She was talking about Pythagorean Theorem with piece of paper.
Tag Archives: Open Lab 8
Videos Irania Vazquez
Part 1 : Doodling in Math Class: DRAGONS In the video, she talks about the lines repetition of zig zags and can for different structures and if in 90 degrees can outline the folds of a piece of paper folded in half multiple times.
Doodling in Math: Spirals, Fibonacci, and Being a Plant [1 of 3] In this video, Vi Hart talks about spirals in nature and how they are related to the Fibonacci series. Her conjecture is that the number of spirals on plants are elements of the Fibonacci series.
What was up with Pythagoras? In this video, Vi Hart talks about how Pythagoras came up with the Pythagorean Theorem and was contradicted by a man who stated his thought off all numbers being rational was false and applied it with his discovery of the Pythagorean theorem.
Part 2: I felt really excited throughout watching several of these videos although Vi Hart does talk pretty fast and was pretty intrigued by the video of “What was up with Pythagoras?”. I was a little confused by the part where they started saying that everything was even but was odd and watched it again and realized that they were contradicting their statements. One of the things I learned from the video was that Pythagoras disliked beans with a passion and found this a little funny and silly. I really liked how she incorporated drawings and examples to show the ideas and concepts. I found her drawings cute and adorable and really help the audience visualize the idea. One of the questions that I have after watching the video would be if Pythagoras was in denial about the existence of irrational numbers, are there concepts today that people don’t set out into the public because they have the same problem as Pythagoras. There are probably many concepts we still don’t fully understand but we should always be open to new ideas.
Part 3: This video shows the origin of the Pythagorean theorem and shows how it was derived. The Pythagorean theorem is most definitely math and students should be shown how the Pythagorean theorem was conjured instead of just given the formula. As Vi Hart said, there were no formulas or variables back then and yet they were able to make this marvelous concept from connecting different concepts. This video is related to the reading from Lockhart’s Lament. It shows the concepts of origination and how they came to be from basic concepts. There were parts in the video were I paused it and was able to see how she worked out a proof by contradiction on how the square root of 2 is not rational. It is always nice to glimpse at something and realize you understand what they are doing. I really enjoyed watching these videos.
Videos – Kenny Pang
Part 1
Proof that some infinities are bigger than other infinities
Proof that .999999… = 1
Proof that .999999… = 1 is wrong. I was confused about this since she proved this to be true in the earlier video, but then i realized that the video was posted on 4/1, and it was a joke.
Part 2
The first video talks about some infinities are bigger than other infinities The countable infinity are the integers you can count, 1 2 3 4 5 … The uncountable are numbers you can’t count, for example, all the real numbers between 0 and 1. This is much bigger than the countable infinity. No matter how close two numbers are, there will always be an infinite amount of real numbers between them. For example, what would the smallest real number bigger than 1? 1.0001, 1.0000001, 1.00000000001…? You would imagine that there would be a 1 somewhere at the end and infinity number of zeros in between. In fact, you just can’t list it because no matter what number you come up with, I can just add another zero in between and it would be smaller than your number. That’s why uncountable infinity is much bigger than the countable infinity.
Part 3
After watching the video, I was really amazed. I’ve learned a lot from it. I always thought that the biggest infinity would be infinite number of nines. I’ve never thought that there would be infinity between two numbers. Now I understand that it’s not the case. The uncountable infinity is much bigger than the countable infinity. Just the real numbers in between 0 and 1 is already larger than all the integers. When I become a teacher in the future, I can definitely teach my students about this.
Videos- Sanaya Brown
Part 1
Part 2
I’m going to focus on the third video I watched
Initially, I chose to see the origami proof of the Pythagorean Theorem because this year in my math ed classes we’ve focused a lot on Pythagorean proofs and the use of origami seemed intriguing to me. While watching I felt excited. Although, I did find myself having to pause the video after each step or idea introduced to allow my brain time to process what she was saying seeing as how she was speaking so fast. However, I realized that this is a proof I’ve seen before but watching her video made it clearer. The first time I seen this proofs, I understood the c^2 part but I didn’t understand how they were able to just refold the paper and equate that to c^2 but now I get it.
Part 3
This video inspires me to pursue math topics in this way when I become a math teacher. Incorporating objects, manipulates, and and tangible things can stir up a deeper understanding of topics. She was able to prove the Pythagorean theorem using something as cool as origami which is a form of art. For students whom often times find math boring, this method of teaching makes learning math more relatable and fun. It is more likely to how the student’s interest rather than the traditional lecture or rote style of teaching. here is also some connection between Lockhart’s Lament and her videos. Lockhart was questioning why mathematics was not classified as an art form and trying to convey that it should not strictly be looked at as something involving reasoning a logic but a play on imagination and ideas. Vi Hart used art in all her video to convey math principles and build upon her ideas. She in a way proved Lockhart’s Lament.
