When looking at this post, the thing that popped out to my the most was that there were only 3 different shapes that could tessellate perfectly. In a way, this sort of bugged me because i thought, how could that be possible? Well on my search for tessellations, i came across multiple pictures that interested me and brought up a completely new thought.What if you used two different shapes? Yeah, its not your typical tessellation, but it gets the same job done. If you use octagons and you matched them up side by side, the space in between them would make a square. Example:

This got me thinking even more, how many different possible two-shaped tessellations are there? My opinion is that there are infinitely many. Which made me think even more.... A tessellation is almost just like a pattern that you see in elementary school. Like: Circle, triangle, square, circle, triangle, square... etc. So... a tessellation could be more that 2 shapes. how about 3? or 4? or 5? Here is an example of 3 shapes:

As you could see, this could become very complex. Having more than 5 shapes would become very difficult to follow.

http://www.mi.sanu.ac.rs/vismath/crowe/cr3.htm
http://amyford2013.wordpress.com/

Probability

There is a probability problem that i have thought about quite often in the past when im on my way to school... Say you come to school around 7:30 everyday. Judging by my experience most of the parking lots are fairly empty at this time. Not knowing the actual numbers, lets assume there are 150 parking spots in sophomore lot. At around 7:30 there are about 15 cars in the lot, taking up the nicest and closest parking spots. This leaves about 135 spots left. There is one spot in particular that i like and it is towards the front and next to a trash can. Usually this spot is open. My problem today, is what is the probability that the spot that i like will be taken by the time i got to school at 7:30? 

Since the first 15 cars pick from the top parking spots, we will say that there are 25 top parking spots that they choose from, from day to day. The spot next to the trash can is included in this number. So, I can looking for this spot to be open, so in order for that to happen, the 15 drivers must pick one of the other 24 spots. The probability of them picking the spot next to the trash can, not including their intellect, is (1/25)*15=.6=60%

Now, having the probability that my spot would be taken, we can find out the probability that It will be open very easily. 100%-60%=40%

Pascal

Within Pascal's triangle, there are man interesting patterns. The simple ones that everyone knows are that each row, when added, is a power of two and that each row is a power of 11. There are others including looking at the triangle diagonally, the first row is all 1's, the second row increases by 1 (1,2,3,4,5....etc) the third row goes up by 2, then 3 then 4, then 5, then 6..etc. The Fibonacci sequence was even found in Pascal's triangle, if, instead of the normal shape of the triangle, you make it look like a right triangle starting each row on the left in stead of the middle, then you add the rows diagonally, you get the Fibonacci sequence. The triangle was not the only thing that Pascal did, he also invented a lot of helpful tools. The Pascaline, the Roulette Machine, the Wrist Watch, and he even had a unit of measurement named after him. When looking at Blaise Pascal's life and accomplishments, its easy to realize that he was a very influential person to mathematic.
http://inventors.about.com/od/frenchinventors/a/Biography-Of-Blaise-Pascal.htm

Humor

Math Jokes :)

Mathematics is the art of giving the same name to different things. -- J. H. Poincare

Algebraic symbols are used when you do not know what you are talking about. 

Q: What will a logician choose: a half of an egg or eternal bliss in the afterlife? A: A half of an egg! Because nothing is better than eternal bliss in the afterlife, and a half of an egg is better than nothing.

To mathematicians, solutions mean finding the answers. But to chemists, solutions are things that are still all mixed up. 

Philosophy is a game with objectives and no rules. 
Mathematics is a game with rules and no objectives. 

A mathematician is a blind man in a dark room looking for a black cat which isn't there.

I do not think -- therefore I am not.

A SLICE OF PI
******************
3.14159265358979
  1640628620899
    23172535940
      881097566
        5432664
          09171
            036
              5

Basically Math is ridiculous... but i like it!!! :)


http://www.math.utah.edu/~cherk/mathjokes.html
http://calculus.nipissingu.ca/jokes.html#top