Wau: The Most Amazing, Ancient, and Singular Number
In this video Vi Hart talks about a number that was discovered in East Asia and in many other ancient societies. She describes the different mathematical relationships, usually infinite fractions, that included Wau (some that just included Wau and others were equal to Wau). She related the special number to nature and other fields of study like physics.
https://www.youtube.com/watch?v=wsOXvQn3JuE
Why Every Proof that .999… = 1 is Wrong
In this video Vi Hart goes through some of the many proofs that are used to show that .9 repeating is equal to one. She goes on to prove or attempt to prove these wrong to say that the two are different numbers that are independent of each other. She invalidates these proofs and then briefly talks about why mathematicians believe it is so.
https://www.youtube.com/watch?v=CfJzrmS9UfY
Doodling in Math Class: Stars
In this video Vi Hart talks about drawing stars and connects this activity to math. She talks about stars with different numbers of points and how the number of points relates to the number of sides in each of the polygons that make up the star. She then makes this star drawing into a “game”.
I was a little confused, especially during Hart’s “Doodling in Math Class: Stars” video not because I did not understand what she was saying just because I felt that she was going a little to quick while speaking and the video recording was also sped up so while trying to process what she had just said she was already on to the next part of her speaking and all throughout her hand was moving very quickly on the paper. She did show what she was saying at the same time that she was saying it. For this reason I had to pause the video multiple times to reassess what she said. There was not anything in the video that particularly bewildered me or made me say wow except for when Hart started drawing the much larger stars with many points (when she began using the protractor): I thought that the stars that she made were beautiful and they also require a lot of talent to make. I learned that a star with p points can be drawn with 2 p/2- gons; this was a mathematical relationship that I had not been aware of. In fact I have not ever looked into the math behind stars before. I also learned that even with a set number of points in the star and a set number of polygons formed within the star, there are still multiple ways of drawing the star even with the restrictions. Although I did have to pause the video ever so often so that I did not fall behind on what Hart was saying, I for the most part understand everything that she said. So the only question I have after watching the video, is not directly about the math or the drawing in the video, it is: how does Hart discover the relationships between things like the sides of the stars and the number of polygons in the star; or rather: how is she so successful at finding things like the “game” in this video, that still relate to math, but that a majority other people would not be able to discover?
I think the video could really help me with my own math teaching, even though I did not really enjoy the fast pace of it. What I can learn from Hart is that I need to implement creativity in the classroom at least every once in a while especially in order to keep the students engaged. As Hart emphasizes in the beginning of the video while talking about how she was bored during her math class while learning about factoring, classes that are only lecture can get boring and can cause students to become distracted. So rather than have my students lose focus like Hart did from what the class was actually about: I will give my students an activity to do in class that directly relates to the topic of the day. This way they have something fun to look forward to and are then more inclined to pay attention during class so that they can preform well during the activity. This way they get the fun that they want in class, without losing focus from the actual class and making fun for themselves. Hart’s video really helped me come up with this idea for my own classroom because she expresses that class can get boring, which is true for any student at one point or another and that there are fun and thought-provoking activities to do during class that can still be mathematical and related to class. Kids have a hard time focusing on school work especially for note-taking and problem solving but they are often all for interactive activities, and so I have come to realize after watching this video that combining the two ways of learning can help to take away some of this lack of focus.
alright, this question is philosophical and somewhat fuzzy. i also admit to knowing little about logic. all in all, this question can possibly be easily resolved by either pointing to (perhaps even well-known) literature i haven’t found or by pointing out a fault in my reasoning. joel david hamkins is a proponent of multiverse interpretation […]
Question: There is a game that involves $n$ ordered boxes each with a hidden value associated with it. The value is sampled from a probability distribution density function $P(x) = \frac{1}{\sqrt{2\pi}} e^{-\frac{1}{2}x^2}$. You observe each box’s value in order from box 1 to $n$. After observing any given box’s value, you must decide to pick […]
Answer In order to verify that the loop variant holds, we must check that it is strong enough together with the negation of the boolean guard to imply the post condition. Check. It is weak enough to be implied by the precondition. That I cannot verify $y\geq0$ don't directly imply $z = x\dot a$. Can […]
Is $\exists y\forall x(Pxy\land Qy)$ always false? I ask because of the following: Let the domain of discourse be the set where x and y are natural numbers and y is always greater than x. Let P be the set of Prime Numbers $\exists x\exists y\left(y>x\land y\in P\right)\rightarrow\exists y\forall x\left(y>x\rightarrow y\in P\right)$ is valid. Also, […]
Intuitively speaking, how do existential quantifiers appear? I'm just starting to get familiar with these definitions. Top and conjunctions appear because of finite products. (Plus, I assume, something that makes them work nicely with the existential quantifiers.) But my understanding of existential quantifiers in categorical terms is by way of them being left adjoint to […]
Suppose we want to formalise some parts of mathematics within set theory, which is itself formalised in a first-order language (in the standard way). Logic is assumed to be classical. In particular, this means that – at the level of semantics – every term must have a denotation, which in turn means that every function […]
In order to prove the completeness theorem we obviously need a framework such as ZFC (I'm aware that ZFC isn't the only possibility) so that we can talk about a language $\mathcal{L}$ and also about models of $\mathcal{L}$. Now the completeness theorem makes perfect sense to me in so far as the language which we […]
A friend of mine showed me an SAT question today in which one of the choices is: No genetic variations that were common to those finches that used technique Q were not common to the finches that did not use technique Q. I just learned a bit about logic so I tried breaking down the […]
I am looking for ways to internalize the modal operator of necessity $\Box$, ending up with a morphism $\Box: \Omega \to \Omega$ satisfying the necessitation rule (if $\phi$, then $\Box \phi$) and the distributive under implication $(\Box(\phi \to \psi)\to (\Box \phi \to \Box \psi))$. The reason why is I would like to study categories in […]
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