Probability + Life... How Beautiful

Probability is all around us, and at times it can work to either our advantage or disadvantage. Sometimes, when life hands us an unfortunate situation, like an extremely large man conveniently jumping into the pool during the 7 seconds Ms. Mariner was near him in the pool.  First of all, when there are 15 open lanes in a pool, and someone decides to get into the one RIGHT next to you, you should immediately resort to thinking that this person is a bit on the socially uneducated side of the spectrum. There was a mere 1 in 15 chance that he would be next to Ms. Mariner, and of course, he proved to be that 6.77%.  Because she is a speedy swimmer, averaging around 22.5 seconds per 25 meters, there was a high probability of 31.1% that she would have some sort of altercation with this very attractive fella, so in order to have minimized her chances, it would have been beneficial to her if she swam slower, allowing the man to adjust himself in the pool, assuming he didn't sink to the bottom.

I live anywhere from a wonderful 4 minutes to a horrific 7 minutes away from school, and this three minute differentiation results from traffic lights.  Nothing kills my vibe more than getting every red light, and every day, the duration of each green/red light changes, so i never know if i will make the next one.  Each of the 4 lights that i go though everyday can be either red, yellow, or green.  Considering that I am a good driver, yet I like to reach my destination in a timely manner, I will count yellow as a "GO."  The probability of me having to "STOP" for all 4 lights is 1/81, but it seems like this happens AT LEAST 3 times a week.  If only the odds were always in my favor, but I guess that just isn't the case :(

Darn Americans

As an American, I have confidence when I say that we always think we are superior and more competent than our international counterparts.  We lack general "street-smartness," make common errors dealing with good old 'dinero' that can later cause trouble, and tell people to put in 110% effort, even though that is literally impossible.  This article exemplifies our math illiteracy and puts a lot of the blame on our teachers.  It claims that they teach in a very monotonous way while never going beyond finding the answer. I think this is basically true, but we have to understand that these tedious skills will help us in the long run( (maybe).  If math teachers emphasized real-life issues such as insurance, taxes, mortgages, or anything else pertinent to our future, I feel like we would be more  wholesome.  Twenty years from know it will be more important if I know how to make a budget than knowing pythagorean identities, but what Americans don't understand is that we need basic math knowledge that comes from the classroom in order to succeed in life.  We don't want to receive a quarter lb burger when we pay for a 1/2 pounder or have more money takeout of our paychecks for taxes than should be.  Americans can be selfish and stingy, and unfortunately real imbeciles at times, but it is not that difficult to avoid this by merely paying attention to a lesson and using parts of it to help you in the real world where decisions and correct answers actually make an impact.  Many have a preconceived notion that they have supremacy over everyone else and because of that it isn't necessary to learn more.  These people will sure be struggling when they are in a bland conversation, wishing they knew how to spice things up with an infusion of questions regarding exponential equations and if the population will really double like the "rule of 72" predicts.

Big Numbers in Relation to the Human Brain

The human brain is inarguably the most complicated 'thing' the world has ever seen.  Everyone of the 7 billion people living on this planet today has one, and this 'machine of sorts' is in control of everything we have ever known.  We would not have thought, personality, interactions, speech, memory, hearing, nothing at all.  For everything that the brain controls, neurologists are still uncertain  about many things this slimy organ can do.  There is no correct answer is to what is unconsciousness, how our personally is determined, why we sleep and dream, how we store memory, why everyone has different perception, among many others.  The reason there is so much uncertainty stems from the complications of the brain.  An average brain has roughly 100 billion (10 to the 11th power) neurons, with each of these neurons having connections with around 10,000 of other neurons, forming synapses to create the sensations and thought that we have.   When one of these 100,000,000,000,000 potential connections occur, something within our thought process will be changed. You should be cognizant that there are merely 400 million blades of grass in a 100 m football field.  The amount of connections in the brain leave me stunned, for I cannot even picture the space they would take up if they were visible to the naked eye.  

It is extremely important to keep the brain healthy because brain cells are only formed in fetal development, and after that there are no new ones made, so it is essential to take care of it by eating correctly, sleeping enough, and being conscience of your decisions.   

I believe that as humans we are incapable of grasping the concept of such large exponential powers and relating them to daily life.  Seeing all the brain holds is truly amazing, for i never new a 3 pounded organ could hold so many connections that make us individuals. 

