Quadratic

I looked up "Parabolas in Real Life" on Google and right away I see the very famous St. Louis Arch, also called the Gateway Arch. I knew I just had to do some research on the construction of the arch, just look at it! It's absolutely amazing, and a perfect parabola (or so I first though)! I couldn't begin to understand how the managed to build such an odd structure because it looks as if the during the construction the entire thing would come crashing down. Apparently though, the arch isn't a parabola at all, it's refereed to as an inverted catenary. A catenary is defined as the "curve formed when you allow a chain or cable to hang from its two ends under its own weight", so in an inverted catenary is one in which the curve hangs up instead of down. 


By observing the construction below I was able to conclude that each leg had to essentially support its own weight until they came close to touching each other. In the 5th picture we see a brace added to the middle that made it so neither side would collapse. Wedges, that could be compared to triangular wedges of cheese, were stacked one on top of the other until the two curves finally met in the middle. There was lots of math involved in the creation of the Gateway and although I don't really understand a lot of it....

The geometric form of the structure was set by mathematical equations provided to Saarinen by Hannskarl Bandel. Bruce Detmers and other architects expressed the geometric form in blueprints with this equation:^[72]

,

with the constants

where f_c = 625.0925 ft (191 m) is the maximum height of centroid, Q_b = 1,262.6651 sq ft (117 m²) is the maximum cross sectional area of arch at base,Q_t= 125.1406 sq ft (12 m²) is the minimum cross sectional area of arch at top, and L = 299.2239 ft (91 m) is the half width of centroid at the base.

(copied from wikipedia)

it is clear that without a lot of time and thought this project would have gone nowhere. It's very cool to see how such a daunting project to light and how it was made!

Math in Jobs

There's one question that is always asked during math class, "Are we ever actually going to use this stuff?" That's one question I've always wondered about. Why are we learning such weird theories, formulas and equations? What good will it do us? How come it is so necessary in our lives? Well, for my blog I decided to research a couple of obscure jobs that require mathematics in order to see why it is so important in our academic curriculum.

The Actuary
With a little help from Google, I was able to find out how interesting the job of an actuary is. They work with predicting and analyzing the consequences of risks. They are a financial planner of sorts. Actuaries use math, financial studies and statistics in order to predict what will happen in the future. For instance, after the event of a large hurricane an actuary's job is to guesstimate long term damage costs, and plan for future kinds of insurances that will need to be given to people living where the hurricane took place. By using math, we are sort of able to see the future!
   
The Cryptologist
Cryptology is the study of ways we can communicate secretly in the presence of other parties. Not only do cryptologists create codes to be used for secrecy, but they also break codes they intercept. A great deal of math and puzzle solving skills is used in cryptology. A crpytologist's main method of breaking a code involves using algorithms. An algorithm is a step-by-step procedure of calculations. They use algorithms to narrow down the different types of code that could could possibly apply to the encrypted message. Without cryptology our greatest secrets and messages would fall straight into enemy hands!
  

Pascal's Triangle

There are many patterns in Pascal's Triangle. One of the most visible is the powers of 11. It goes like so:
1=11^0
11=11^1
1 2 1=11^2
1 3 3 1=11^3
1 4 6 4 1=11^4
1 5 10 10 5 1=11^5
1 6 15 20 15 6 1=11^6
1 7 21 35 35 21 7 1=11^7

So we all know that 11^2 is 121 but once the numbers start getting to the double digits like 1 7 21 and such we have to carry number over in order to get the correct answer. 11^7 is really 19487171. In order to get this answer from Pascal's Triangle we carry all of the tens to the next column. So from right to left- 1 7 1, now add the 2 from 21 to 5, 7, now add the 3 from 35 to 5, 8, now add the 3 from 35 to 1, 4, now add the 2 from 21 to 7, 9 1. 1 7 1 7 8 4 9 1. There we go!

