Tessellation Analysis

Welcome back to the Blog about Mathematics. This week’s topic will be the tessellation. I will be analyzing my featured image and connect it to mathematics. A tessellation is a picture that is created by using patterns. The patterns can include multiples of the same shape or multiples of the same shapes. The picture created by the patterns must be able to fill the space of any paper without overlapping or gaps in order to be considered a tessellation. In this tessellation, two shapes are used. Triangles and the shapes that form flowers are used here. Tessellations are created as works of art. Mathematics can be applied in order to create works of art. I chose the tessellation as the picture for this week because tessellations are the works of art where application of mathematics is most obvious. The sum of measures of angles that share a point must be equal to three hundred sixty degrees in order to form a tessellation. Many transformations are used to create tessellations. Triangles that share lines are exact reflections of each other. Translations are the most common transformation in any transformation. (If anyone can prove me wrong, they should post the link of their proof as a comment.) All of the triangles are exact copies of other triangles that are pointing in the same direction. Glide reflections can be found in this tessellation. The triangles are translated both horizontally and vertically. All of the triangles are translations of other triangles pointing in the same direction and reflections of triangles that are in the same row, but pointing towards each other. I hope I analyzed the tessellation well. Let me know in the comments if you are still confused. I won’t be back for a while. You could follow my other blog while you wait for me to come back here.

©Crystal A Murray(CC BY-NC-SA 2.0)

My Interview with Mr. Peabody

Thien Han: Hi, readers. I am going to do another interview. This time, our special guest of honor will be Mr. Peabody. I will let those of you who saw my interview with Pythagoras that this interview won’t be done by my butler, TNT. Mr. Peabody has modified his WABAC in order to be able to travel between dimensions. He traveled to our world to learn what it was like to be outside of a world of cartoons and inside a world of real pictures. I was lucky enough to run into him while walking home and he was more than happy to share his knowledge with our world. Today, I will be asking Mr. Peabody about how he used mathematics in his life because there is no better way to learn about how mathematics are applied to problems in real-life than to speak with a genius who has used it many times. Mr. Peabody, can you tell our audience how the mathematics courses in school have been beneficial to your life after your graduation from Harvard?

Mr. Peabody: The first and most obvious example that most of you have seen was the time when I escaped the guillotine. I understand that I explained to my son, Sherman how I escaped the guillotine too quickly for most people to understand what I said. When the men who rebelled against the queen tried to drop the guillotine on me, I noticed that there were many sewer lids that were close to the guillotine. The distance between the sewer lids remained consistent and used that knowledge to find out that there was a sewer lid under me.

Thien Han: How would you escape the guillotine? Even if there was a sewer lid under you, wouldn’t the guillotine behead you faster than you could escape?

Mr. Peabody: That’s what most people would believe. However, the sewer lid under me wasn’t the only object that I used to my advantage. I also knew that there was a floor board under the basket where my head would’ve dropped. I moved the floor board in order to let the sunlight hit Sherman’s glasses and move at an angle that would blind the executioner long enough for me to escape. Did I explain my escape too quickly for you? I am willing to repeat myself.

Thien Han: When I saw you explain your escape to Sherman, I couldn’t keep up with you, but I heard everything you said right now. Do you think you can give us another example of how mathematics have been useful to you?

Mr. Peabody: My knowledge of geometry has saved Sherman’s friend, Penny from falling from a very tall height. I stole a Trojan’s horse and a rope while fighting to protect Sherman. I calculated the horse’s speed, found the circumference of the wheels of the Trojan Horse that Penny was trapped in, and found the angles that I should make when roping the Trojan Horse in order to catch it before Penny fell to her death.

Thien Han: Is there more to mathematics than just formulas and computations that involve shapes?

Mr. Peabody: Yes. Math is also about logic. You probably wrote conjectures in your geometry class and did proofs as an eighth grader.

Thien Han: Oh yeah. Thanks for the quick reminder, but how did logical thinking help you?

Mr. Peabody: I used geometry and logic to escape the guillotine. I used my logical thinking to assume that there was a sewer lid under me when I was about to get executed.

Thien Han: Thank you for your time, Mr. Peabody.

Mr. Peabody: Thank you for inviting me here to speak with you. I feel honored to be invited here by you.

Thien Han: I will repeat. Thank you for your time. I will be out for this week. Peace out.

