Math Challenge - Parameterization

Here’s the challenge: Parameterize a Möbius strip of width 1 and radius 2. It must not be piecewise. All work should be shown.

http://mathworld.wolfram.com/MoebiusStrip.html

Okay, the goal is to do it without looking at that.

Yes, apparently he forgot to show his work.

Step 1: https://www.google.com/search?q=mobius+strip+equation

Step 2: Click the first result.

Step 3: win.

Seems unnecessarily complicates, cut your work in half by clicking I’m Feeling Lucky instead of Google Search

Does this mean that no one actually wants to try the challenge? I don’t think this should be too difficult if you think about it the right way.

Not sure why people are giving you a hard time when Ether has good responses to his math threads.

The big difference, from my perspective, is what needs to be done to find a solution - in Ether’s problems, the only recourse is to actually understand the math involved and solve it yourself. This one is a standard mathematical item where the answer and derivation of the answer can be quickly and easily Googled.

Sure, but that’s not the point. This is still a problem that requires some thinking and knowledge of the topic if you intend to solve it yourself (which is what this thread is about).

I disagree to some extent on this: one of Ether’s recent quizzes was to calculate the integral of sqrt(x^2 + 4). Mathematica can do this with Integral[Sqrt[x^2 + 4], x] (or something similar) really quickly. But he asked for steps, which seems to mean you have to do it out by hand. Or not:

  1. Use a free integral calculator like Symbolab that gives the steps
  2. Wolfram Alpha) has step by step solutions if you have the pro version (or the trial)
  3. Mathematica has a Wolfram Alpha input (type == at the beginning of a line) that gives step by step solutions

Similarly, for the one about whether a series converges, Wolfram Alpha also has step by step solutions, and even with just the regular one, they tell you which test you can use to get the answer.

EDIT: Sorry if the wording made it sound like those quizzes aren’t worth doing–they are, and they’re really fun to do–or that they weren’t well thought out–they are, and just how complicated the integral got should be proof of that… I was just saying that there are ways to get around the vast majority of math questions without actually doing them (if there wasn’t, I’d probably never finish my math homework)

Math has really become about interpreting the problems and setting them up so a computer can do them rather than doing pure calculations. Yesterday my math teacher (I’m in multivariable) decided we needed more practice with integration in polar coordinates (\integral (stuff) r dr d heta), so he gave us this quiz: Set up the polar integral to find the area of the region bounded by the lines x=0, x=6, y=0, and y=4.
The easy part of that question is finding the area, since it’s just a rectangle. The hard part is setting up the integral, which isn’t fun. The nice part is that I can use Wolfram Alpha to compute my integral to make sure it’s correct.

It’s like making design sketches: SolidWorks can do the math, but you need to know how to represent it or it’s useless.

/off topic

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Back to M1KRONAUT’s quiz:
x = (2 + cos(0.5t))cos(t)
y = (2 + cos(0.5t))sin(t)
z = sin(0.5t)

In the future, if you create more math quizzes (and I hope you do–they’re fun and CD can always do with more math :slight_smile: ) consider making quizzes that require more interpretation of the question and can’t be easily googled / wolfram alpha-ed. Consider something like these:

  1. From my math teacher: Set up the polar integral to find the area of the region bounded by the lines x=0, x=6, y=0, and y=4. (no, I’m not cheating, I finished it already…) Or worse: Set up the integral in spherical coordinates to find the area of the cube bounded by the planes x=-1, x=1, y=-1, y=1, z=-1, and z=1.

  2. The birthday question or one that doesn’t have as many videos explaining how to solve it… (I don’t really get why it has been so difficult for many people to solve, but I guess I’m used to Singapore’s math questions after using their workbooks for many years)

  3. Any sort of word problems–in general, the type of questions that even Wolfram Alpha can’t interpret. The types of questions that say “set up the ___” vs “solve ___” or even if they ask for a final answer, that require understanding the question before purely plugging in numbers.

EDIT: Look at some of Ether’s math quizzes for inspiration on these. Even his “solve ___” ones can’t easily be gotten on a CAS software / by googling it / from Wolfram Alpha, with the possible exception of the integral, which was interesting enough that I think it deserved to be one. Although I still believe that the first step of identifying how to do it, rather than all the steps in the middle, is the hardest step that requires the most creativity. (Sorry Ether, I agree with you that we’ll have to agree to disagree on this)

Great answer! I haven’t tried it yet, but I was learning about orientable surfaces last week in math class, which gave me this idea.

I solved the birthday problem in about 20 minutes, but my solution makes a couple of assumptions (namely, that both people will announce that they know the answer when they do).

Maybe I’ll try to come up with a better problem later today.