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


(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)


(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)