If you like
We're closest to the Sun in January; I'm sure you knew that.
This IS a TEST; Do you know the ACTUAL reason division by zero is not permitted?
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Evolving wrote:I don't know what point, if any, was being made with reference to circular orbits; but the Earth's orbit, in the current phase of its history, has an eccentricity of about 0.02, which is not very much. (Eccentricities vary between 0 and 1. Or, to be more precise, an eccentricity of more than 1 means we have a hyperbola.)
scott1328 wrote:
If I recall correctly, GR rules out orbits following simple curves such as the conic sections.
Now on to the physics. Circular photon orbits are usually ignored, because they are unstable: any tiny perturbation and the photon will end up shooting out to infinity, or plunging into the black hole. Still, they’re useful to understand (see e.g. reference 5), and they’re just fun to visualize.
scott1328 wrote:scherado wrote:Another thing I remember from college-days is that multiplication is addition by a different name: 7 x 3 = 7 + 7 + 7.
For division, we have subtraction by a different name: For 6/2, we subtract 2 from 6, take the reduced value and repeat UNTIL we either reach 0 or there's not enough remaining; count the number of iterations:
6 - 2 = 4
4 - 2 = 2
2 - 2 = 0
3 times we subtracted 2: 6/2 = 3
You learned THAT in college? Must be University of Florida.
scherado wrote:Another thing I remember from college-days is that multiplication is addition by a different name: 7 x 3 = 7 + 7 + 7.
For division, we have subtraction by a different name: For 6/2, we subtract 2 from 6, take the reduced value and repeat UNTIL we either reach 0 or there's not enough remaining; count the number of iterations:
6 - 2 = 4
4 - 2 = 2
2 - 2 = 0
3 times we subtracted 2: 6/2 = 3
Now, do the same for 3/0:
3 - 0 = 3
3 - 0 = 3 ...
Infinite iterations.
There's that pesky infinity, again. (Not whistling Dixie.)
OlivierK wrote:scherado wrote:Another thing I remember from college-days is that multiplication is addition by a different name: 7 x 3 = 7 + 7 + 7.
For division, we have subtraction by a different name: For 6/2, we subtract 2 from 6, take the reduced value and repeat UNTIL we either reach 0 or there's not enough remaining; count the number of iterations:
6 - 2 = 4
4 - 2 = 2
2 - 2 = 0
3 times we subtracted 2: 6/2 = 3
Now, do the same for 3/0:
3 - 0 = 3
3 - 0 = 3 ...
Infinite iterations.
There's that pesky infinity, again. (Not whistling Dixie.)
You think you reach 0 after subtracting 0 from 6 an infinite number of times?
How precious.
scott1328 wrote:Part of your challenge is to read back through the thread and find any of the comments where I presented you the challenge. It isn't hard.
newolder wrote:Do these circles live solely in the Platonic world or do the approximations found in nature suffice?
scott1328 wrote:... For extra credit, we can ask Scherado why using L'Hopital's to evaluate sin(x)/x employs circular reasoning, and is technically invalid.
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