# 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.

# Group Process Paper – Grading Criteria

Hi everyone,

The group process paper will be worth 35 points towards your Project grade.  I will be filling out the sheet below for each paper submitted.  Please let me know if you have any questions.

Best,
Prof. Reitz

Semester Project – Puzzle Process Paper

_____ points (3 possible).  Basics/formatting.  Length (1500 words required).  Group members names.  Semester/Date/Course.

_____ points (2 possible).  Puzzle description. Description given in own words, demonstrates understanding of puzzle mechanics.

_____ points (16 possible).  Proof process narrative.

_____ points (4 possible).  Shows progress across various stages of the project.

_____ points (4 possible).  Includes all participating members of the group.

_____ points (4 possible).  Includes objective facts (“what we did”) as well as experience (“how it felt, what it was like”).

_____ points (4 possible).  Tells a story.

_____ points (5 possible).  Conjecture.

_____ points (3 possible).  State your group’s conjecture.

_____ points (2 possible).  Proof or disproof of conjecture. If no proof or disproof was obtained, these points can be earned by clear explanation of proof process in the preceding account.

_____ points (9 possible).  Images (3 points each).  Original or clearly attributed.  Includes caption.  Connection to puzzle/process is evident.

____ points TOTAL (35 possible)

# videos abdelmajid

part 1

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.

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”.

part 2

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.

part 3

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

# Videos : Yuyu Chen

Part 1

A Song About A Circle Constant

A music video about the circle constraint, Tau.

Origami Proof of the Pythagorean Theorem

A visual example and proof of the Pythagorean using nothing but a piece of paper.

Angle-a-trons

Create the angles you need by folding a piece of paper systematically into a quick and ready to use protractor.

Part 2

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.

Part 3

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.

# 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.

# Rahat Javed Videos

Part 1:

Angle-a-trons: https://youtu.be/o6W6P8JZW0o

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.

Part 2:

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.

Part 3:

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.

# Videos Josiel Nunez

Part 1.
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?

Part 3.

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.

# Week 11 Assignments

Written work, Due Tuesday, November 10th, in class
Chapter 8 p145: 3, 7, 18, 19
Chapter 9 p152: 3, 4, 5
WeBWorK – none
OpenLab – none  (work on your group paper!)

# Semester Project – Group Process Paper

In his essay A Mathematician’s Lament, Paul Lockhart says “A good problem is something you don’t know how to solve.” This is quite different from most of the “problems” that appear in our mathematics education.  In the past weeks, you’ve all spent some time individually and in groups working on such problems, in the context of graph theory (“Bridges and Walking Tours”).

As a group, write an account of your experiences working on your puzzle/problem.  You should include the following elements:

• Description of the Bridges and Walking Tours problem, in your own words.
• An account of working on your problem as a group, from playing with the problem to formulating and perhaps proving a conjecture.  What did your group do/think/feel?  You can include examples of puzzles and solutions if you wish, as well as work by individual group members completed outside the group (both optional).  Your goal is not to go over every detail, but to tell a story that your readers will enjoy – “what was it like”?.
• A statement of your group’s chosen conjecture, and a proof (or disproof) of the conjecture.
• At least three images (more if you wish).  They can include images of puzzles you’ve created or solutions, but you can also be creative with images or photos related to your puzzle, your group or your story in some way.  Each image should have a caption describing.  NOTE: You may freely use your own drawings, images or photos.  If you wish to use photos from another source, they must be from a legal source (for example, Creative Commons licensed, with proper attribution – the library or your professor can help with this).
• Basic details: the names of all group members, the date, course and section numbers, and your professor’s name.

I will be meeting with each group next Thursday, November 12th, in class.  Please be in touch with your other group members before then!  Be prepared to discuss your progress so far – at the very least, you should be able to describe how you are dividing up the work of the paper among your group.

The first draft of this assignment is due in class on Thursday, November 19.  Each group should submit one paper, of no less than 1500 words.  You may decide as a group how to divide up the work.  Be aware that you will be asked at a later time to describe your own specific contributions as well as those of each group member.

The final draft of this assignment is due in class on Thursday, December 3.

UPDATE REGARDING SEMESTER PROJECT:  As you may recall from the Course Description, the semester project is worth 10% of your overall grade.  The project consists of a number of interrelated activities (many of which have already been completed) – complete details can be found on the Project Overview & Deliverables page.  The group paper assigned here forms a significant portion of the project.

# In-Class Group Project Activity 10/29/15 – Refine Your Group Conjecture

Assignment.  Your goal for today is to refine the conjecture you decided on during your last class meeting.  Some things to consider:

• Specificity: The conjecture should be stated clearly.  It should include all information necessary to be understood by someone who is familiar with graph theory terms (vertex, edges, paths) and familiar with the assignment (walking tours).  A reader should be able to tell from the statement whether a conjecture applies to a given drawing or not.
• Generality: Your conjecture should apply to more than just a single specific graph (it can apply to a collection of similar graphs, for example, as long as you describe exactly what types of graphs you are considering).
• Drawing: You can create a drawing to accompany your conjecture, but your conjecture should be understandable without the picture.
• You can revise your conjecture as a group if you wish – but try to come up with something similar.