OMGeom

Geometry deals with shapes. Pretty simple really. Even preschoolers do geometry. In fact, I bet it’s the first type of math anyone has ever done; putting blocks in the right place, stacking up Legos to make towers, drawing scribbles or irregularly shaped objects. We’ve been applying geometry before we’ve even started talking. But as we get older, we soon find out that geometry is not just about circles and triangles. Nope. Unfortunately, we find out about what’s inside of each one like the area or the angles and the lengths of the different sides blah blah blah. It’s not a piece of cake. It’s a whole lot of pieces.

My group and I started the session with a game. The goal of the game was to make the required shape with toothpicks. Not as simple as it sounds. The instructions were quite specific and not all that easy to get. It definitely required some brain work.

Then we had a debate on whether or not all buildings should be rectangular. I was on the con side. In terms of stability, the triangle was the most stable shape (according to an architecture student). Economically, the shape is just a small factor. What really matters here are the materials used, may it be expensive or not. By the end of the debate, it was sought out that the different shapes of buildings serve different purposes.

We then made a video about the different types of geometry, namely: Euclidean geometry which is the study of flat space, Riemannian geometry which is the study of curved surfaces, and Hyperbolic geometry which is the study of a saddle shaped space. Who would’ve thought that there were different types of geometry? I certainly didn’t before making the video.

This activity broadened my knowledge on geometry. Though preparing for all of this was quite burdensome, I have to admit I did have a bit of fun.

Geometry is everywhere. It is happening in the world all around us. Whether you’re aware of it or not, geometry quite literally shapes our lives.

LET’S PLAY A GAME, A MATH GAME

“Pure mathematics is the world’s best game. It is more absorbing than chess, more of a gamble than poker, and lasts longer than Monopoly. It’s free. It can be played anywhere – Archimedes did it in a bathtub.” – Richard J. Trudeau

In Professor Stewart’s Cabinet of Mathematical Curiosities, a book by Ian Stewart, the attention is given to the mathematics that is not taught in school. It depicts that the mathematics we learn at school is not the only mathematics in the world. It is about the oddities of mathematics from games to puzzles and also includes facts and tidbits about mathematics that will give you the feeling that you have satisfied your curiosity when you didn’t even realize you were curious about it in the first place. In this book, Professor Stewart shows that the real fun of mathematics can be found elsewhere. A collection of the most entertaining curiosities of mathematics is contained in this book.

He starts off this book by talking about how it all began with one notebook that he kept to write about the interesting details of math that wasn’t taught in school. One notebook led to another and then another and soon, he had a cabinet of them. Afterwards is a series of short math-related stories that show the fun side of mathematics. The first was about the three aliens belonging to different species: one that tells the truth and one that lies. The second was a math trick called Tap an Animal. The next one is about the math tricks through the calculations done by a calculator. Next are segments about the triangle of cards, how to make a pop-up dodecahedron, the sliced fingers trick and the topology behind it, the short story on how many turnips did the farmer sell, a descriptive background of the four-color theorem, a mathematical problem in the form of a story about the lady, a knight and dogs, a shaggy cat story, a mathematical problem about rabbits in a hat, river crossing puzzles and other kinds of puzzles, making a pentagon and the definition and value of pi. Then there is another puzzle, this time about empty glasses. More puzzles and stories can also be found in this book including those about the knight in chess, a mathematician’s knot, cats with white tails, mathematical jokes, dice, a Greek cross, round numbers, the bridges of Konigsberg, Euler’s pentagonal holiday, Ouroborean rings, the ourotorus, Pythagoras, Fermat’s Last Theorem, prime factoids, squares, hexagons, wallpaper patterns, age problems, cubes, magic stars, the square wheel, why can’t you divide by zero, percentages, numerical spells, spelling, the universe, the golden number, Fibonacci numbers, the plastic number and many more. After all the mathematical puzzles, games, anecdotes and stories were introduced to the reader, Professor Stewart shows the answers and gives a short informative yet funny explanation to each. This book is literally filled with lots of interesting bites of mathematics that start off simple at first then become more challenging as you get deeper into it.

