Palindromes and Symmetry

It is quite interesting that humans are naturally attracted to symmetrical visuals.  Facial recognition is hardwired at birth, and from very early on in life, babies can tell one "attractive" face from another, for they spend longer amounts of time gazing upon some people rather than others. This alluring physical attraction that starts at a young age obviously has to do with someone's facial characteristics, and it has been scientifically proven that faces with symmetry are commonly referred to as more "pretty" than one with less exact/perfect features, for they tend to signify that that person is healthy which of course brings up the notion of natural selection.  Of course, math isn't all about choosing faces and picking which one we like best, but it is about numbers, and here are some pretty numbers that display symmetry beyond what the naked eye sees:

Taking a number, 87 in this case and then adding it's reversed digits (78) will get you 165.  Then you take 165+ it's reversed digits (561) which equals 726.  After this, you add 726+627 which will get you 1353.  Finally, you add 1353 + 3531 = 4884....would you look at that, its a palindrome!!! According to http://www.jasondoucette.com/worldrecords.html , all numbers, if you continue to add ab+ba, will become a palindrome by using the submerse from the sums!

This non-numerical palindrome is my favorite because it incorporates real names, and somehow it all works in a beautiful way to make one beautifully crafted and simultaneously symmetrical list of names that seem to represent people who misbehaved! WOW!

Symmetry sure is a fascinating concept

Fun with Probability!

    The Monty Hall problem is one that stumps many.  In fact, I had to watch two YouTube videos on it several times each before I could fully grasp how the answer was what is was.
    So here is the outline of the scenario: You are in a gameshow, let's say The Price is Right, and have the opportunity to win a brand new Range Rover.  It is shiny black with chrome rims, and you really want it, unfortunately, you must choose the correct door, A/B/C, and Bob Barker has already revealed what's behind C.  Behind C there is the undesirable presence of a goat.  At this point, you're probably thinking, "hmmm I have a fifty/fifty chance of choosing the car because the goat was already behind one door, so the only options left are either another goat or the beautiful car," but here is where you are wrong.
    Initially, I would say it makes no difference whether you decide to stick with A or change your door of choice to B.  But, apparently this isn't right, even though it makes complete sense.  Because a goat was already picked, this situation becomes Not Independent, and swapping your door of choice will double the likelihood of getting the car.  At the start of the game, the probability of picking a goat is 2/3, because there are two goats and three doors.  If you don't swap, the probability of picking the car remains 1/3, and that of picking a goat is still 2/3, and does not change to 1/2.   Switching to B is a auspicious decision because you are going to win a goat at least 1/3 of the time if you switch from the winning door to the goat door.  If you pick the goat one first and then change to the other door, the probability of getting the car turns into 2/3.  Always swapping to the remaining door will invariably double your chances.  
    Before entering any game show, I strongly recommend that you brush up on your probability, and review the difference between independent and Non Independent events.  I hear that Ms. Mariner is great at assisting with that!  Here is a wonderful diagram that perfectly exemplifies this situation and is based upon the preconceived notion that a goat was chosen first.

   

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.