Geometry Students,There's one more link I'd like you to do. Make sure it says ADVANCED at the top. Please read, take notes on Euclid's proof, and try to appreciate the unbelieveable combinations. Learn the equation for forming triples. Make sure you know the most common Pythagorean Triples from the previous link.
At the bottom of the link are 3 questions. Please do those too.
http://www.mathsisfun.com/numbers/pythagorean-triples.html
Finally, Be sure to provide a "value added" comment either on the work we've been doing or built off of a fellow student's comment. Here's a thought: the graphic in this post is determined by Pythagorean Triples. Try searching on math, art, Pythagorean Triples and dig a bit under Google Images. Find out how this is built and comment.
You are doing a great job. I read your comments daily. Keep it up!
6 comments:
Hi, James from Block B here. This pythagorean triple link was great to continue learning about the concept of pythagorean triples. I began to get the idea yesterday, but this explained in much greater detail why they are important how to find them. I found this like more helpful on constructing pythagorean triples. I found it very interesting how algebra and geometry came together so well here. The use of systems of equations to solve a right triangle problem was very cool.
Hi, this is Nat from Block B.
I think that the concepts that we are learning about Pythagorean triples is quite interesting. It almost reminds me of Pascal's Triangle, or the Fibonacci sequence which we covered last year. Pascal's Triangle is a triangular sequence of numbers, which reminds me of the work that we are doing now. Here is a diagram of the triangle: http://bit.ly/10mS2TY
The Fibonacci sequence is an infinite sequence of numbers that begins like this: 1,1,2,3,5,8,13,21,34... To continue the pattern, add the last two numbers to get the next one. The Fibonacci sequence relates to Pythagorean Triples because every second Fibonacci number is the third number in a Pythagorean Triple. To read more about it, visit this Wikipedia page detailing it: http://en.wikipedia.org/wiki/Fibonacci_number
Adam from A block
I though this article was interesting for a few reasons. First of all, the Pythagorean theorem is something i have known and used since i was in seventh or eighth grade. That being said, i had never completely understood it until this year where I learned about it more in depth. This article is extremely useful because it provides problems that allowed me to apply my knowledge.
Adam from A block
I though this article was interesting for a few reasons. First of all, the Pythagorean theorem is something i have known and used since i was in seventh or eighth grade. That being said, i had never completely understood it until this year where I learned about it more in depth. This article is extremely useful because it provides problems that allowed me to apply my knowledge.
Emma from block B. This webpage had a lot of information and took me awhile to understand it all. First off, I was amazed by the conclusion that Euclid came to. It took me a little to fully understand his logic, but once I got it I was amazed. The most complex part of the page was how to construct triples. I'm still not quite positive how that works. The variables m and n confuse me because how do know which numbers to use? My closest guess is that mathematicians use the three equations to test three numbers if they think they might be a triple. Lastly, I want to add that the whole idea of the squares of the sides equaling the square of the hypotenuse is very cool. If you're not sure what I'm talking about, it's this picture: https://www.google.com/search?q=pythagorean+triples&aq=1&um=1&ie=UTF-8&hl=en&tbm=isch&source=og&sa=N&tab=wi&ei=LYKJUc7sNZb_4APY6YCYCg&biw=1366&bih=667&sei=MoKJUYrpLLao4AOXn4DoAw#imgrc=e3r4DWc5-oIfzM%3A%3BKTE60ipuRQp9hM%3Bhttp%253A%252F%252Fwww.mathsisfun.com%252Fgeometry%252Fimages%252Fpythagoras-abc.gif%3Bhttp%253A%252F%252Fwww.mathsisfun.com%252Fpythagorean_triples.html%3B209%3B230
It's really neat how mathematicians from a very long time ago were able to make that connection between the sides of a triangle.
Hi this is Hannah G from Block B. I find the Pythagorean Triples very interesting. It's cool how they always work into infinity. Although, I am confused on how this work with the triples ties into the work we have been doing in the book about circle. Never the less the triples are interesting and the practice problems you do with them really help me fully understand the topic. I like how they show you the answer and explain how they got it. The art that is made from Pythagorean triples is extremely compelling. I looked at some pictures of it and I found that a lot of the art involved squares or was in a spiral.
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