             What I like most about this book is how it was arranged and organized. I felt like I was playing a fun game instead of just plainly reading something about math of all things. It was easy to understand and relate to because Professor Stewart doesn’t talk about mathematics from a normal teacher’s point of view but from a point of view that even the everyday student can find entertaining. I like it that he understands how students see mathematics and that he tries to instill the thrill of it in his readers. To be honest, I was expecting it to be boring even before knowing what the book was about but the cover peaked my interest so I read on. Then I noticed that I wasn’t just reading about mathematical games, I was having an intellectual yet fun conversation with the author. That was the feeling I got when I read the book. I realized afterwards that I wasn’t simply reading about the fun side of mathematics, I was learning from it. A type of hands-on learning that is different from that in the classroom. When you are actually shown how mathematics is used in real life and how it is used in an exciting way that stimulates your desire for answers. This book has made me realize that mathematics isn’t as dull and boring as we thought it would be. Mathematics is actually a game, we just think of it negatively because we always seem to lose. Yet, once we understand its mechanics and we get to play it properly, we will find it as pleasurable and enjoyable as any other game.

A Peek Inside Stewart's Cabinet

Ian Stewart’s Cabinet of Mathematical Curiosities is a compilation of mathematical puzzles, jokes, facts, and other mathematical curiosities collected over his lifetime. This book is easy and fun to read since the entries are brief and easy to understand an example of this is his entry about global warming. However, the book doesn’t give moral and a main point that is why some of the entries are not very entertaining to read or you would lose interest in the topic.

The mathematical problems are stimulating and NOT easy to answer but still a fun way to learn things. Most of its problems covers the field of arithmetic, geometry, statistics and different theorems.

There is an entry in the book which made me wonder whether it was true or not or it was a joke and I just didn't get it. It says that “Pure mathematicians do not trust applied mathematicians, and applied mathematicians do not understand pure mathematicians".

After reading the book, I was amazed with Ian Stewart’s love for mathematics for you can see it just by looking at this great collection of mathematical curiosities. Because of this I sometimes wonder where my love for mathematics when I was in elementary went and hid. I would definitely recommend this to other people, especially to those that wants to know mathematics more and in a different way.

BY: DAISIC DE ASIS BELLO

Statistics

For our presentation of our topic, Statistics, we opened it with games. The first game was a quiz bowl wherein questions about statistics were asked. It has 15 items with a corresponding points, level of difficulty and time for the other groups to answer. The second game was kind a betting game wherein each group would bet whether a given card is a high card or a low card.

“Statistics as a Science or an Art” was our chosen topic to discuss in a debate like manner. Some points were made by the groups representing the Statistics as a Science and Statistics as an Art. Some of this points is that Statistics is a Science because it is a science of learning data, measuring, controlling and communicating uncertainties.

Statistics is an Art because a statistical data is be represented by graphs, charts and other visual aids. Statistics is not just an investigative art but is also a skill of handling facts. Through statistics, one can express his or her creativeness through his presentation of data. One could also interpret his own version depending of his understanding of a given problem. In the end, we concluded that statistics is both science and art because they work hand in hand in order for us to have an accurate statistical data.

We ended our presentation with a role play wherein one student is having a problem with his statistics subject and his friends came in and helped him. And that summarizes our Statistics report.

BY: DAISIC DE ASIS BELLO

Curiosity Could Not Always Kill the Cat

BOOK REVIEW

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Prince Stewart’s Cabinet

Of Mathematical Curiosities

Ian Stewart

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          Totally amazing and entertaining! This book by Professor Ian Stewart was filled with bunch of mathematics that could stimulate interest on the mind of anyone who would dare to take the “cool ride” of exploring these new ideas. This compilation of mathematics was the ones that were not taught in the classroom yet discovered and made this thrilling by the author. I never expected that I would be that carried away while reading the book even though I myself was not that fan of mathematics.

