Trillion Triangle Problem
Feb 23rd, 2011 by corricelli
Link to article: http://www.sciencedaily.com/releases/2009/09/090922095651.htm.
Please respond meaningfully and uniquely to one of the following questions. Use good grammar and complete sentences. Think about QUALITY, not QUANTITY.
1.) How is this related to topic(s) you have seen this school year in mathematics?
2.) In what way is this meaningful to you in school?
3.) How is this related to you/your life?
4.) How is this connected to another subject (beyond mathematics)?
5.) Can you find a related article/discussion online? What light does this article shed on this news story?
Thank you,
Mrs. Corricelli
1) I think that it can relate in some way to this year in Algebra II but I do think that it relates better to last year in Geometry. I specifically remember the right traingles because there were so many theroems to prove them with.
2) I think this shows how if you put your mind to it, you can discover great things. If you want an A in a certain class, you can do it if you set your mind to it.
3) I think this relates to my life because it makes me believe that people want to discover more and don’t think that we have found answers to everything. It can seem that way, but it’s not true as the article proved.
4) I don’t think it is related with another subject but with other fields such as architecture and engineering. Geometry can be used in many ways, we jsut have to find them.
5) I could not find a related article but, I think that more great discoveries are going to be made in math.
The reading for homework was really interesting. The first part of the article talked about geometry whcich immediatly made me think of the pythagorean theorum, all though we didn’t learn that this year, it brought me back to last year. They mentioned that the numbers in the long sequence were all congruent and followed a specific pattern. We learned about patterns early in the year. On the second page it talked about the Persian mathematician and how his version did not follow the method used today but used the square integers of certain numbers, what we learned about too this year. I think this article is meaningful because it shows how technology has come so far and thats relevent to our school because in our class we use a SMART board, and thats so technological. I honestly didn’t really see a big connection between this article and my personal life, but I can see how a message of trying to figure out a very difficult problem and feeling of accomplished for finishing it. This article will be helpful when it comes to technology classes I think or history because it shows how they had to create a whole new machine to calculate and prove the trillions of congruent numbers with patterns and the fact that people from different time periods all around the world can connect to this problem because they all attempted to figure it out as well.
I found this article that seems very related because its all about solving complex problems using technology. I think it was also used in this triangle problem.
http://www.sciencedaily.com/releases/2008/03/080314145039.htm
The Trillion Triangle problem is related to many topics in mathematics. First, I recognized that we have used right triangles while finding the area and perimeter of it using polynomials. In addition, an example of the Pythagorean theorem is shown in the article, which we learned and utilized greatly last year. This article is meaningful to me because it provides real life examples of how mathematical concepts are being used outside the classroom. It shows us the material we are learning can come in handy in the future. This article is also related to my life because it shows the major advances in technology our society is making and how the aid of computers help us reach these milestones. I feel this article is connected to the subject of history because a time line can be created displaying each advance in mathematics over the centuries, similar to the time line that is displayed in Mrs. Corricelli’s classroom on the walls.
The following website talks about the Trillion Triangle problem in a more generalized manner and also gives the opportunity to have discussions on the matter as well via blogging. It seems as though the person writing this article is impressed with the mathematical advances and likes the fact that technology is helping our society solve these problems.
http://stemnews.blogspot.com/2009/11/mathematicians-solve-trillion-triangle.html
I thought the article was really interesting. This related to some stuff we are doing in school because we do a lot of problems with shapes such as triangles. I don’t really see how this is related to me in school other than this assignment or if we are learning about it this year or later in my future math classes. Although I will be able to use this if I ever need to find the area of a triangle so I wouldn’t need to do the equation out, that way I could complete the problem faster. This is not really related to my own life as far as I can tell unless its this that holds up the roof on my head or helps hold up other buildings. This can go beyond math like I said before about it holding up buildings. I found this really cool website that gave a descripton of how this works and then went way deeper explaining it. It was really long but i found what I read of it to be interesting. http://www.math.uconn.edu/~kconrad/blurbs/ugradnumthy/congnumber.pdf
I thought the article was sort of interesting. I found parts of it to be interesting like the Fibonacci numbers, but I don’t see the practical use the trillion triangle problem. How can it help us? What I do find interesting was how huge the numbers that are being multiplied together. The distance to the moon is around 250,000 miles so to get there and back is half a million miles, that’s a huge number.
