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    How to find the area of an n-dimensional triangle?

    A = {2,1,2,4} B = {4,1,6,2} angle = arccos( (A.B)/(norm(A)*norm(B)) ) area = (1/2)A.B sin(angle) Is this correct? if yes, it is easy to generalize for Rn.
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    How to find the area of an n-dimensional triangle?

    I've literally typed out the question as it has been given. I think take it as a standard triangle in n-dim space
  3. L

    How to find the area of an n-dimensional triangle?

    Some elaboration on that would help, is possible?
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    How to find the area of an n-dimensional triangle?

    ? Let me know if I've explained the problem sufficiently
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    How to find the area of an n-dimensional triangle?

    Find the area of the triangle with sides A = (a1 ... an) B = (b1 ... bn) and A-B = (a1-b1 ... an-bn) I don't even know where to start. I know how to do it in 3D with the cross product, but that obviously won't work for higher dimensions. So I need help generalizing for Rn.
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    How to find the area of an n-dimensional triangle?

    1. Homework Statement How to find area of an n-dimensional triangle using vectors? 2. Homework Equations 3. The Attempt at a Solution
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    Why do 2nd-order linear ODEs have at most two independent solutions?

    1. Homework Statement Why does the following ODE ALWAYS have two linearly independent solutions? x''(t) + a(t) x'(t) + b(t) x(t) = f(t) The characteristic polynomial argument is not sufficient?
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    Simple Lagrangian for constrained motion - please give your input

    Thanks a lot man. But what I've done is correct, right? Literally can go on to find equations of motion with my lagrangian?
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    Simple Lagrangian for constrained motion - please give your input

    Thanks. Would it be similar for all y=f(x)?
  10. L

    Simple Lagrangian for constrained motion - please give your input

    Hello fellow PF members I was wondering how one would go about finding the lagrangian of a problem like the following: A particle is constrained to move along the a path defined by y = sin(x). Would you simply do this: x = x y = sin(x) x'^2 = x'^2 y'^2 = x'^2 (cos(x))^2...
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    How do I solve this differential equation?

    Yes that's the equation, just swop t for x. How have I done it wrong? I cross-checked with peers...
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    How do I solve this differential equation?

    partial derivative of (y')^2/y wrt y = - (y')^2/y^2 partial derivative of (y')^2/y wrt y' = (2 y' y'')/y derivative of (2 y' y'')/y wrt x = (2 y (y'')^2 + 2 y y''' y' -2 (y')^2 y'')/y^2 finsihed. everything i've done is correct
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    How do I solve this differential equation?

    I've done it wrong because you can't solve the equation.... right....
  14. L

    How do I solve this differential equation?

    By plugging (y')^2/y into the Euler-Lagrange Equation
  15. L

    How do I solve this differential equation?

    6 replies and all of them useless. Fixated on something frivolous. I gave you guys the correct differential equation in the first line anyway, so there's absolutely no problem imo.
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    How do I solve this differential equation?

    Why are you guys so fixated on that line?? That's not even the crux of the question I'm asking! lol I obtained this differential equation from applying the Euler-Lagrange equation to the following function: f(y,y') = (y')^2/y That's how I know my reverse quotient rule is...
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    How do I solve this differential equation?

    @SteamKing Reverse quotient rule. All I know is that what I wrote is definitely correct. I just have no idea how to solve it.
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    How do I solve this differential equation?

    1. Homework Statement Solve the following differential equation: 2. Homework Equations 2 y (y'')^2 + 2 y y''' y' -2 (y')^2 y'' = - (y')^2 3. The Attempt at a Solution I don't know if the following is useful, but if you divide both sides by y^2, the LHS of the above...
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