©RobKleine(CC BY-NC 2.0)

Programming the Hound

Mechanical HoundThis week’s topic will be Fahrenheit 451. I know that most of you are wondering how this novel is related to mathematics. I thought that the book couldn’t be related to mathematics in any way. However, after taking some time to think about it, I remembered that the technology in Fahrenheit 451 is related to mathematics because everyone who operates machines needs to know their science and science uses mathematics. I will be explaining why a person would need to know how to do their computations in order to operate the Mechanical Hound. I recommend that everyone who reads this blog post clicks on the Mechanical Hound shown above in order to see how the Mechanical Hound hunts its victims through the perspective of the Mechanical Hound itself. Click on Mechanical Hound in order to learn about the construction of the Mechanical Hound and how the Mechanical Hound attacks the people it was programmed to attack. Now that you know the Mechanical Hound’s appearance and how it hunts, I will explain how knowledge of mathematics is applied to operating the Mechanical Hound.

The Mechanical Hound is a robotic dog that “lives” solely for the purpose of tracking and attacking. I put the word “lives” in quotes there is more to life than just survival. Life is about survival and thinking for oneself. The Mechanical Hound isn’t really living because it is just doing what it is programmed to do, not what it wants to do. On page twenty-six of Fahrenheit 451, Beatty, the Captain of the firemen, explained to Montag that the Mechanical Hound is programmed to attack certain people by entering the correct amino acid combinations. The people who operate the Mechanical Hound need to know their science in order to enter the correct amino acid combinations (and chemicals like sulfur and alkaline). They need mathematics in order to make sure that they have the correct percentages of each chemical implemented into the Mechanical Hound’s memory.

I hope all of you liked this post about mathematics, science, and technology. I will be editing my whole blog this weekend and do what I can to improve. I will be seeing all of you readers next week.

The Furious Hound (Character Analysis by Ray Bradbury, the author)

©DaveParker(CC BY 2.0)

Math and the News

http://http://www.timesunion.com/news/article/Next-up-math-NY-Students-face-2nd-round-of-6216170.php

(I will warn those of you who don’t enjoy reading the news that this blog post is all about an article that was written recently. I will let you know that this blog post is just my summary of a news article and a question that I have for my readers and followers.)

The article shown above was written on April 23,2015 at 8:34. (If you saw this post after April 24, disregard everything that will be in this set of parentheses. I know that April 23 was yesterday for those of you that just saw this post today, but I thought it would be good to give the date for people who will read this blog months after this post and maybe even in a few years or longer. What I am trying to say is that I want to give the exact date and time for people who will read this post a long time after I post it and yes, the exact hour and minute are important.) This article is about students who decided to refuse standardized exams because of the Common Core Standards. Last week, they refused to take the standardized ELA exams. This week, other students joined the students who refused the ELA exams. Last week, fifty-five percent of all students in Rotterdam, New York refused to take the ELA exams. This week, that percentage increased to 60.6 percent by the time the first day of math testing ended. This increase in percentage is expected because it has occurred before. The percentage of students refusing math exams is generally higher than the percentage of students refusing ELA exams. The US Department of Education requires all states to have at least ninety-five percent of their students take the standardized testing. The US Department haven’t had to take action against states that don’t meet the requirement, but they are thinking about punishing the states that have low participation percentages.

Should states with high refusal rates be punished? Why or why not?

Post your answer in the comments.

Peace out until next week! (I will try to post next week’s post as soon as possible in order to compensate for posting this post late into the week. I will also try to make it more interesting than just a summary of an article accompanied by a question. I will let those of you who have read this blog for the first time that my blog posts are usually better than this.)