“Old problems like this may seem obscure, but they generate a lot of interesting and useful research as people develop new ways to attack them.”
I want to know why people are researching this and how it will help us. I couldn’t find any real connections to this and my real life or school except for last year when we were studying the Pythagorean theorem and Pythagorean triples. The Fibonacci numbers were interesting to me because math and nature seem like opposites but its interesting to see math reflected in nature.
I found a website that shows Fibonacci numbers with nice visuals and animations
http://britton.disted.camosun.bc.ca/fibslide/jbfibslide.htm
I found this article very intersesting and relevant to this years math couarse. We have frequently talked about triangles whether it be finding the area or perimeter or even looking back at last year, using the pythagorean theorum to find a certain side of the triangle. It is interesting to see that ancient math meticans delt with the same problems today but were just restriced by technology. These days our technology allows us to find diffrent routes and trickes to solving these problems as said on the first page. This article made me think about how numbers are related and how people back then must have been fascinated by how numbers have patterns and tricks to them. The idea of these numbers started simple and continues to grow and connect as technology becomes more advanced. This connects to really everything because as technology advances, we do to. Things become more easily solved and more patterns are shown. Also we will become much more efficient with new technology because we will be able to communicate globally and solve problems from many diffrent viewpoints and routes.
I found this first website relative to this article because it deals wih Al-Karaji’s ideas. http://science.slashdot.org/story/09/09/22/1512237/Finding-the-First-Trillion-Congruent-Numbers
Also this website relates to the congruent numbers incorperated in these ancient problems. http://www.jstor.org/pss/2006279
This article relates to my life because it shows how much more effective things get done with teamwork. The more people who work on the problem, the more progress they make in solving it. Fibonacci came up with the theory that 1 is a congruent number, but he was not able to prove his theory. Hundreds of years later Fermat discovered the proof for his theory. Without eachother they would have never been able to solve the problem. This also relates to what we do in class because we always work in groups. Working together is more efficient than working alone because you can solve the problem faster, easier, and you will have a better understanding of what you are doing.
3.) This article is related to my life because it lets me see that people are willing to put in that much effort over such a long period of time all trying to figure out a problem and to prove that their solution is right. So when I read this it and realized what these people where doing and how much effort they were putting in, it makes me more cooperative when a teacher will ask me to go into more detail on a question or a problem because I can just think to myself that this will be easier than trying to explain the “Trillion Triangle problem”. “The numbers involved are so enormous that if their digits were written out by hand they would stretch to the moon and back.” They could make so many mistakes so they have to put in so much effort and time to make sure that it is right. All I have to do is go into a little detail. That is how this article relates to my life.
This article was very relevant not only to the math that we do in class, but to my life in school. Every day in math Mrs. Corricelli has us work together or talk to the people around us to try and solve problems that we could not solve alone, and this is exactly what the mathematicians who were working on this Trillion Triangle Problem were doing. They got together people who except for math may have nothing in common, and brought them together to solve a problem that has been around for thousands of years. The people who were solving this problem may not be from the same culture, or share the same language but they all use the same math terms and can come together to work on the problem. I also think that it is very interesting how old this problem is, it was introduced between 953 and 1029 by Persian mathematician al-Karaji and it is still being worked on today. I think it is something very unique to math that people can be thinking about the same problems that mathematicians were thinking about thousands of years ago, and will be thinking about thousands of years from now. Also, this problem relates to our math that we do in school because in algebra and mostly in geometry we were dealing with right triangles and the pythagorean theorem and proving right triangles. In algebra we have been working on area of right triangles in the unit we are in right now.
Hello!
At this time – Sat, February 26, comments are past due for this article. You can still post for partial credit, but your comments are late.
We are at about 50% participation. Next time will be better – I just know it!
Have a great weekend and thanks for your thoughts!
Mrs. Corricelli
I thought this article was actually pretty interesting. The Trillion Triangle Problem relates to my life because it shows how much can be done when using teamwork, and that’s a saying constantly used in the sports I play. In the article it says that Fibonacci came up with a theory that 1 is a congruent number, but he was not able to prove it. A long time later Fermat came up with the proof for his theory. This shows that neither of these men could have solved the problems without one another. Which is true in all sports. It takes everyone’s hard work and attention to win a game. This all relates to what we do in math class because you taught us that team work is key, and that you can accomplish so much more when you have others to rely on, and it really does help.