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

Alexis Lemaire was declared the faster human calculator when he took the 13th root of a 200 digit number in his head in 70.2 seconds. This was the world record and Alexis was very proud of himself. The first 200 digit number that he tried to 13th root took him 40 minutes to complete in his head. He then put himself through many training exercises to repeatedly cut his time. When asked, Alexis would not give away his secret but he did say that it was not all about math. It was also a lot of memorization. Daily Mail challenged Alexis with a 30 second challenge that he completed, in 8 seconds. 

This really makes you think that maybe its possible to become a human calculator. At first i had thought that it was just a born talent that people had but the way that Alexis puts it, it seems to be more of a self taught skill.

http://www.dailymail.co.uk/sciencetech/article-501232/The-human-calculator-393-trillion-answers--picks-right-70-seconds.html

Normal swimmers don't think about math when they are swimming. No offense Mrs. Mariner :). But it is interesting to see what the graph of a swimmer looks like. The most interesting thing when looking at swimming is that it can be related to math. For instance, if a swimmer is swimming at a constant pace for a certain amount of time, that can be graphed. When graphed, this would look like a straight line starting at the bottom left corner of the graph and diagonally going up and to the right. If the swimmer was thinking about math and knew alot about their sine values, they would be able to swim in a way that this graph would resemble a sine graph. In order to do this, the swimmer would have to constantly increase then decrease their speed and keep going. Also, the swimmer could make their sine graph stretch both vertically and horizontally. in order to do this, the length of the pool and the time would have to be messed with until the graph matched what they wanted. Now that we have talked about sine graphs and straight lined graphs, what other graphs do you think we could make? a Triangle graph? a cosine graph? tangent? secant? A triangle graph would be very easy to make, the swimmer would have to swim at a constant speed from one side of the pool to the other and then swim back at the same speed. In order for the swimmer to make a cosine graph, they would have to follow thew same procedure as they did for the sine graph but just adjust their speed accordingly. For the two swimmers, there would only be 1 intersection and that would be at the point in which they started. The faster swimmer (the one going the 50m) would get to the starting point at the same time as the slower swimmer (the one going only 25m). JUS

Who uses trigonometry?
This question has been used by many students when they are trying to argue to their parents that their math class "isn't important". "Who uses this stuff anyway?" they might say and in fact, there are many instances of Trigonometry use throughout the world. One use of trig is in the military. With planes dropping bombs or with artillery shooting down planes, there are equations. If you could freeze frame an action scene in a war battle, you could draw a triangle connecting the plane to the ground and then to the artillery equipment. When artillery and airplanes with bombs were first used in the military, they pilots of the equipment would have to do all of the calculations in the air and in the heat of battle. They would use trigonometry to find the angle of depression and to calculate the distance so that when they drop the bomb, it would hit right on target. Now, since technology has been upgraded so much, the machine does all of those calculations on the spot and it takes no more than a split second. But the military is full of jobs that use trig to calculate direction and distance.

When looking at the grade of a road, it becomes apparent that it resembles a trig function. The Grade of a road is exactly like the slope, just put in different proportions. if a road has a 10% grade, you might not think much of it especially when in a car but in reality, a 10% grade is a rather steep road. To find the grade of a road, you have to take the rise over the run and multiply it by 100. So this means that a 10% grade would be rising 1 foot for every 10 feet traveled. Still doesn't seem like much right? Well most hills around Albuquerque do not exceed a 6% grade. So what does this mean for the roads themselves? Is getting a 100% no longer what is strived for? If a road had a grade of 100% it would be at a 45 degree angle to the ground. This would be nearly impossible to drive up. This can tie back into our last discussion about uninformed students. This can cause for confusion especially with kids. They might ask their parents, "Mommy, why does this road have such a bad grade? a 6% is terrible, what did it do?" The explanation of this to a little kid would be very difficult, which would cause anger in the parent, thus creating a tumbling ball of frustration! haha This is yet another example of when math can be applied to the real world.

I find this blog very interesting. Mostly because ive never thought of any of that in such detail and its funny how stupid some of the things we do are, but we do them anyway. Im going to talk about a mathy idea that i find interesting. 

Basically the collest thing about math is when you can apply it to the real world. Whenever i find a problem in the real world (i work construction on weekends) that i can solve using cosine, sine, the pythagorean theory, or any other part of math, i get happy. It makes me feel like ive accomplished things and it answers the question that students ask all of the time "Why do we have to learn this? when will i ever use this in real life?". I find that awesome that ive been able to see how much math is in our lives. We cant escape it. Thats why math is near the top of my favorite subjects list. Love it!

Math and Peaches

This blog brings up many potential ideas. Some of these ideas may be long shots, but they can all be related to the jam and peaches. In this story, i feel like the roses represent math. In my case, and many cases of other teenagers, math is not something that we live and breathe. It something that we do because its required. Thats not to say that we don't get enjoyment out of it, some of us even do more math because we like it that much, but i admit that i do not eat and sleep math. In this story, the roses were something that you didn't pay much attention to. But as you went along in your life, they grew on you. They started to mean something bigger. You grew connected to them. I think this is what happens with math. I think at first, students are annoyed by math, but once they finally realize how much it can be applied and how easy it is for math to be in almost everything that you do, it grows on them. This is what has happened to me, i enjoy math a lot more than i have in years past. It means something to me now. Like the peaches and the jam. The rewards are starting to show up, and as time goes along, they will continue to grow and become a bigger and better part of my life.

The way i feel towards math is best described as a love hate relationship. Math can be very useful at times. It has helped me solve many problems especially at work (i work construction). When i can apply the math that i have learned to my life and to problems around me, i get a smile across my face. It makes me proud of my self that i accomplished something. The hate side of the relationship is that sometimes, math can be very difficult. It gets to the point that i get so frustrated that i cant finish what i am trying to do. Usually it is because i am missing some sort of small detail which aggravates me even more. In the end, i enjoy math, and i really enjoy math class. Without it, i think society would be lost.