©UH Manoa Library(CC BY-NC 2.0)

Mathematics with Romeo and Juliet

I just came back from Spring Break. I hope all of you enjoyed the week that you didn’t need to go to school. (I understand that some of you had two weeks or more. I hope you are enjoying the Spring Break you are having right now.) Today, I can post whatever I want and I have many more interesting links to show you. (I know that you people may not think my posts are interesting, but I think they are and that is what matters most. Please comment and tell me how I have been doing with this post and all my other posts. I might not post all of what I have found immediately.) This time, I will try to post a useful site related to math along with other sites even though I don’t have any restrictions that I need to think about while typing this post. My WordPress blog is not the only blog that wrote about Romeo and Juliet. (Those of you who haven’t read it yet should try reading it some time. Everyone in my English Honors class including me will tell you that it is the best play we have ever read if you ask us in person. However, try to acquire an expanded Shakespearean vocabulary because you will need it in order to understand everything the characters say in the play.) I will post links from blogs that wrote about Romeo and Juliet as well as some clips about them (if I can find any). I hope you enjoy everything you see on this page and comment. I want to hear what all of you think of this post. Peace out until next week.

https://www.youtube.com/watch?v=1v47WtKDu8U (Unit Circle)

-Don’t watch this if you are in Mr. Ngo’s class unless you need to.

https://luneytoons.wordpress.com/2015/04/06/a-fictional-love-story/ (Romeo and Juliet)

https://schoolblog09.wordpress.com/2015/04/04/romeo-juliets-love-vs-eren-mikasas-odd-love/

(Romeo and Juliet)

https://hopenguyen.wordpress.com/2015/04/04/romeo-and-juliet/ (Romeo and Juliet)

https://gameingisfun.wordpress.com/2015/04/04/link-it-to-league/ (Romeo and Juliet)

https://datdailydosagedoe.wordpress.com/2015/04/03/the-ping-pong-player/ (Romeo and Juliet)

https://lillliandoann.wordpress.com/2015/04/02/romeo-and-juliet/ (Romeo and Juliet)

©LukeMontague(CC BY-NC-SA 2.0)

Romeo and Juliet and their Connection to Mathematics

My English Honors class was finishing the Shakespearean play “Romeo and Juliet” during the last week of school before Spring Break. We started reading “Romeo and Juliet” at about the same time that I started writing this blog. During the time we were reading, we would also watch scenes of movies based on the play whenever we would finish an act. We would watch the scenes of the movies that were based on the acts we just finished. Whenever we watched the movies, we would compare the original script of “Romeo and Juliet” to two different movies. We watched the Zeffirelli and Luhrmann versions of “Romeo and Juliet.” (Anyone who has watched both movies would know that the Luhrmann version is so much better than the Zeffirelli version, but both versions are worth watching.) The Zeffirelli version is set within the Elizabethan era that the original script was written in. The Luhrmann version is a modernized version of “Romeo and Juliet” (and in my opinion, it is better than the Zeffirelli version). It has proven that the themes in “Romeo and Juliet” can occur in today’s world like it did in the Elizabethan era. I know that those of you who have read this blog before know that this is a blog about mathematics. What does “Romeo and Juliet” have to do with mathematics? Those of you who are reading are about to find out.

I just explained what I have been doing in my English Honors class during the last month before Spring Break. I know that most of you are wondering how “Romeo and Juliet” can be connected to mathematics. I will explain how Shakespearean plays are similar to graphs. Most if not all Shakespearean plays have five acts. William Shakespeare didn’t write all of his plays in five acts on accident. He had his purposes. Shakespeare was using the “bare bones of a plot” when writing his acts. Most of the first act is the exposition, the introduction of the characters and the story. The ending of the first act and the whole second act is the rising action, the action that leads up to a conflict. The third act is the climax and usually, the most enticing act of the play. The fourth act is the falling action. The fifth act is the resolution of the conflict introduced in the rising action. The resolution is also known as the denouement. Shakespearean plays are similar to graphs because all of them will rise slowly at first and then rise more quickly. Eventually, the graph will begin to reach a point in which it can no longer rise, but it must begin to fall. While some graphs (especially graphs displaying logistic growth) will remain at approximately the same points once the graphs reach their peaks, others will begin to fall until the graph is almost as low as it was to begin with.

I hope all of you readers and those who followed me enjoyed reading this post about how Shakespearean plays can be compared to graphs. Peace out for two weeks. Have an awesome Spring Break.

