Parabolas

Although I have known the "idea" of a parabola for quite a long time, my first formal introduction to the concept came at the Museum of Science and Industry in Chicago. An exhibit at the museum allowed you to adjust the angle of elevation, power, and other details on a machine which would launch a basketball across the museum depending on the numbers you plugged into the program. The goal was to get the ball to into the hoop on the other end, meaning you had to experiment with different combinations of numbers to find the angle and power that gave you the best parabola, to try and get the basketball in the hoop. As a little kid, I was so intrigued by this concept. After this experience, it was easy to realize that parabolas were everywhere, especially in sports (which is a relatively big part of my family). In soccer, when you kick the ball; in diving, when you take off of the board, and in many other sports, the concept of the quadratic function is vital. 

Here are some pictures to give a visual:

Regular Tessellations

What exactly is a tessellation?
A tessellation is when a shape is repeated over and over, covering a plane without any gaps. In a Euclidean plane, triangles, squares, and hexagons are the only regular polygons that can tessellate.

Why is it that there are only three regular tessellations?

This is because if you find the interior angle of a polygon, the angle measure must be a divisor of 360 degrees in order for the tessellation to occur without any gaps in-between. You can find the interior angle measure of a polygon by taking the total interior angle measure (ex: 180 degrees for a triangle, 540 degrees for a pentagon, etc..) and dividing that number by the number of sides the polygon has. If this number is a divisor of 360, then it is a regular tessellation. Interestingly, only triangles, squares, and hexagons produce these types of numbers- which is part of what makes them such unique and interesting shapes! 

Pascal's Triangle

Considering how amazing and neat Pascal's triangle is, I thought it would be nice to have some background on the mastermind that discovered this incredible tool. Blaise Pascal was born in 1623 in Clermont-Ferrand, Auvergne, France. Pascal was not only a mathematician, but also a physicist, inventor, and writer. Pascal was a child prodigy, and is known not only for his triangle, but also for "Pascal's Wager."

For more information on Pascal you can visit the following site:

http://www.biography.com/people/blaise-pascal-9434176

Pascal's Triangle is one of the most helpful and neat tools in math. In math class this far, we have learned that Pascal's triangle is formed by adding the two numbers above them to the left and right. Additionally, we have found Pascal's triangle to be extremely helpful with our expansions. Pascal's triangle has many neat little tricks to it. For example, if you add all of the numbers in each row together, it is equal to a power of 2 (2^3= 1=3=3=1=8). Additionally, if a row starts with a prime number that is not one (every row begins with 1), each number in that row is divisible by that number. The Fibonacci sequence can also be found in Pascal's triangle by adding the numbers in their diagonal rows consecutively. Doing this will give you the Fibonacci sequence.  Lastly, a cool trick of Pascal's triangle, is that if you take the sums of the rows horizontally, up until row 5, it will be equal to 11^n power, where n= the row number that you are in. It is important to note that the very first row is row 0, NOT row 1. With this pattern, when you arrive at row 6, the trick still works, but you have to do a little bit of different addition to get the same answer.

Math Humor

GA2- Miranda Martinez

Math Humor

Maybe it is because I go to the Academy, but I have noticed that since I started at the school in sixth grade, that I have heard countless math jokes and chemistry jokes. We chuckle and say, "only at academy," because it is so true and I doubt this sort of joking takes place at any other school to the magnitude in which it does at Albuquerque Academy. One of the most recent chemistry jokes that I have heard is, " What do you do with a dead chemist? Barium!" Math and Chemistry humor shines a different light on the subjects, one in which I enjoy, because it just goes to show how math is a part of everything we do in our everyday lives. You can not deny that no matter how cheesy or dumb the math joke is, they are always good for a chuckle! Some of the recent jokes I  discovered regarding some of our newly learned material is:

Why are you so negative?  Just take me for my absolute value! 

What did pi say to the imaginary number? "Get real. "But the imaginary number retorted, "Be rational."

