Palindromes and Symmetry!

Numeric: As I was researching these numeric palindromes, I found myself reading a blog about palindromic dates in the 21st century(link:http://faculty.up.edu/ainan/palindrome.html). As I perused his site, I saw a few interesting dates, but for some reason, January 2nd 2010 caught my eye. Not only is this date the 2nd day of a new decade, it was also the first time in almost 9 years that the date was palindromic. The last time before that was 620 years ago on 08-31-1380. As i researched further, I noticed many palindrome dates from this month. In one of his videos, the professor mentioned that January is appropriate for palindromic dates, since it is named after the Roman God Janus, who is commonly depicted with two faces looking in opposite directions.

Word or Phrase: My absolute favorite palindrome has to be that the fear of palindromes is actually a palindrome in an of itself. This fear is called aibohphobia. Whoever names theses phobias is not a very nice person.

The Bus Route Problem

For this blog I chose to write about the bus far problem. I like this problem because many people get it wrong just by guessing. It seems so simple and obvious as to what the answer is and many people are surprised to find that they are wrong. Just to test this, I showed both of my parents this problem. Not surprisingly, they both answered wrong after thinking about the problem for a few short seconds. As I explained it to them, I felt my understanding of the problem and what makes it so interesting grow. What the problem does is that it measures two separate things. As the diagram shows, you have a far greater chance (over half) of showing up to the station during the 35 minute interval. So to many  people, especially those waiting for a bus, it would seem that the average time for the bus to arrive was between 20 and 30 minutes. But this is not what the question is asking. If you average all the times on the diagram out, it comes to a perfect 15 minute interval between buses. So in fact, this bus service is indeed doing their job and buses are arrival at 15 minutes on average. My parents got quite the kick out of this one :)

Probability in Baseball

After reading Ms. Mariner's latest prompt about probability, I began thinking in my own life of situations where I use probability to help me. My immediate thought was baseball.

When I play baseball I am always trying to get the upper hand on my opponent. We just began our season this past Tuesday playing the Belen Eagles. One of the ways I can gain an advantage is analyzing pitch sequences and being able to guess on what pitch the pitcher is going to throw in any given situation. 

The pitcher we faced on Tuesday threw 3 pitches. A fastball, change-up, and a curve ball. By the end of the second inning, I had made a mental note of how often he was throwing each pitch and in what kind of situation he was throwing it in. He threw his fastball 60% of the time,  his change-up 10% of the time and his curve ball that 30% of the time. When I go up to the plate to hit, I begin to think what pitch I am most likely to see. If I consider his pitch usage, I know that there is a 3/5 chance of me getting a fastball and because of this knowledge I am able to sit and wait on the fastball so I can crush it. This brings me to consider what the probability is of him throwing me two straight fastballs. (3/5)(3/5) = 36% chance of a fastball. These probabilities can be found out for all of his pitches in any given situation. 

Another thing I have to consider that is not measurable is how he pitches certain players. While my fractions are very helpful, that is not the only thing to consider. Say in my first at bat I hit a double to the wall on a first pitch fastball. My next at bat the pitcher will remember this and try to not throw me the same pitch. This means that the probability of a fastball decreases and the probability of a curve ball or change-up decreases. 

I could write on this topic for quite a long time but I want to keep this one a bit shorter. (Don't want to  waste any of your time :) )

Innumeracy

The title of the article was 'Why Do Americans Stink at Math?'
The rival chain was A&W (Do these even exist anymore)

In general, I believe that the reason people aren't up in arms and making a stir out of this situation is the simple fact is that math can be challenging. Many people, like myself, can struggle at times in math and its very frustrating. Instead of trying to learn the difficult concept or explore it further, many people will simply give up, saying that its just too hard. And the reason they believe this is okay is because you can live a successful life without the use of mathematics but its hard to live without being literate. That's not saying that math isn't important or that we shouldn't learn it, because it is and we should. Many people think they can live without it.

A question I commonly hear in math class is, "When will I ever use this?". It is true that many avenues that we explore in math might not have much practical use in our future careers but its the problem solving skills and the ability to tackle hard ideas that stay with us forever. I think if Americans realized this then our country and its citizens wouldn't be having these types of problems.

Infinity

As I pondered this topic, a simple google search came up with an interesting story about a Hotel Infinity. It was a bit on the long side but was very interesting and relevant to this topic. Here is the link if you are interested: http://www.c3.lanl.gov/mega-math/workbk/infinity/inhotel.html

I also came across a shorter story that focused on infinity that had a similar premise as your hotel story. The story is as follows:

A very large mathematical convention was held in Las Vegas. The conventioneers filled two hotels, each with an infinite number of rooms.The hotels were across the street from each other and were owned by brothers. One evening, while everyone was out at a bar-b-que, one of the hotels burned to the ground. The brothers got together and worked out a plan. In the remaining hotel, they moved all guests to twice their room number -- room 101 moved to 202, room 1234 moved to room 2468, etc. Then all the odd number rooms were empty, and there were an infinite number of odd rooms. So the guests from the other hotel moved into them. I really liked this story because it made me think. At first i thought it was impossible but since there is no end to infinity, I realized that it is actually very possible, as long as you can build a hotel with an infinite number of rooms.

Transcendental Functions

In mathematics, we discuss "Transcendental Functions."  Trigonometric functions are transcendental. We are now exploring exponential and logarithmic functions which are also transcendental.  Why?  How?  What does this have to do with the use of the word, "Transcendental" in English literature? 

Google defines a Transcendental function as a function that cannot be expressed in algebraic terms. This raises the question how do you define a function like this? To get a better understanding of these functions, an example that we used everyday in class last semester were the trigonometric functions and their inverses. There are also transcendental numbers. We also have extensive use with two use these numbers, pi and e. These numbers and functions help us understand more complex concepts and functions and allow us to work with them easily.

As for literature, the Transcendentalism is the belief that knowledge could be arrived at not just through the senses, but through intuition and contemplation of the internal spirit. This is similar to functions of this manner because a function of this sort cannot be constructed in a certain amount of steps from the elementary functions(trigonometric). 

And to end, just a funny joke I found online about Transcendental functions: 

Q: Why didn't the mathematicians use their teeth?

A: They wanted to transcend dental functions.

Wolfram Alpha

As our year continues and the concepts we delve into get more and more complicated, sometimes classroom learning and textbook learning isn't enough. One method I have personally used this year is checking my work using an online software development that makes all systematic knowledge immediately computable by anyone. This website is called Wolfram Alpha and I have found it incredibly useful in my studies this year. I have found it particularly useful in checking my work on difficult problems since it provides step by step instructions on how the problem is solved. One of the things I really like about this site is the graphing capabilities it has. You simply type in the function and it will give you a picture of the graph, the integer solution, the domain, range, the derivative, and even allows you to interact with the graph to manipulate it. Another interesting feature of this site is it's random feature. You simply click the button and it takes you to a random problem. This is interesting because you can learn about all sorts of different math problems and how they are done with relative ease.

One thing I have learned is that you cannot simply rely on this site to do everything for you. Like many things, nothing beats instruction from a knowledgeable instructor where you can ask questions and interact in real time. I have found that this is best used as review and checking your work rather than relying on this site to teach it to you.

Once again here is the link to the site incase you were interested about looking into it further: WolframAlpha.com