at it!

Food Mandalas

There is a theory out there that people find things that are symmetrical to be more beautiful in nature. This could be how we are drawn to objects we like, or people’s faces we are attracted to all based on symmetry. When we look at something and it looks so intriguing, do a little digging next time because chances are that what you’re looking it is symmetrical in a way. Our brains are drawn to it, some scientists believe.
The other day in class we got to color and draw our own Mandalas, and it was fun. I noticed when we were all showing our papers to the class, not one was remotely the same and that was very cool. Each of us had a reason why we chose to do what we did, places to start and what techniques we used. I came across some really pretty symmetrical food pictures and they are suppose to represent mandalas. They are very visually appealing to look at, and I wonder if that has to do with the fact if you sliced it down the middle or in any way rather, that it would be the exact same reflection on the opposite side. They are shown below

 

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.

Monument Valley

During our class Thursday as we looked at various optical illusions,  I thought back to a smartphone game I used to play a few years ago.  The game is called monument valley, and it’s a puzzle game based on optical illusions.  The goal of the game is to shift the landscape of the levels to make a path to the exit.  The paths you make seem impossible, and they should be, but our perspective of the levels make them possible. 

What reminded me most about this game from class was when we made the origami Penrose Triangles and had to look at it from a certain angle to make the sides line up.  You have to use your mind the same way when playing this game to be able to complete the levels.

This is an example of what one of the levels looks like.  It doesn’t look like much of an optical illusion with a still image, so I’ll link a video too.

 

Skip to about 5:10 to get an idea of what this game is and how it uses optical illusions to entertain.  At one point during that level, there’s a clear Penrose Triangle that must be climbed to progress through the level.  I think Monument Valley is a great amount of fun and I recommend it!  It’s more difficult to figure out than the video suggests.