Romeo and Juliet Luhrmann

©Meg Pickard (CC BY-NC-SA 2.0)

Mathematics and School

If I was blogging about any other topic, I would’ve tried connecting it to school and explained how it is related to an academic course. Since my topic is an academic course that is offered in schools everywhere, I was thinking about blogging about how mathematics are useful for life, but then I remembered that I already did that in most of my other blogs. I do not plan to pointlessly reiterate something I have already done in many of my previous blog posts in this blog post. Instead, I will try to post some formulas, pictures, videos, and anything else I think might help someone learn something about mathematics. However, I may not have everything you need because I am still a high school freshman studying math. The help you will get on this blog post will be very limited. I might come back to this post later to update and add more links to it as the years pass and my knowledge increases, but I probably won’t be coming back to this blog post after this year. If you want me to update, post anything you want me to do into the comments and I will try to answer if and probably only if you do it within this year while I am still a freshman. I wouldn’t recommend commenting for updates during the summers for this blog, any future blog posts I may have, and any future blogs I may have if I plan to create a new one in the future. Enjoy everything you see below. I hope that those of you who found out about my blog through comments in blogs that I follow liked this post and tried checking out other posts in this blog. If anyone likes this post or any other post I have, let me know by clicking on the star that is right next to the word “Like” to let me know that. Make good use of these links. I hoped that you have gained some new knowledge through this post. Peace out until next week.

https://www.mathsisfun.com/geometry/unit-circle.html (Unit Circle)

https://carolmorey.files.wordpress.com/2013/04/area-formulas.jpg (Geometry Area Formulas)

https://grievancedotme.files.wordpress.com/2015/03/d710c-volume.jpg (Volume Formulas)

http://www.mathwarehouse.com/trigonometry/images/sohcohtoa/sohcahtoa-all.png (Trigonometric Functions)

http://akorra.com/wp-content/uploads/2011/11/pi.jpg (Digits of Pi)

http://www.scientificamerican.com/article/what-is-pi-and-how-did-it/ (History of Pi)

(Anyone who is taking a class under Geometry probably shouldn’t look at this page because it will be useless to them. I might change my mind in the future, but I haven’t yet. Everything you see on this page probably won’t change for most of the remainder of this school year.)

©Dylan Ng (CC BY 2.0)

Entertainment Portal of Blogs and Videos

This post is the second post that I posted without having any restrictions. I will try to make this post better than the other post that had no restrictions. I am thinking about just posting clips and many other links here. Some of them may have nothing to do with mathematics. I hope everyone who reads this post will like everything on it. Tell other people about this blog if you liked this post. I might even recommend blogs that I follow by posting their links into this blog. If you don’t like a post for a blog I posted into this blog, try reading other posts within the blog. I will try to label the links if I know what the topic is, but if I don’t label it, you will have to find out what the topic is by checking it out. If anyone thinks they have something I should post in the future, send the link to me as a comment for this blog and I will try to use it. I would like to get some comments. Does anyone like this page better than the other one?

https://datdailydosagedoe.wordpress.com/2015/03/14/but-soft-what-light-through-yonder-window-breaks/

(Blog from Paul Vu)

https://obstaclesofahighschoolstudent.wordpress.com/2015/03/14/movie/

(Challenges of High School)

https://hopenguyen.wordpress.com/2015/02/27/an-eye-opening-experience/ (Hope Nguyen)

https://gameingisfun.wordpress.com/2015/02/21/league-of-legends-in-my-community/

(League of Legends)

https://bbtran.wordpress.com/2015/01/30/why-technology-and-science/  (Technology)

https://schoolblog09.wordpress.com/ (Attack on Titan)

https://www.youtube.com/watch?v=MK0xhvtSelA (Attack on Titan)

https://www.youtube.com/watch?v=vYf1A9brtUE (Attack on Titan)

https://www.youtube.com/watch?v=9siFexm1I9c (Dating and Stuart Edge)

https://www.youtube.com/watch?v=iEVGQKwKeCc (Donald in Math Land)

https://www.youtube.com/watch?v=ta3yi5J7uZo (Stuart Edge)

https://www.youtube.com/watch?v=mRA3qXuwjjI (Stuart Edge and Proposal)

https://www.youtube.com/watch?v=R54_y3TXyGA (Ice Bucket Challenge)

https://www.youtube.com/watch?v=733pWkwd8d0 (Wrestling Cat)

https://www.youtube.com/watch?v=LsMpxczieQs (Evil Laughing Baby)

(The picture in this blog post is a mobile upload from Facebook. I won’t cite this picture the way I cited other pictures because this picture doesn’t have a CreativeCommons license that I can use in order to cite it.)

