What if a polygon has 179 degree angles?

During class on Thursday, we talked for a moment about the angle measurements for numerous shapes, such as hexagons and octagons.  We did an activity where we had to find out the angle measurements of a pentagon using triangles, with the knowledge that there is 180 degrees in a triangle.  I heard chatter about the maximum degrees of an angle, which inspired this post’s main question: How many sides are on a polygon with 179 degree angles?

After some research online, I discovered that we can find the measure of the exterior angles if we have the measure of the angles.  To do this, just subtract the angle measurement (179) from the straight line measurement (180).  This leaves us with 180-179=1 .  If each exterior angle represented a 1 degree shift, then to meet back at the starting point, there would have to be 360 sides on the polygon! Isn’t this nuts here’s an example of what it looks like:

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?







Wallpaper Patterns on Tapestries

I’ve always been obsessed with tapestries whether they are authentic fabrics from other countries or just ones that you can buy off of Amazon. I have a black and white tapestry in my room above my bed that I just love, and it was on sale so I had to get it.

In the picture above is the design in the center of my tapestry.  It is dihedral and can rotate around the center 16 times from what I can count here, because I wasn’t sitting there counting the pattern in my room in my free time.

As you can see here, there is rotational, horizontal, and vertical symmetry here.  This is the pattern surrounding the main design on the inside.  It repeats over and over again all throughout the outside.

If you’d like to learn more about how tapestries are made, I’d advise you to check out this website. Enjoy!


Real World Symmetry

I was thinking about what I could post about this week and decided to try and find some cool pictures of symmetry in photography. While I was looking I found this really interesting picture of a tower that has most of the types of symmetry in it.

While also just being a cool picture, this tower has both types of reflective symmetry, over the horizontal and vertical axis. It also has 180 degree rotational symmetry. The power lines at the top of the tower threw me off a little bit because I thought they broke the symmetry, but it seems like even they are symmetrical. I just thought this was a pretty cool picture and wanted to share it with you all.

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


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