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

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

Four Color Theorem

So you guys might remember the Four Color Theorem from class, which states that any planar map needs no more than four colors to be colored in so that no bordering regions are the same color. This got me thinking, does this really only work for a flat map, or can it work on something that is also 3D?

In this example, a 3D figure was completely colored in using only 4 colors, confirming the theory that it can, in fact, be done.

In this 3D object, you will notice that 2 of the blocks are not filled in (the ones that are a yellow color and look like they are caving in), but can easily be filled in with a green one on the top and a blue one on the bottom.

Other 3D objects can be colored with four colors if they are flattened first. This does not work for all objects though, as most maps on a torus require 7 colors.

Below, I have posted a video of Torus Earth, to show how the flattening process has created the map.

Here is a link to read more about the sphere:

https://www.quora.com/Does-the-four-color-theorem-apply-on-a-sphere

And here is the link to the 3D four color theorem:

http://mathforum.org/mathimages/index.php/Four_Color_Theorem_Applied_to_3D_Objects

 

Graph Theory and the Ramsey Theory

After our last class, I was curious to see if graph theory could solve any other forms of problems. After a little digging, I found the Ramsey Theory. The theory was named after Frank Plumpton Ramsey, who had spent all 26 years of his life devoted to it.

Image result for frank plumpton ramsey

A typical result in the Ramsey  Theory states that if some mathematical object is partitioned into finitely many parts, then one of the parts must contain a subobject of an interesting kind.

He is most known for his dinner party problem, which is to find the minimum number of guests that must be invited so that a certain number will know each other and a certain number will not know each other. I was very curious to see what that problem would look like, so I did a little more research. This is what a completed graph for the problem looks like:

Each letter/vertice represents a guest, the blue lines represent guests who know each other and the red dashed lines represent people who don’t know each other. This little animation shows the number of triangles that are formed using lines of the same color. The number of triangles will be the minimum number of guests that need to be invited.

More on Dinner Party Problem:

http://mathforum.org/mathimages/index.php/The_Party_Problem_(Ramsey’s_Theorem)

Weird Taxes

Let’s face it, taxes can be a boring, painful experience. This is why I have decided to focus my post on some of the weirder taxes out there. I’m picking out the ones that I thought were interesting, but I am leaving the link in case you guys want to take a peek.

  1. Illinois has a very strange candy tax. The state has a 5% candy tax on top of the 1% food tax, but if flour was used to make the candy, it is just considered an “ordinary food” and is only taxed at the 1% rate. This means that you would pay the extra 5% for M&M’s, but not a KitKat bar.
  2. Colorado considers coffee cup lids to be “nonessential,” and there is a 2.9% sales tax if you want a lid on your cup.
  3. The state of Nevada gives out a free deck of cards when a tax return is filed.
  4. The state of Alabama has a 10% tax on cards decks with 54 or fewer cards.
  5. If you want vending machine fruit in California, there will be a 33% sales tax on it. You will not have to pay that if you buy the fruit at the grocery store.

Hope you enjoyed these facts! The link to these facts is right below!

Link to these facts: https://turbotax.intuit.com/tax-tips/fun-facts/12-strange-state-tax-laws/L4qENY2nZ