meta user
network profile
| bio | website | natesoares.com |
|---|---|---|
| location | ||
| age | 23 | |
| visits | member for | 2 years, 2 months |
| seen | 3 hours ago | |
| stats | profile views | 67 |
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May 21 |
awarded | Commentator |
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May 21 |
comment |
How come the Euclidian distance for n-space involves only squares? Cool! Are there any uses to such alternative definitions? Also, what do you mean by saying that one allows rotation while the other does not? How can a distance metric prevent rotation? |
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May 21 |
asked | How come the Euclidian distance for n-space involves only squares? |
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Mar 14 |
awarded | Yearling |
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Mar 6 |
revised |
What's so special about sine? (Concerning $y'' = -y$) corrected spelling, fixed formatting |
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Mar 6 |
suggested | suggested edit on What's so special about sine? (Concerning $y'' = -y$) |
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Mar 3 |
comment |
What's so special about sine? (Concerning $y'' = -y$) I understand that, but I don't completely buy this. Wherever there is a circle in nature, looking closer we find it not a circle. Orbits are actually ellipses, the earth isn't quite spherical, and so on. |
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Mar 3 |
comment |
What's so special about sine? (Concerning $y'' = -y$) "Nearly every"? Which ones can't? Also, given the taylor series approximation for sine, can't anything approximated by a harmonic oscillator be modeled by even simpler functions? |
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Feb 29 |
comment |
What's so special about sine? (Concerning $y'' = -y$) Thanks! I suppose I probably should take this question over to physics, I'm also curious as to why physics seems to care so much about the second derivative (in everything from F=ma to the position/momentum interaction). |
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Feb 29 |
accepted | What's so special about sine? (Concerning $y'' = -y$) |
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Feb 29 |
awarded | Nice Question |
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Feb 28 |
awarded | Editor |
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Feb 28 |
revised |
What's so special about sine? (Concerning $y'' = -y$) added 448 characters in body |
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Feb 28 |
asked | What's so special about sine? (Concerning $y'' = -y$) |
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Jun 6 |
comment |
Can you explain $(1 + iX/n)^{n}$ without using e, sin, or cos? That helped a lot, thanks. In my own terms, the key point that I was missing was that taking $\lim_{n\to\infty}$ negates the drift off the unit circle that you see in $1+iX/n$, but does not negate the rotation caused by $1+iX/n$. It still astounds me that by taking the limit in this situation you negate the drift but not the rotation - that's an incredibly beautiful and powerful idea. :) |
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Jun 6 |
accepted | Can you explain $(1 + iX/n)^{n}$ without using e, sin, or cos? |
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Jun 6 |
comment |
Can you explain $(1 + iX/n)^{n}$ without using e, sin, or cos? I get it! Multiplying by $1+ix$ gives us rotation by x but doesn't keep us on the unit circle. However, if we divide by n and raise to the power n, we manage to quell the drift off the circle but maintain the rotation. The drift is lost if we divide by and raise to the power n, but the rotation is not. Looking deeper, is there any field of math concerned with which operations are susceptible to elimination by such limits and which operations are unaffected? |
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Jun 6 |
comment |
Can you explain $(1 + iX/n)^{n}$ without using e, sin, or cos? Thanks! I don't quite understand the image above: I understand the first frame represents $1 + i*\pi$, but I don't understand the following frames. I know I'm being a bit dense, but could you break frame 3 down for me into what each segment represents? |
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Jun 5 |
asked | Can you explain $(1 + iX/n)^{n}$ without using e, sin, or cos? |
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May 23 |
comment |
Complex Exponents Thanks, that clears a lot of things up. I still don't quite understand why multiplication by (1+iX/N) is equivalent to rotation by X/N - do you think you could clear that up a bit for me? |
