Facial Symmetry

Getting my wisdom teeth taken out has inspired me to talk about the face and teeth for this post! Facial symmetry is actually a little more important than I assumed. It happens to be very important when we search for a mate. We happen to be more drawn to someone who has a perfectly (or close to perfectly) symmetrical face. I, personally, have not noticed this when looking at people, but when I really thought about it, a lot of people look for some sort of facial symmetry. Ladies, we all like a guy with a nice straight-toothed smile, am I right? These little forms of symmetry subconsciously help us find out mate! Here are some pictures of symmetrical faces and not so symmetrical faces and you can decide for yourself.

Image result for celebrities with symmetrical faces

Image result for celebrities with symmetrical faces

Image result for celebrities with symmetrical faces

Image result for tom cruise face not symmetrical

Image result for celebrities with symmetrical faces

Here is a link to see what celebrities faces would look like if they were completely symmetrical: https://www.buzzfeed.com/omarvillegas/heres-what-15-celebs-would-look-like-if-their-faces-were-sym?utm_term=.tuggo1B2Y#.ir7eMd2WZ

Rosettes in Nature

Something I find really fascinating about rosettes is that they, like many mathematical shapes, can be found in nature. A great example of that is the difference between jaguars and leopards. Aside from the physical differences in the builds of the cats, with jaguars being stockier and slightly larger overall, their markings are different kinds of rosettes.

Source: https://sciencing.com/jaguars-endangered-animals-8187721.html

As you can see with this jaguar, its body is covered in black rosettes over a golden-tan coat for camouflage. Said rosettes are comprised of dots forming a circle, within which there is always at least one dot, sometimes more.

Source: https://financialtribune.com/articles/people-environment/46479/doe-seeks-severe-punishment-for-leopard-poacher

As you can see with this leopard, it also has black rosettes over a golden-tan coat, but its rosettes are smaller, but, more importantly, comprised of circles of dots, without anything in the center. Being able to see the differences in these rosettes is very helpful in distinguishing between these two species, and being able to spot natural rosettes and other kinds of designs can be helpful in distinguishing differences between numerous species, all over the world.

Flying with Math

This month I have been on a plane like 6 different times, doing random vacations, a wedding, music festivals and hanging on the beach/surfing when I can. While escaping these horrible cold weather snowstorms, I was on the plane Monday night coming back from Fort Lauderdale Florida, and I noticed the layout of the land was so symmetrical in a way, and also very organized. When you are driving around on land, you don’t realize how specific architecture (if that is the right word lol) is and how it is laid out. Everything is almost a perfect square, circle, or rectangle when you are in the sky. It is very cool because during the day you can see the green, and the blues in the ocean, and at night you can see all the lights which show the boundaries of land, water and forest pretty clearly. Here are some cool pictures I took at night!! Goes to show when people structure building on land, they really have a method to it. I always thought people paved roads and blew out rocks for highways in random ways…interesting. 🙂

bottom picture is just off the coast of florida (east side), that is Miami you are looking at. You can see the land, and the water is the darkness you see on the left of the land.  The others are pictures of the land I flew over while in South Carolina.

Frieze pattern on my curtains!

Today as I looked at the snow melting in my out the window, I noticed the pattern in my curtains.  I can now recognise it as a Frieze pattern! A frieze pattern is a repeating pattern, and is also dubbed as an infinite strip pattern.  My mom must have great taste in symmetry since she picked out these curtains! I wouldnt have thought anything of them before, but thanks to this unit on optical illusions and symmetry, I can now recognise these curtains as a Frieze pattern!

Frieze Patterns in Real Life

Brad Wall

4/5/18

Excursions in Mathematics

I was able to find a frieze pattern today in school by looking at the texture of some chairs. These are the theater style seats in the screening room on the fourth floor.

I notice that this pattern has reflections however, there is not rotational symmetry at all. The dots threw me off when I first looked at it. There is also no glide reflections in this pattern as well. It seems to just be a simple repeating reflection. The reflection repeats over the vertical axis.

Bolivian Frieze Patterns

Hola compadres!

In July of last year I had the incredible opportunity to travel to La Paz, Bolivia to serve impoverished families, an orphanage, a free medical clinic, and lose 16 pounds in 12 days because there’s LITERALLY 30% less oxygen that high up (roughly 13, 000 feet above sea level!) so even walking up one flight of stairs was like a full-body workout. (Altitude sickness SUCKS you guys. It sucks HARD. When I got off the plane security could tell I was turning pale [hard for me to do, mind you] and I had to sit for TWENTY MINUTES before the room stopped spinning and my stomach decided to remain in my body.)

Anyways, while there, I (fashionista that I am) bought a crap ton of Bolivian printed fabrics/artworks and they were the first things that came to mind when I thought of frieze patterns!

What you’re looking at is a fabric photo frame (with our group standing in front of a free health clinic we volunteered at) and then a fabric covered notebook. While the photo frame is at an angle, the original fabric is full of straight frieze patterns, as is the middle bar design of the notebook.

Bolivian fabrics are rich in color and patterns of all kinds with glide or rotational symmetry:

The fabric is typically woven from llama, alpaca or sheep wool and usually cut into shawl-like clothing called “aguayo”. Different regions have different predominant colors or patterns that relate to the country’s rich history. If I remember, next class I’ll wear the shoes I bought there that also have (significantly smaller) patterns on them. 🙂

Here’s a picture I took at one of the park days we hosted for families – you’ll see a woman on the left sporting a baby carrier with similar patterns on it:

Math, culture, art, FASHION!

(P.S. If you’re ever thinking “Huh, I wanna support a third world country but I have no idea which one/how to give the most I can, Bolivia needs HELP. They don’t like the American government so they’ve kicked out the Red Cross and Salvation Army even though SEVENTY PERCENT of the FRIGGIN ENTIRE NATION is under the “$2 a day” international poverty line. A ton of the 3-16 year olds we worked with at the orphanage won’t have teeth when they’re adults; dental care is that poor. We spent a day working with families in an area where having a real roof (not just metal sheeting) was a luxury. Abuse of all kinds is very common and kids suffer most. They don’t have a postal system in the ENTIRE COUNTRY meaning aid needs to be delivered with volunteers or sent by parcel service which is pricey. HOWEVER One American Dollar is worth almost SEVEN (6.93 to be exact) Bolivianos, meaning you multiply by nearly SEVEN any money you donate! If you want more info let me know – Bolivia and her people totally changed my life and I want to spread the word on how to help. 🙂 )

Adios! (Me right outside of a LITERAL hole-in-the-wall pasterleria [bakery] in Western La Paz.) Did I mention the sky is bluer there because there’s less pollution? #NoFilter

 

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