Recent content by PLAGUE

  1. PLAGUE

    B How to interpret Pascal's Triangle for negative numbers?

    I think I know the answers to your questions. But is there any physical significance at all?
  2. PLAGUE

    B How to interpret Pascal's Triangle for negative numbers?

    This answer shows an extended version of Pascal's Triangle that works for negative numbers too. In This video, Sal shows how to interpret the members of Pascal's Triangle as the sum of all the possible paths to get to that member. Is there any way we can use this same 'sum of all the possible...
  3. PLAGUE

    I What's the physical meaning of Curl of Curl of a Vector Field?

    How about $$\nabla \times (\nabla \times \mathbf{B}) = \nabla (\nabla \cdot \mathbf{B}) - \nabla^2 \mathbf{B}$$? Here B is the magnetic field. What do they represent here physically?
  4. PLAGUE

    I What's the physical meaning of Curl of Curl of a Vector Field?

    So, curl of curl of a vector field is, $$\nabla \times (\nabla \times \mathbf{A}) = \nabla (\nabla \cdot \mathbf{A}) - \nabla^2 \mathbf{A}$$ Now, curl means how much a vector field rotates counterclockwise. Then, curl of curl should mean how much the curl rotate counterclockwise. The laplacian...
  5. PLAGUE

    I Why "time part" represents energy in Four-momentum?

    I was going through Spacetime Physics by Taylor and Wheeler and came to a point where they said, and I quote, This part feels too abrupt for me and I am looking for a more elaborated explanation. Here is a link to that chapter.
  6. PLAGUE

    I Proof of Invariance of Spacetime Interval

    Isn't relativistic velocity is for, in such cases, horizontal motion? As I understand, our particle have no horizontal motion, but only vertical motion. Or am I getting it wrong?
  7. PLAGUE

    I Proof of Invariance of Spacetime Interval

    I was going through Spacetime Physics by Taylor and Wheeler and came to a point where they showed a proof of Invariance of Spacetime Interval. You can find the proof Here and Here is the second part of that proof. They used an apparatus that flies straight "up" 3 meters to a mirror. There it...
  8. PLAGUE

    I What is meant by Newton's Rules, if A+B=C, A=C and B=C?

    What is it meant by Newton's Rules in point (vii)?
  9. PLAGUE

    I Relation Between Beta and Gamma functions

    So, my teacher showed me this proof and unfortunately it is vacation now. I don't understand what just happened in the marked line. Can someone please explain?
  10. PLAGUE

    I How Feynman proves momentum is conserved in this example?

    Here is what Feynman says, "Suppose we have two equal masses, one moving with velocity v and the other standing still, and they collide and stick; what is going to happen? There is a mass 2m altogether when we are finished, drifting with an unknown velocity. What velocity? That is the problem...
  11. PLAGUE

    I Why prove Taylor's theorem with p(x)=q(x)−((b−a)^n/(b−x)^n)q(a)?

    yes it is
  12. PLAGUE

    I Why prove Taylor's theorem with p(x)=q(x)−((b−a)^n/(b−x)^n)q(a)?

  13. PLAGUE

    I Why prove Taylor's theorem with p(x)=q(x)−((b−a)^n/(b−x)^n)q(a)?

  14. PLAGUE

    I Why prove Taylor's theorem with p(x)=q(x)−((b−a)^n/(b−x)^n)q(a)?

    Here is the proof:
  15. PLAGUE

    I Why prove Taylor's theorem with p(x)=q(x)−((b−a)^n/(b−x)^n)q(a)?

    Here is a proof of mean value theorem: Consider a line passing through the points (a, f(a)) and (b, f(b)). The equation of the line is y-f(a) = {(f(b)-f(a))/(b-a)} (x-a) or y = f(a)+ {(f(b)-f(a))/(b-a)} (x-a) Let h be a function that defines the difference between any function f and the...
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