https://www.facebook.com/photo.php?fbid=334473586732199&set=a.286223698223855.1073741827.100005086816938&type=3&src=https%3A%2F%2Ffbcdn-sphotos-b-a.akamaihd.net%2Fhphotos-ak-xap1%2Fv%2Ft1.0-9%2F10411963_334473586732199_8595370263612355160_n.jpg%3Foh%3Dfd32149dee1d23b2279fbbd7581a094b%26oe%3D55732C67%26__gda__%3D1437718459_81484620bf2de94d33c31b91e6421951&size=400%2C400

I hope you enjoyed checking out the links shown above. Make the best of the entertainment available here because I might not do what I did here when I come back. I would like some suggestions for what I should post when I post links into this blog. Peace out until next week.

Thien Han Nguyen

A Post for “A Beautiful Mind”

As you can all see, this page is all about the movie “A Beautiful Mind”. This blog post is not another long lesson about how math can be used to solve problems that we face every day that will bore you out of your mind and either make you fall asleep while reading or post hate comments. All of you will probably like this post because it is about a movie. This page will be about a movie that uses math. Those of you who have already seen the movie “A Beautiful Mind” already know that this movie is about a math genius who used to study at Princeton University and developed game theory during his time at Princeton University as a student. The movie starts with John Nash, the main character majoring in math at Princeton University. Princeton University is not your average college. Only the smartest geniuses who apply will be accepted. This university is not only a school for those the gifted and talented who are seeking education beyond high school in order to prepare them for the workforce. This college is a school where the students are enforced to use the knowledge they acquire to write papers that will change the world during their time as students. John Nash developed a new course of mathematics called game theory. Game theory is math that is used to win games and maximize the number of winners as much as possible. Nash developed his game theory while he was at a bar. Those of you who have watched the movie have noticed that Nash can never stop thinking and he doesn’t know how to do anything outside of work. Nash would always try to crack any codes he thought he saw while reading a newspaper. He would cut the pieces and then splice them back together in a way that he thought would “reveal a hidden message.” In one of the first few scenes of the movie, Nash told a fellow student that his tie wasn’t looking good for mathematical reasons. Nash returned to Princeton University as a professor after his graduation. During his life as a teacher, he met a student who married him later in the movie after she graduated from Princeton. When the time came for him to become a father, he didn’t know what to do because all he knew was work. John Nash won the Nobel Prize in his old age for developing the game theory. Even though he has retired from his teaching life, John Nash continues to contribute to mathematics as much as possible. As all of you readers can see, “A Beautiful Mind” is an entertaining movie that uses math and tells the story of a genius’s life. I hope  you all liked this post. Peace out until next week.

(OK. I understand that this wasn’t the best I have done, but I hope you enjoyed it anyways. Try reading my previous two posts.)

©K嘛(CC BY-NC-ND 2.0)   

TNT:Interview with Pythagoras

Thien Han: Today won’t be about me and my opinions like my other posts were. For the next hour, we will have a historical guest,  Pythagoras. TNT, an archeologist who works for me as a butler has finally learned how to travel to any time of my choice and decided to bring Pythagoras to our time. Many of you probably already know him because of his famous theorem. Everything you see below is an interview with Pythagoras. Today, I won’t be speaking. TNT will be asking Pythagoras about his discoveries and learn about the religion he created.

TNT (aka Dynamite): Hello, Pythagoras. How does it feel to be in the twenty-first century?

Pythagoras: It is my honor to visit a time where everyone knows about me and my people. What did you bring me here for?

TNT: I just wanted to know how your theorem was created because I have heard that you stole the theorem from the Egyptians? Is this true?

Pythagoras: It is true that the Egyptians discovered my theorem long before I did. However, it is still rightfully mine. They may have discovered it, but I was the one who shared the theorem with the whole world and made you people of this century who you are today. I also found out how to prove the theorem to be true. Therefore, it is rightfully my theorem even if the Egyptians owned it.

TNT: How did you prove your theorem?

Pythagoras: There are hundreds of proofs for my theorem. You should learn about President Garfield’s proof. However, I like the proof for my theorem that actually uses squares. The area of any square is the length of a leg multiplied by itself. If you found the area of squares that share the legs of any right triangle and added those areas, you would find out that the area of the square that has the hypotenuse as a side is equal to the sum of the areas of the squares that have the legs as sides. I know this may be confusing, but I hope understand what I just said. I am sorry to say that I can’t explain any better.