            A person like the author who decided to spend years collecting not paintings, not stamps, but a rare kind of collection, and that was mathematics. Math puzzles, stories, and more about math were such a collection to bow down for. Not everyone would dare to step out and say out aloud “Hey, I have a huge collection of mathematical ideas.” This person would definitely freak out the whole class where he or she belongs and would even gain the tag “weirdo”. A sad scenario but is totally true though.

            I think that it’s about time that we open our eyes to the beauty of mathematics. There are lots to scrutinize for and limiting ourselves to what we learned only in the classroom due to fear of rejection might lead us to not appreciating mathematics forever. It would be all too late if one could not be able to discover what may have been his or her forte in the future. For me, reading this book would really change one’s perspective towards mathematics and a whole new person with an open mind and heart to mathematics will arise.

            It’s totally a remarkable experience to be able to finish every segment of the book and so, I got my two thumbs up for the author of this book for sharing his collection with a youth like me. I truly believe that this book could change lives therefore; I recommend that other people especially the youth could be able to share the same experience with me and appreciate the curious world of mathematics.

The Missing Link

BOOK REVIEW

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ROCK, PAPER, SCISSORS

Game Theory in Everyday Life

Dr. Len Fisher

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            The title of the book is a simple yet popular game that I know most of us had already encountered or most likely played often during our childhood years. It’s so funny how from this very basic concept, the author Dr. Len Fisher, was able to come up with certain explanations on the behavior or way of thinking of people especially during instances when they are in the middle of competitive situations.

Most of the ideas cited by the author were just neglected in real life and thought of as “not so important matters” for us to bother ourselves, but as one would continue reading the book as I did, sudden realizations would really make one think twice and discover the ugly truths happening around us that really affect our lives in totality.

One example of these very common scenarios is cheating, in which even a plain student had resorted to when he or she didn’t know the answer yet wanted a high score for competition purposes. As this acquired attitude was utilized to its fullest, this led to more intense applications that went as far as national and worldwide concerns. This then had a so-called “domino effect” on the lives of people from different places passed on from generation to generation that even the thought of having this “cured” was already near to impossible.

            This was all so due to competition which originated a long time ago. It existed, is existing and will exist whenever the situation calls for it. In this world, and in our everyday lives, there is always competition and so accompanied with the survival of the fittest which is then the basis of the development of human interactions and strategies. The author’s mind would really have been this deep to be able to scrutinize all aspects in life in which what the author referred to as the Game Theory.  Humans tend to step on another in order to get what he or she wants; in such a way that that person would be the better competitor than the other. I felt that this version had some kind of relation or connection to our very own Filipino negative characteristic which was the “crab mentality”; a proof that this had somewhat of an occurrence in different customs or practices around the world.

            The author of this book proposed some ways on how to develop and maintain cooperation within us, people, in which the start would be to change oneself (most emphasized and recommended point or idea) before anything else. He believed that after we solve this missing link to better view and approach towards life, the rest would follow which would include the resolution of almost all of the social dilemmas and conflicts.

            As the author aimed to, I was able to understand the complexity of life that revolved around the Game Theory. I hope that other people would also realize the importance of fair divisions in everything we choose to do. Let us not take what was not intended for us and instead, learn to be contented in what we have.

            Although the author was not able to cite the effects of understanding the Game Theory in details with regards to the huge social problems he mentioned, a clear and better understanding of the Game Theory within our lives was already enough for me. I still salute the author for being able to relay the message of change to all of us. I recommend that more and more people would patronize these kinds of books that may not be so essential for some but may really affect our lives in a large perspective.

