She was talking about Pythagorean Theorem with piece of paper.
She was talking about Pythagorean Theorem with piece of paper.
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.
b. Rhapsody on the Proof of Pi = 4: https://www.youtube.com/watch?v=D2xYjiL8yyE
proves that pi= 4.
b. Dialogue for 2: https://www.youtube.com/watch?v=dBVoIUASFS0
This video showed that there are lots of number you can add and the result will be 2. You can say 1+2=2, ½+½+½+½=2 etc. Also 2 is so friendly and easy number.
c. How I Feel About Logarithms: https://www.youtube.com/watch?v=N-7tcTIrersThis video
This video shows different way to add, devices and multiply numbers. Which is easier to understand and logical.
When I watches the first video, I was lost. I did not understand the proof even though she drow nice. I felt like she was rushing while she was explaining. If she would have take more time to explain the problem then I would understand it. I learned that the students’ understanding is based on the way a teacher teach. My question is, why does a pi relates with a circle?
From my knowledge, this video did not shows a good method of teaching. As I said in last paragraph, it was fast and not clear which makes me confused to understand how does pi=4. It was a poor math teaching video. From this video we can see that if a teacher take time, ask question and explain clearly then the students will more like to understand the concepts.
A. “Math Improv: Fruit by the Foot”
This video is about how we can play tick with strip paper or fruit snack.
B. “Pi Is (still) Wrong.”
In this video, the author cooked pies to show Pi is not Pie and Pie is not Pi.
This is also a video which talks about how to play with paper by folding it into different shapes.
I would like to focus on the video C. I did enjoy watching this because it is very interesting to see how math is being used in real life. I like this video because it reminds me how I used to play games with paper by folding it into different shapes. I felt excited about this video as I never thought different colors will make the “hexafexagon” so special. It will be fun and meaningful if we could teach little kids to play with this idea. Also, since it is about shapes, which makes it connected to math in some sense.
I think it will be a good idea if we could apply some of Ms. Vihart ‘s thoughts into teaching. This helps teachers make students engaged in some class activities. It also helps students learn the relevant materials better by doing something interesting to them. I agree it is Math as we know Math is everywhere. We could not limit Math at the work we do in class, for instance, written assignments. In Lockhart’s Lament, he talked about how Math is a form of artistic work along with its elegance. Similarly, in Vihart’s videos, she uses different tricks and games to show Math in a fun and easy way. As a result, besides classwork, it is encouraging that students should watch some videos like these to enrich mathematical minds. The same to teachers who should also learn how to deliver these ideas and knowledge to their students.
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.
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.
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.
here is videos I watched:
1- Doodling in Math: connecting dots https://www.youtube.com/watch?v=v-pyuaThp-c
This video is about a game of connecting dots and come up with an interesting shapes . Vi Hart talked about parabolas, hyperbolas, connecting 2 dots by a line, connecting 2 semi circles in many different ways, and criticized the way algebra is though overall in schools. and said that’s the reason student get bored in math classed. they always forced to admit things and apply them rather then letting them be creative.
2- 9.999….Reason that .999=1 https://www.youtube.com/watch?v=TINfzxSnnIE
In this video Vi Hart talked about 10 reasons why .9999=1 by giving a valid proofs. she started by assuming that .9999=X and she multiplied by 10, subtracted .999, divided by 10 and concluded that .9999= X =1. according to here is a valid proof. she bucked it up other example like .3333 and 1/5.
3- Why Every Proof That .999=1 is Wrong https://www.youtube.com/watch?v=wsOXvQn3JuE
In this video Vi Hart proved that ” .9999=1” is wrong witch was a statement that she proved in the first video ”9.999….Reason that .999=1”.
For this part I choose to focus on the ” Doodling in Math: connecting dots”, I was entertained and fascinated by Vi hart talent of combining the drawing and well spoken words of proofs and logic. In this video VI Hard applied the concept of drawing a parabolas to just connect dots and see what can of shape it will turn into, first she tried 2 dots and a strait line, 2 dots and semi circle 2 circles that share 2 dots, they all turned them to interesting shapes witch looks like something in real life. I guess she was just trying to answer students who are asking about why they have to learn how to graph parabolas. after I watched this video Vi hard inspired me to think about other possibilities when dealing with math problems and to try to approach them in a different way. and last my question is why we don’t have a class like this in school where students get to do something similar to VI hart.
After I watched this video I would say that Vi hard and Lkhart have similar approach to math problems solving, they both want to implement creativity in math rather then just following learned steps. this video inspired me to think about developing teaching methods and strategies that I will use when I become a teacher. math is about reasoning and logic but adding creativity to it definitely will make my future students interesting in the material . and the concept of connecting dots is similar to our project in class
A music video about the circle constraint, Tau.
A visual example and proof of the Pythagorean using nothing but a piece of paper.
Create the angles you need by folding a piece of paper systematically into a quick and ready to use protractor.
The video, A Song About A Circle Constant, talked (sang) about the idea of Tau. Prior to this video, I had no idea what this concept was so I was trying to learn and understand it. . Vi Hart created a video to explain the concept of Tau, a measurement of 2pi used as a proportion for diameters, in ways of music, visuals, and geometry. The music and song helped to internalize the idea of Tau more concretely as you can hum its tune or sing its numbers. Vi Hart even used visuals like circles and an unraveled earphone wire to show Tau’s applications and value on paper. The humorous drawings of the two stickmen arguing about Tau cemented the idea that Tau’s value comes from twice Pi, but is a specific term and value used for discussing diameters.
