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Rippling Hysteresis's latest activity
R
Rippling Hysteresis
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Infrared's post
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Why Torsion = 0 => Planar Curve in this Proof
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Like
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Your vector ##v## is wrong. The binormal vector for ##\alpha## is ##(0,0,1)##, as you should compute. You're right, it's not obvious...
Aug 26, 2020
R
Rippling Hysteresis
replied to the thread
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Why Torsion = 0 => Planar Curve in this Proof
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⋅ Thanks for your patience. It's still a challenge for me to make sense of proofs in concrete terms-- work in progress. I went back...
Aug 26, 2020
R
Rippling Hysteresis
reacted to
Infrared's post
in the thread
I
Why Torsion = 0 => Planar Curve in this Proof
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Like
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For a fixed vector ##v\in\mathbb{R}^3## and constant ##C\in\mathbb{R}##, the set ##\{x\in\mathbb{R}^3: x\cdot v=C\}## is a plane. Your...
Aug 26, 2020
R
Rippling Hysteresis
reacted to
Infrared's post
in the thread
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Why Torsion = 0 => Planar Curve in this Proof
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Let's just take ##r=1##, so in your example ##\alpha(t)=(\cos(t),\sin(t),0)##. Then...
Aug 26, 2020
R
Rippling Hysteresis
replied to the thread
I
Why Torsion = 0 => Planar Curve in this Proof
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So would the α(s) (a circle) I've chosen be wrong or would it be the vector (1/sqrt(2)(1,1,0). It seems like the vector is constant and...
Aug 26, 2020
R
Rippling Hysteresis
replied to the thread
I
Why Torsion = 0 => Planar Curve in this Proof
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Couldn't the vector also be v= (1/sqrt(2), 1/sqrt(2), 0), which then wouldn't equal a constant? So the dot product would be...
Aug 26, 2020
R
Rippling Hysteresis
replied to the thread
I
Why Torsion = 0 => Planar Curve in this Proof
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The lecturer has used α(s) in the past to be any curve in R^3. I'm not sure why dotting that curve with a constant value represents a...
Aug 26, 2020
R
Rippling Hysteresis
posted the thread
I
Why Torsion = 0 => Planar Curve in this Proof
in
Differential Geometry
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I was watching a lecture that made the conclusion about the torsion being equal to zero necessitated that the path was planar. The...
Aug 26, 2020
R
Rippling Hysteresis
replied to the thread
I
Advice toward Mastering Challenging Vector Calc Problems
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Thanks! I will check those links out. Might be cool to tackle some.
Aug 21, 2020
R
Rippling Hysteresis
replied to the thread
I
Advice toward Mastering Challenging Vector Calc Problems
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Thanks for your reply. In past searches I have found a lot of basic problems (calculate the line integral of this function, use the...
Aug 21, 2020
R
Rippling Hysteresis
posted the thread
I
Advice toward Mastering Challenging Vector Calc Problems
in
Calculus
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I've taken multivariable/vector calc and can do most of the basic operations and have an OK understanding of the fundamental concepts...
Aug 21, 2020
R
Rippling Hysteresis
replied to the thread
Multivariable Limit Problem: Find Values of k That Make Limit Exist
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OK cool! So I see it this way then: If z=r, it simplifies to r^k(e^(r^2)-1)/(4r^(2k). Using the expansion e^(r^2) ≈ 1 +r^2, we get the...
Aug 14, 2020
R
Rippling Hysteresis
replied to the thread
Multivariable Limit Problem: Find Values of k That Make Limit Exist
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Wait, now I'm doubting myself and thinking I made a mistake with the z=0, r -> 0 part. Won't the numerator actually become...
Aug 13, 2020
R
Rippling Hysteresis
replied to the thread
Multivariable Limit Problem: Find Values of k That Make Limit Exist
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Thanks once again! The numerator then becomes (1+r^2)-1= r^2. So the expression reduces to r^2/r^(2k). In order for the limit to go...
Aug 13, 2020
R
Rippling Hysteresis
replied to the thread
Multivariable Limit Problem: Find Values of k That Make Limit Exist
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Ooh, yeah, thanks. Substituting those parameters gives me: z^k(e^r^2 -1)/(r^2+z^2)^k So for the limit (r=0, z->0) would be...
Aug 13, 2020
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