Recent content by Fantini

  1. Fantini

    MHB How many oranges were there in the morning?

    Do you have references where I could learn more about this method?
  2. Fantini

    MHB How many oranges were there in the morning?

    What is the Singapore model method?
  3. Fantini

    MHB Topic of presentation: Elementary Geometry vs Fibonacci & its sequences

    Mathmari, what is the target audience for this presentation? I don't think I've seen you mention this. It matters a lot when it comes to structuring your talk.
  4. Fantini

    MHB Is This Integral Divergent as t Approaches Infinity?

    Mark, this does look like a test. I'd wait for the 48h before replying.
  5. Fantini

    MHB Definite Integral ∫xe^(ax)cos(x)dx

    My attempt:
  6. Fantini

    MHB Is the Plane MKPN Possible Inside Pyramid ABCD?

    HallsofIvy, I would just like to point out that tetrahedrons are also pyramids, but not every pyramid is a tetrahedron. A pyramid is a polyhedron of which one face can be any polygon (called its base) and all other faces (called lateral) are triangles meeting at a common vertex. A pyramid can be...
  7. Fantini

    MHB Why is theta restricted to [0,pi] in mathematics and physics?

    Perhaps this less-than-artistic picture will help. When we consider angles between lines (and vectors) we always assume the angle that is less than or equal to $\pi$. The picture illustrates the scenario you are considering. In this case what we call the angle between the vectors is the...
  8. Fantini

    MHB Why is theta restricted to [0,pi] in mathematics and physics?

    Because in the interval $[0,\pi]$ the sine function $\sin(\theta)$ is nonnegative. He could have chosen $| {\mathbf a} \times {\mathbf b}| = {\color{red} (-1) } |{\mathbf a}| |{\mathbf b}| \sin(\theta)$, but then he would have reversed the orientation of the cross product.
  9. Fantini

    MHB On the cruelty of really teaching computer science

    Thank you for your response, Ackbach. I wanted to read that book since I've seen it in your signature, but I didn't buy it. Glad to know it is online. :) Let me discuss Dijkstra's arguments. Indeed, programming is no longer a radical novelty, although I agree that some people still believe in...
  10. Fantini

    MHB On the cruelty of really teaching computer science

    This is an article I just found out about. It deals with computer science on about half of it, but the most interesting discussions concern educational values. Here is the article: https://www.cs.utexas.edu/users/EWD/transcriptions/EWD10xx/EWD1036.html I would like to know others' thoughts on...
  11. Fantini

    MHB First Approach to Differential Forms

    Yes, that is what I'm saying. It is fine to use Weintraub even as he doesn't use the wedge notation. :)
  12. Fantini

    MHB First Approach to Differential Forms

    Sorry for not answering earlier, I didn't see you answered the thread until two days ago. The answer to your question is no. I don't think the wedge makes much of a difference, notation-wise. You know it is there and what you must pay attention is to operate with it according to the wedge rules...
  13. Fantini

    MHB First Approach to Differential Forms

    The whole set is expensive, so perhaps if you stick to your decision of acquiring it you should buy only volume one at first. As for the proofs, his proofs and methods are not all short and slick. In fact, he is rarely short and slick. He prepares the chain rule for three sections before...
  14. Fantini

    MHB First Approach to Differential Forms

    While not a book on differential forms, I recommend J. J. Duistermaat and J. A. C. Kolk's two-volume set Multidimensional Real Analysis. It aims to teach you analysis in $\mathbb{R}^n$ but it is just as much a beginning differential geometry book. Differential forms will be touched upon in the...
  15. Fantini

    MHB Vector or Parametric Form of the Equation of a Plane P

    You are right. There is an infinite number of parametric representations of a plane. :)
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