Transcendental

The definition of transcendental is anything "of or relating to a physical or nonspiritual realm" and this definition is quite appropriate for a transcendental number, for these numbers are irrational and never repeat or end.  You may think of Pi when this term comes to mind and if you do, you are correct! Pi is the epitome of a transcendental number!  In conjunction with the definition, atranscendental number may seem like something of the supernatural due to its ability of never ending and making one's mind do summersaults in order to grasp the all of the digits of a transcendental.  Transcendentalism was a religious and philosophical movement at the heart of the American Renaissance. Philosophers who led this movement had an insatiable craving to find out about the unknowns and the potential presence of the supernatural.  Just like unknown beings, transcendental numbers go on for so long that one will stop the quest before getting the answer one is looking for.  While these numbers are irrational, it is a radical concept to believe that a number can go on forever without ever stopping.  It will be interesting to see how these numbers continue playing a large role with our mathematic studies and maybe if we are lucky, we will feel like we are interacting with the world of the creepy and the confusing.

Trigonometry in Architecture

Trigonometric identities are used heavily in architecture. All of the six different identities come in hand when finding the length of the sides of a wall, or at the angle the material must be placed at to receive the desired outcome for the given location. Before architecture became primarily digital, architects had to be very good at math. Blueprints of a given structure always involve trigonometry, because something must be built perfectly, and a structure simply will not hold if the walls are not made to match up with the ceiling properly. Knowing the sin and cosine of an angle between two walls, allows the architect to evaluate the amount of material that will be necessary to complete the project. Trigonometry allows one to be as accurate as possible when determining the correct sizes of geometric structures. Intricate bridges, benches, and buildings that have curves can use trigonometry by mimicking the unit circle and following the rules of this genre of mathematics accordingly. It is much easier to build a structure when positive of all of the measurements. Even Vectors, which have a starting point, magnitude and direction -- allows one the ability to define the forces and loads that a given structure can support. Trigonometry is obviously based upon the principles of the triangle, and this shape is a main component in architecture.  By understanding the key concepts of trig, one can obtain all information regarding angle measurements and lengths, which is a necessity when building a strong, aesthetically pleasing structure.

Sin

        Dr. Stefano Bertozzi's speech given at the 2014 convocation for Fountain Valley School of Colorado evoked many solutions as to fixing our world.   I thought he did an excellent job of conveying his message through metaphors and real life experiences.   The main concept outlined throughout his "send off" to the graduating class was to give to this world as much as you take.  Of course, as he noted, as a teenager one takes substantially more than giving, but that is only because they have yet to begin their actual life.
       Out of all of the nations in this world, Americans are specifically notorious for being consumers.  We take your food, we take your jobs, we take your home, we take everything we can if it is lucrative and beneficial to us.  I perceived Bertozzi's message as moving and motivational.  He highlighted the atrocities in third world nations and how they could use assistance desperately, while making his audience question their greed.  By listening to this I had doubts about my own morals and I began to think of the good I have contributed to this world-- i already know I am "that person" who literally eats more than she brings!  In order to move forward, we need to be more conscientious  of our surroundings and stop being so selfish, and I think carrying on that advice was Bertozzi's principle purpose of addressing high school students.

The Quadratic Function

Not only is the quadratic extremely helpful and used in abundance in math class, but it is pertinent in daily life as well- especially in sports. Any ball thrown up into the air will follow the trajectory of a parabola, which of course is the parent function of x squared. In order to find the height, time, or speed of a throw, you must use the quadratic function. This can be used in any sport such as tennis, soccer, football, etc, and a lot in architecture.  In addition to these uses, the quadratic function can be applied when calculating the area of an object or finding the profits a company makes, like in this example:

• Unit Sales = 70,000 - 200P
• Sales in Dollars = Units × Price = (70,000 - 200P) × P = 70,000P - 200P²
• Costs = 700,000 + 110 x (70,000 - 200P) = 700,000 + 7,700,000 - 22,000P = 8,400,000 - 22,000P
• Profit = Sales-Costs = 70,000P - 200P² - (8,400,000 - 22,000P) = -200P² + 92,000P - 8,400,000

 We say all the time in class, "when am I ever going to use this?!" but in reality, you most likely will use it during sometime in your career. There are so many forms of a quadratic, (such as vertex form), but one thing that's always true is the parabolic shape that it graphs. Knowing how to graph is extremely important because it brings an equation to life and it becomes visually apparent how it would look if it were a ball thrown in the air.

Mapping the trajectory of a ball.

https://www.youtube.com/watch?v=ReHwNtoRMrY
A video bringing the quadratic formula to life.