By the end of the video, I was very amused but at the same time bewildered. Needless to say, the music and lyrics were very provoking but what was shocking was that I actually learned. In other words, I would never have hoped to think or even imagine that teaching can be in this form. Certainly, I wouldn’t expect this in a school setting. This approach to teaching a concept is incredibly refreshing in my mundane routine school schedule and learning experience. It is math. It is teaching. It is a music video. It is not in today’s schools. It’s disheartening to realize that I have lost my strong youthful enthusiasm for learning. This video was able to revert me back into a child, happily and playfully learning about anything and everything that piques its interests. I wish my future students would achieve, and even go beyond, the same level of enthusiasm that I had when I watched this video.
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.
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.
This video showed that one can make angles and shapes without actually using or carrying a protractor. Adding on that, if one knows the basic form of the 60, 90, and 180 degree angles they can use paper folds to help them mimic the job of a protractor.
Borromean Onion Rings: https://youtu.be/4tsjCND2ZfM
This video showed how to cook onion rings in a unique shape called the “Borromean Ring”. This edible rings were used as a topper in the video. Moreover, the video explained the concept of how the Borromean Rings are linked and how to link the onion rings the same way.
Re: Visual Multiplication and 48/2(9+3): https://youtu.be/a-e8fzqv3CE
This video was trying to shed light on a new multiplication method and also to explain how crucial proper math notation is. Lastly, that there are more than one way in math to solving a problem.
Origami Proof of the Pythagorean Theorem: https://youtu.be/z6lL83wl31E
This video explained the proof of the Pythagorean Theorem by folding different triangles into a paper. It explained the basic concept of the a^2, b^2, and c^2 sides, and how and why all the sides add up and work.
For this part of the assignment I chose to focus on the “Re: Visual Multiplication and 48/2(9+3)” video. I found this video so fascinating because not only was it a response video to a concept or trick used for multiplication that I was unaware of, but because of what I learned through Harts simple statement and showing that there are more than one way to solve equations. Like I have previously mentioned, the video was in response to a multiplication trick, but the fascinating or knowledgeable part to me was when she didn’t know how to multiply 6*7. She then shows a alternative way, despite the trick, which was to draw a whole bunch of dots and multiply by grouping simpler numbers that once can multiply then multiplying the remainder. I just thought one needs to know there times table. Moving on, the second half of the video also interested me and I learned something new. She explained how crucial math notation is. I mean, I always new how crucial it was but not until I saw the video example of how one can mess up on a simple multiplication and division equation if it was not in the right form. Since math is my major, I could easily identify how to do it, but I can also see how tricky the equation would have been for someone not so passionate about math. They wouldn’t have the necessary skills to pick up on bad notation. In conclusion, the video was well explained, leaving me with no questions.
Well I do believe that this video was math, probably not numerical or algorithmic actual type math, but it used these concepts to explain the fact to not look at every single mathematical problem in one way. Sometimes, there are more than one way to do something that might be more convenient and easy to understand. While for others the conventional way would be best applicable. This of Hart’s lesson, yes, i do think i would use in my future teaching career because not all students learn the same. So its always beneficial to keep options and various methods on hand of doing problems, catering to the students needs. This way math breaks out of its ‘boring’ or ‘usual’ ways, hence making it fun. This also connects to Lockhart’s idea of making math fun and actually introducing new concepts into math, allowing students to explore on there own, beyond the conventional boundaries. In conclusion, Hart’s video do shed a more concrete and visible light on basic math and notational importance, so well that these will, for sure, aid in my steps to my career and once I am there.
Wau: The Most Amazing, Ancient, and Singular Number
This video literally talked about the most interesting number called Wau! WOW! A number that is so complex there are infinitely many ways to express it itself. You can use it in conventional ways but with complexity, you will end up with wau.
Infinite Trees Are Super Weird
This video talks about infinite numbers. She goes on about how you can create a number tree and this number trees has branches and nodes to it so essentially you can go along these branches and reach these numbers infinitely. Also wonders if there is a pi node.
Math Improv: Fruit By The Foot
She wants to know if there are math elements to fruit by the foot, and does something interesting with the candy. She relates it to the famous mobius strip.
This video amazed me. I honestly don’t know if wau is real I didn’t bother searching about it but it blew my mind. She kept comparing wau with fractal fractions and e and derivatives, and it was mind blowing what this ‘wau’ number is. What I actually learned in this video is that if you infinitley take a pattern for example (x+x^y+x^(y^x))/(y+y^x+y^(x^y)) and so forth, equals wau. My question is, why don’t they teach us this in school?
I believe this video could mean nothing to my own math teaching. I mean, it’s talking about a topic that isn’t even teachable. It seems like just a concept, something to get you thinking. Wau would make a great excercise in terms of the idea of infinite patterns in math. I believe this concept is math but it isn’t teaching. It is an idea that will leave everyone wondering. And the reason for that is math, well numbers in general is a complex idea that we as humans have taken control of the topic. It’s like measurements for example. Measurements were created by people to define a set of rules and precision. But no doubt, there is ‘no such thing as measurements’ we’re just safe with them. Do you understand? Like we know what pi is but we don’t really know what pi is. This is wau. I believe that in Lockhart’s Lament, it was the same idea.