Now for the other patterns in Pascal's Triangle. The sum of any given row is 2 to the rows number power. Example: Row 1= 1+1= 2^1, Row 2 = 1+2+1=2^2, so on and so forth.

Another pattern in the triangle that we have is Fibonacci's number. The pattern goes 1,1,2,3,5,8,13,21 you take the number you are given and at it to the last number to get your new number. In Pascal's Triangle if you make a sorta angled diagonal we get this pattern. First diagonal is 1. Second diagonal is 1. Third diagonal is 1+1=2. Fourth diagonal is 1+2=3. Continue.

There are probably many, many more patterns in Pascal's Triangle we just have to be willing to work it out far enough!

Math Humor

I feel like a lot of people are like this. Hah!

Whenever we ask why this all matters.

This relates to the blog we did on %. This is the kind of stuff that tricks us everyday!

Percents. This reminds me of all the people that give the odds of winning the lottery and such.

Hilarious! "Most of"

Maybe something along the lines of "I'm allergic to math" would have worked just as well as this.

IMAGINARY!

Pretty sure this is true for rabbits.....

I can only imagine how hard it would be to write something like this.

There are always reasons why Calvin can't do math.

I bet this would actually work.

http://mrart.wikispaces.com/Math+Cartoons

http://math.sfsu.edu/beck/quotes.html

I decided to read up on Wim Klein. Klein worked as a physicist at CERN from 1958- 1976. He is considered to be one of the world's first human calculators. He worked at CERN at a time when there weren't many computers and because of this the scientists there greatly appreciated his ability to calculate calculations that may have taken much longer to complete without his help. Even the computers back then couldn't keep up with his calculations. When the computer eventually did become much smarter and faster it became Klein's job to make the equations inserted into the computer much simpler for it to read. He was an inspiration to future human calculators and will always be remembered as one of the best.

I calculate things really fast sometimes like this, but I don't think I could multiply three or four two digit numbers together in my head! Sometimes when my family and I are playing a bored game together and we have finished the game and are tallying scores I already know who won. It takes time for each person to individually add up their own score, but for me it's simple. My dad tells me to be quiet sometimes as I blurt out the scores and winner of each game we play. Maybe someday I will be able to multiply numbers like Klein.... but not today!

Source:
http://www.symmetrymagazine.org/article/december-2012/%E2%80%98human-calculator%E2%80%99-wim-klein-advanced-physics-inspired-others

Beauty and Geometry

Haha! That interview was quite short! It's obvious to me that Zhang was never in any of this for the fame or fortune he would receive by solving this problem, but instead he was in it for the pure joy of simply knowing the answer. I don't know if anybody else is like this, but when I get the right answer on a test question that I worked so hard to find the answer to... it's such a great feeling. That's the same way I think Zhang felt. He didn't want to become famous, he didn't want to be interviewed, he simply was in it for his great love of math.

Math is a beautiful thing indeed. It's all around us. I don't really think of it that way very often, but it is. In nature, we see patterns in all sorts of plants and perfect shapes and angles everywhere around us. Take the simple example of when you cut an apple down the middle, a perfect little star is formed. Simple, yet beautiful. Everything can be tied back to math!

The math I use in secret isn't exactly in "secret" so to speak. My family often plays board games where you build out your specific little area or section of the game and then calculate all the points at the end. The addition/multiplication just comes so quickly to my head that I end up knowing who has won the game before we actually tally all the points. My dad yells at me to stop telling us the scores before we get the chance to add them up, but I just end up blurting it out, revealing who the winner is.

Time calculations is also a big part of the math I do "secretly". During long cross country runs i will time mile by mile and deduce how far we have gone and how far we have to go. It's not the best habit to get into, but it gives me something to do while I run. I also am constantly making myself timed schedules of the things I will do in a given day, how much free time I will have after them and what I can do to speed things up.

I hope to be able to figure these sorts of things faster and faster as the years go by!