Tesselations

There are only three regular polygons that tessellate on the Euclidean plane.  These polygons include triangles, squares and hexagons. I recently found out what it even meant for something to "tessellate".  I did an artistic project involving the, a while ago, but I have long forgotten the actual definition. One with no knowledge on this matter, in other words, me prior to some research, would think that "to tessellate" is to decorate a surface with mosaics, but in the math world, a tessellation is what's created when a single shape, is copied and repeated throughout a whole plane, covering every area and leaving no gaps. Regular tessellations are made up of congruent regular polygons.  It makes sense for a hexagon to be capable of regular tessellation considering 6 triangles make up a hexagon, but the reason that triangles, squares, and hexagons are the only regular polygons that tessellate, is because the interior angles of these three shapes, (60, 90, and 120 degrees), are exact divisors of 360. It is possible to create tessellations using a variety of different polygons in a repeated and uniform pattern, but that is not considered a regular tessellation.  Tessellations are not only mind boggling to grasp the concept of, but when you put color and flare onto them, they are truly beautiful.  Having mathematical knowledge about them is not only useful in the world of numbers and shapes, but in architecture and decorating as well.

http://mathforum.org/sum95/suzanne/whattess.html

Pascal's Triangle

      In the 10th century, hundreds of years before the birth of Blaise Pascal, Indian mathematicians utilized the triangle in addition to Middle Eastern.  Following the Iranian mathematician, Omar Khayyam, a Chinese mathematician used it and discovered how the triangle provided coefficients for expanding (a+b) to a certain degree which is an imperative fact to be aware of when in high-school math class.

       There is a plethora of different patterns which can be made by shading in specific numbers on Pascal's Triangle.  Whether you shade in odd numbers, even numbers, multiples of 6, or multiples of 11, you are bound to see  a trend within the patterns. Blaise Pascal, who was a French mathematician, was a sickly child and lived from 1623-1662, and obviously, the triangle was named after him.  Even though Pascal receives the majority of credit for this mathematical gem (for it is named after him), other people from other nations such as China, India, Western countries, and Iran discovered it long before.

     Aside from Pascal's triangle, Blaise discovered the first digital calculator, the Pascaline.  His calculator was not very popular amongst the people, for it could only perform addition.  He created this device in order to make his father's job involving finances to be easier. His father was a major influence on his life considering he was home-schooled by him and grew up with no mother.  Not only was Pascal a math guru, but he was a philosopher as well and he laid the foundations for theories of probability.

"Small minds are concerned with the extraordinary, great minds the ordinary"- B.P.

Math Humor

WELL TOO BAD- Here they are:






 How Immodest!







 Who new that cats have the Greek alphabet at the bottom of their paws?




Poor Emily



http://www.buzzfeed.com/babymantis/20-spectacularly-nerdy-math-jokes-1opu

Q: Why should the number 288 never be mentioned? A: It's two gross.

: http://www.jokes4us.com/miscellaneousjokes/mathjokes/

mathjokes.tumblr.com 

 
math-fail.com 

www.cafepress.com

Q: Why did the doctor send the expression to a psychiatrist? A: Because it wasn’t rational.

: http://www.jokes4us.com/miscellaneousjokes/mathjokes/algebrajokes.html

www.pinterest.com 

doblelol.com 

www.cafepress.com   

Human Calculator Skills

     I am certainly not the epitome of a human calculator.  I tend to mess up on the easiest addition problems that contribute to a test question, simply because I don't think about them for long enough.  Without a calculator, I would be failing not only math class, but chemistry as well.  The extent of my human calculator skills occurs in multiplication and division problems, in which instead of punching in the numbers of the calculator, I visualize in my head what I'd be writing down if I was doing the problem with pen and paper.
     On the opposite side of the spectrum of me, Julia Baca, there is an incredible mathematician by the name of Scott Flansburg.  Flansburg today is considered the "Greatest Human Calculator" by the Guinness Book of World Records.  He grabbed this title for being able to mentally calculate the same number in his head nearly 40 times in fifteen seconds.  Based upon his video interviews with several worldwide talk-show hosts, Flansburg certainly isn't the most modest character, but he is so great with numbers, that's okay.  When Scott Flansburg tries to verbally state what's going on in his head as he calculates numbers, his mouth can't even keep up with his train of thought.  Flansburg is a strong believer that a digital calculator holds back those who are trying to learn math, because it leaves them no room for thought.  With calculators, all we need to do is press buttons, but if we had to learn how to do somewhat complex calculations in our heads, we would be better at math all around, and understand the process of the calculations that occur before reaching your final answer. 
     For many years, Flansburg has been traveling around the globe to spread his knowledge and techniques for this laudable skill.  Currently, Scott Flansburg lives in Scottsdale, AZ, and is still sharing his methods of math and his theories over how mental math in simple areas such as multiplication, addition, subtraction, and division, provides a wonderful foundation for the rest of one's math career, and ultimately, it will make you a better student. 
     The best part about being able to do calculations in your head, is being perceived as intelligent to your contemporaries.












Sources: Scott Flansburg, The Human Calculator.
             scottflansburg.com
             Coast to Coast A.M.
             http://www.coasttocoastam.com/guest/flansburg-scott/5903
             Scholastic
             http://www.scholastic.com/teachers/contributor/scott-flansburg

The Beauty in Math

     When doing a math problem for homework, you may think to yourself: "When will i ever need to know this in real life?" The answer is: You probably won't.  Most jobs don't require the knowledge of how to find the minor arc of a circle or the height of a triangle , but the more facts filled in your brain will make others perceive you as smarter in general. Everything we learn in math may not seem substantial, but when put together, you will in fact use it when your older.  Whether your an architect, or a surgeon, or even a cashier, math will come in handy one way or another.
     Beautiful may not be the adjective to come to mind when describing math, for it can be strenuous and very time consuming, but when you get the correct answer to a difficult problem, it is one of the best feelings. All the effort that goes into a problem is beautiful, for it takes organization, skill, and hard work, and dedication itself is beauty.
     Applying math to realistic situations, and trying to figure out a problem that could actually occur, can actually be quite entertaining.  Not only is it not just a bunch of random numbers, but you're actually trying to figure out what would happen in real life under these circumstances.
     Sure, math can be tricky, and it certainly isn't for anyone, but it sure is interesting how there is always a solution to a problem.  Out of all things having to do with math, I find it compelling how people have spent their lives dedicated to math applications, theorems, proofs, and they work so hard in order to get published in a Math magazine, newspaper, textbook, etc.
     Math may cause tears and headaches, but in the long run, as humans, we wouldn't be anywhere without it, and it's really the one subject imperative for us to be familiar about- and that is simply just cool.