TNT: Don’t feel sorry. I understood what you said. I learned this from the Glenn Research Center. I will let you know that our interview is being posted online as we speak. Give me a second to speak to the audience.

Pythagoras: What does it mean to “post something online?”

TNT: I might not be able to explain to you. We have something called the Internet. You probably don’t know about because the people of your time don’t have it yet. We use the Internet to learn, to entertain ourselves, and to post whatever we want people to see just like my boss Thien Han Nguyen is doing with our interview. When people of this century say that they are “post something online”, that’s just another way of saying that we are posting something on the Internet.

TNT: For those of you who are reading this interview, I want to let you know that you will have a better understanding of the proof Pythagoras was talking about by checking out this link.

http://www.grc.nasa.gov/WWW/BGH/pythag.html

Pythagoras: What do you think of the proof I just gave you?

TNT: I like it better than the proof from President Garfield. Are you a religious or did you just devote your life to mathematics?

Pythagoras: I was also in interested in science. Yes, I am a religious man. I started my own faith, Pythagoreanism. My followers are called the Pythagoreans.

TNT: Pythagoras, did you find all of your discoveries all by yourself or did your Pythagoreans help you?

Pythagoras: I  had help from  my people. When we found out that my theorem is actually true, we decided to work with it daily and that is how we found another discovery.

TNT: What did you discover?

Pythagoras: My people discovered the numbers that you call “irrational numbers.” At first, when we discovered them, we called them “the unspeakable numbers” because we believe that numbers and shapes rule the universe, but we didn’t know anything about these numbers. Once we discovered these numbers, I told my followers to refrain from speaking about these numbers to outsiders until we learned more about these numbers, unless they wanted a death sentence.

TNT: How is Pythagoreanism a religion if it is all about math? Don’t religions have beliefs that are about deities or topics related to something outside the material world?

Pythagoras: The faith I created is a legitimate religion for this reason. We worship beans during the time that we are not studying mathematics or science. Beans are very sacred. My order believes in trans-migration of the soul. When we die, our souls will live on in other bodies. Most of the time, our souls will migrate into the bodies of pea plants. Worshipping pea plants is our way of respecting our loved ones after they have passed away. The pea plants not only contained our ancestors’ souls, but they also bear a strong resemblance to human body parts. Eating pea plants is an act of cannibalism.

TNT: You have a very interesting religion. I know about your contributions to mathematics, but what have you done for science.

Pythagoras: Science uses many formulas. My people and I try our best to contribute our formulas to science. I have a question about this hi-tech world of yours. Were any of my discoveries useful for the advancement of technology in any way?

TNT: I don’t know if any of your work contributed to the advancement of technology in any way. However, I do know that science and math have helped people advance in technology even if your work wasn’t responsible for it. We have used formulas to help us build. Science has helped us in technology more than anything else has and it continues to do so even now. I want you to know that your theorem is very useful and is very easy to learn. Many people will remember your theorem long after they forget any other mathematical formulas.

Pythagoras: I am glad to hear that.

TNT: Thank you for your time here with me.

Pythagoras: Thank you for inviting me here to your time. I really enjoyed learning about my fame and how I have helped people of this generation. I have to go now. I don’t want to stay here and let my work go to waste.

(A few minutes after Pythagoras returns home and TNT is back, he sees his master)

TNT: Hi, Thien Han. I am back. Are you thinking about recording my interview with Pythagoras in your blog. I think that it will boost the number of likes and followers you have for your blog. Even if it doesn’t, it is still worth recording.

Thien Han: That is exactly what I have been doing during the time you were interviewing Pythagoras. Now hand the time over to me and let me speak to my readers.

TNT: Okay. I will let you speak for the rest of the time you have with your readers..

Thien Han: What you saw above is TNT’s interview with Pythagoras. You have had two weeks off of my lessons about the application of math to the real world. I hope all of you enjoyed my joke page. Please leave comments even if you didn’t like this post or even if you disliked the whole blog up to this post. I need feedback from all of my viewers in spite of the fact that many of them probably don’t like this blog according to my stats. I will teach another lesson next week unless I change my mind or get interrupted by another guest speaker. I won’t be posting until next week. Peace out until next week.


©GavinBaker(CC BY-SA 2.0)