A MATHEMATICAL GUIDE ON LIFE AND ON PEOPLE

“Books are the compasses, telescopes, sextants and charts which other men have prepared to help us navigate the dangerous seas of human life.” – Jesse Lee Bennett

In this book called “Rock, Paper, Scissors”, Len Fisher talks about the applications of game theory in real life. He relates game theory to the strategies and the means that people take to interact with each other on a daily basis on different occasions. He talks about using game theory to develop strategies for cooperation and social interactions in different environments. That it helps us understand the holes in our interactions towards other people that lead to broken promises and cheating. It is a guide on what to do in situations like competitions and conflict. It is applied to different sectors from business to military.  Fisher then talks about the two different sides of game theory: the cooperation and collaboration side and the confrontation and competition side. In the field of biology, it is shown in the cooperation involving in the evolution of nature. While in the field of sociology and psychology, it is used to explain the problems of cooperation and resolution in the social relationships between people.

The book started off in a quite slower pace than I had expected. In the first chapter, Fisher gives an informative description about the Prisoner’s dilemma and a somewhat negative notion of the Nash equilibrium being a logical trap. Afterwards, he gives a lot of interesting examples and explanations. Fisher then introduces the different concepts of minimax and fair division in the second chapter. On the topic of fair division, he tells stories about how much trouble he got in when he was shooting fireworks as a kid. It was then that he arrived at an answer and now, he realized that it was an application of the minimax principle. Fisher then gives a discussion on the principle of equal division of the contested sum. Now, chapter three talks about seven of the most interesting yet challenging game theory problems, some would even call them deadly. In this chapter, a summary of these problems like the free rider issue and the game of chicken is given. The title of the book is the focus of chapter four. It talks about the “rock, paper, scissors” game and how it is being played around the world. Here, Fisher explains how this game is a means of conflict resolution; his reason being that this game has no pure strategy to speak of. No strategy that purely dominates the others. So the situations and games which look like they seem to be standing still can actually be solved through strategies and looking at them as rock-paper-scissors situations. The fifth chapter talks about the twin keys that can be used to resolve social dilemmas and these keys are communication and negotiation. It is through these keys that we can form alliances and share information and ideas though these also have their negative sides. The rest of the chapter is focused on how to make the communication between people more reliable, their negotiations fairer and their alliances more stable. Chapter six is about trust. Fisher starts this chapter by recalling a scene from the Peanuts cartoon. An unfortunate effect of both the game theory and the real world is due to the fact that people don’t trust each other. He talks about how he once did something nice for other people and how they doubted his intentions. Communities are built on trust and the lives of people would be easier and more fruitful with trust. He then uses the game theory to prove his claim and to understand how people can prove their trustworthiness. He believes that trust would lead to win-win situations. He then talks about his social training as a child in chapter seven. He talks about the book he was given when he was a child about two women whose personalities seemed to be based on the game Tit for Tat which is a payback strategy that comes into play when two people or groups are likely to meet repeatedly. There is a cycle of retaliation and counter retaliation and in order to break this cycle, one side must stop and just forgive. He then recalls more memories with his grandmother relating to this topic. Another way to break the cycle is to just apologize. Fisher then talks about the social norms and how they guide us to cooperation. Chapter eight is about how to change the game to improve the chances of cooperation. This can be done by introducing new players and using quantum mechanics to read each other’s minds. Fisher then talks about how quantum game theory and classical game theory provides us with a range of strategies to overcome social dilemmas. Then in the last chapter, he reviews these strategies and creates a top ten list of tips for strategies that can be used to promote cooperation.  

This book is a wonderful thing to read for me. While reading it, I didn’t feel like I was reading something about mathematics or the feeling you get when you read those types of academic and educational books. It was very insightful all throughout and even comical at some points. It wasn’t a book on equations or algebraic problems; it was more of a book about life for me and about how people are in general. It was such an eye-opener; it made me see the problems that society has and how the simple mathematics of game theory can be used to explain it and even solve it. This book speaks about life so the reader can really find a way to relate to it and therefore find reading it more pleasurable. I learned a lot from this book about how to interact and deal with people and how to develop a deeper relationship with others. It has a lot of life lessons along with personal stories that made it easier to understand and read. I would recommend this book to other people because its approach isn’t too technical and doesn’t come across as too strong. It also comes with some mind-boggling realizations and tips on how to achieve a better social relationship with other people.