"Why can't anyone see you"- the number eight
"Beats me"- Square root of negative one

Shakuntala Devi

Shakuntala Devi, who passed away in April of 2013, was not only known for her "human calculator" skill, but was also a master in many different fields of which included astrology and literature. Shakuntala Devi's father noticed her skill at the ripe age of three, which is remarkable not only considering she was so young, but also because such a skill of calculating large numbers in your head would be difficult for someone with a PhD! Devi holds a record in the 1982 Guinness Book of World Records, along with numerous other achievements.
It is interesting to think about how one is able to compute difficult equations such as "7,686,369,774,870 x 2,465,099,745,779" and not only come up with the correct answer, but also do it in 28 seconds. How is she able to keep track of all the digits in her head and not get mixed up by the slightest mistake?  It is truly remarkable. 
Some other famous human calculators include Scott Falnsburg, Alexis Lemaire, Willem Klein, Mike Byster, and Devi's fellow Indian, and probably the other most famous, Srinivasa Ramanujan. Some of these human calculators spent their entire lives training to become this skilled, and others, such as Devi, were born with this remarkable feat.

Below, I have attached a link to a video of Shakuntala Devi.

http://www.youtube.com/watch?v=l0fXPzcbmPk

Sources:
http://www.csmonitor.com/Innovation/2013/1104/Shakuntala-Devi-and-other-human-calculators
http://www.indiatimes.com/technology/internet/google-doodles-the-human-calculator-shakuntala-devi-110118.html

"The Big Willie"

GA2:

To me, it is interesting to be able to identify math in our everyday lives. Whether it is simply the shapes you look at all around you or something more complex than that, math is everywhere. Like I stated in my previous blog, math is frequently seen in sports, but is also often seen in architecture, nature, and limitless other places. In this blog, I am going to focus on how it can specifically and blatantly be seen in present day architecture.
Chicago is undoubtedly one of my favorite places in the world. Every time we go visit my grandma in Wheaton, a suburb of Chicago, and drive into downtown, the magnificent Willis tower is the first to greet you. Standing at 1,482.6 feet with 110 floors, the Willis, formerly Sears tower, is clearly composed of 9 separate  "tubes," as they are called in architecture. The 9 tubes are bundled together to form a 3 by 3 cube, with the towers standing at four different heights. Building the Willis Tower took extreme precision, accuracy, and mathematical skills.

SOME COOL FACTS ABOUT THE WILLIS TOWER:
-The Willis tower has about 4.56 million gross square feet( approx. 101 football fields)
-The building cost about $170 million dollars to build in the 70's, but would now cost upwards of $790 million
-The entire structure(made of steel) weighs over 222,500 tons
-You can see four different states from the top of the Willis Tower(Illinois, Indiana, Wisconsin, and Michigan)
-104 elevators moving 1200 feet per minute.

Math in Secret

For six years of my life, I did gymnastics. I would go almost everyday after school and spend my entire evening at the gym. Gymnastics revolves around shapes, angles, and lines. On every event, whether it was vault, floor, beam, or bars, your body was always supposed to be in a certain shape at a certain angle. For me vault was my best event. Why? It was because after years of perfecting my front hand-spring vault, I knew the secret. It started out with a good run, hurdling, and hitting the spring board with your knees should be in-between a 90 and 145 degree angle, for the maximum spring off the board. Next, you should hit the vault at 45 degree angle to the table, so you will pop off the table and reach your maximum height. Throughout the entire vault, your body should remain in a straight line. If you do all of this correctly, you should have an excellent vault.

Today, in diving, I use angles and shapes in the same way. Dives are done in four different positions. Tucked, meaning your knees are bent and as close as possible to your chest, piked, meaning your body is folded in half, like a 90 degree angle, but your face should be against your knees. Next, there is the straight position, meaning your body remains in a 180 degree line throughout the dive, and free, which is only used if you are doing a dive with a twist in it. Angles are everywhere. From when you hit the end of the board, to when you are in the air, and lastly when you enter the water. Diving combines power with grace, which can be seen in this video on how angles are relevant to diving: diving.http://www.youtube.com/watch?v=7ZGSHAmTspM