To answer the question of how many shapes tesselate and why?: There are only three shapes that tessellate. The reason there are only three shapes that tesselate has to do with the interior angles and their measures. There are only three shapes that when placed together so that the vertices of the shapes meet to form one point, the angles that this forms have to equal 360 degrees. If the interior angles do not sum to this then there will not be a whole number of shapes surrounding that center point, leaving you with pieces of shapes. There are only 3 shapes that will form interior angles that form 360 degrees, and that will tessellate.

So say you have 27 songs by a certain artist that you like, and 15 that you absolutely cant bare to hear. You also have 370 songs total in your ipad mini. What are the chances that you get two of your favorite songs in a row, the probability that you get one bad and one good, and two bad. So what is the probability of these if you then said that there were only 13 of the 27 favorite songs that were under 3 minutes. So the probability of you getting 2 favorite songs under 3 minutes, and then 1 favorite under 3 minutes and a really bad one.

 So 15 lanes left, so 1/15= 6% chance that he chooses the lane next to you. 7 seconds of time, so 7/45=15% chance that he jumps in during those 7 seconds. So the overall probability is 1/15 * 7/45 = 15.5 % So the guy probably choose to jump in next to you, and is incredibly inconsiderate. Eventually both people will collide. so if it takes 90 seconds for one and 100 for the other, then if we multiply it by 10 we get that after 900 seconds for You and 1000 seconds for the guy you all will collide. So after 15 min you guys will collide. Then due to the time it takes for the accident the entire pattern will be messed up and the time to collide will change.      

Pascals triangle is very interesting because it seems that so many other things can be found in it. It makes you wonder if math was all created at one time and if the Math brains got together and put all this together. Or if they just decided to start with a small idea like the powers of 11 then built off of that. In Pascals triangle we can find many different things. For example if we line up all of the number on the right side, we get the Fibonacci numbers. Then we can also see the powers of 11 in the triangle. So say you have 11 to the 7th, then if you were to right out Pascals triangle 11 to the 4th is equal to the numbers in the 7th row of the triangle. What i wonder is if pascal realized all of this or if it just happened. To form Pascals triangle you start with 1 then you add the two numbers above it.

I think that math jokes can go one of two ways, they can be really funny, or absolutely terrible. Here are some that i think are pretty funny. 

Mathematics is made of 50 percent formulas, 50 percent proofs, and 50 percent imagination. 

Old mathematicians never die; they just lose some of their functions.

Mathematicians are like Frenchmen: whatever you say to them, they translate it into their own language, and forthwith it means something entirely different. -- Goethe 

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

Classification of mathematical problems as linear and nonlinear is like classification of the Universe as bananas and non-bananas

Q:What do you get when you add 2 apples to 3 apples?
A:Answer: A senior high school math problem. 

Teacher: Now suppose the number of sheep is x...
Student: Yes sir, but what happens if the number of sheep is not x? 

Write the expression for the volume of a thick crust pizza with height "a" and radius "z".

Explanation: The formula for volume is π·(radius)2·(height). In this case, pi·z·z·a.

A: "What is the integral of 1/cabin?"

B: "log cabin."

A: "Nope, houseboat--you forgot the C."

The integral of 1/x is loge(x).

However, since it's integration, you've got to add a constant.

So ∫(1/cabin) = loge(cabin) + c, or "a log cabin plus the sea." 

A mathematician, an engineer, and a chemist were walking down the road when they saw a pile of cans of beer. Unfortunately, they were the old-fashioned cans that do not have the tab at the top. One of them proposed that they split up and find can openers. The chemist went to his lab and concocted a magical chemical that dissolves the can top in an instant and evaporates the next instant so that the beer inside is not affected. The engineer went to his workshop and created a new HyperOpener that can open 25 cans per second.

They went back to the pile with their inventions and found the mathematician finishing the last can of beer. "How did you manage that?" they asked in astonishment. The mathematician answered, "Oh, well, I assumed they were open and went from there."