Cito di Pense wrote:

Evolving wrote:Thé Earth’s orbit is very close to circular, compared to other planets.

Shall I compare the orbit of the earth to a summer's day?

If you like

We're closest to the Sun in January; I'm sure you knew that.

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.)

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.)

My eccentricity is greater than 1. That must explain why my posts are so hyperbolic.

I knew there must be a proper scientific explanation.

scherado wrote:

scott1328 wrote:... God created the Natural Numbers, all the rest are the work of man.

What's the reason God did not create circular orbits? (This question assumes that there is NOT one circular orbit in the Universe, which, I'm certain, we can "count" on.)

If I recall correctly, GR rules out orbits following simple curves such as the conic sections.

scott1328 wrote:

scherado wrote:

scott1328 wrote:... God created the Natural Numbers, all the rest are the work of man.

What's the reason God did not create circular orbits? (This question assumes that there is NOT one circular orbit in the Universe, which, I'm certain, we can "count" on.)

If I recall correctly, GR rules out orbits following simple curves such as the conic sections.

See also Kerr spherical photon orbits where one can play along.

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.

Allowed by the mathematics but almost certainly disallowed in nature.

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.

I genuinely remember learning that when I was six or seven years old.

At university it was made explicitly clear in courses involving things like axiomatised field theory that multiplication and addition were defined separately, and that division and subtraction were defined as the inverses (with the noted exception in the case of division by 0) of those operations.

It's the fact they are inverses that prevents them having arbitrary definitions. An arbitrarily defined mapping or function (whether named division or not) can of course be given a value at 0.

This is all aside from the reality of why when asked "What is 1,000,000,000 divided by 10" nobody, including an algorithm that has been well designed, would subtract 10 from 1,000,000,000 100,000,000 times.

There are lots of interesting answers on stackexchange, in threads like https://math.stackexchange.com/question ... arithmetic or https://math.stackexchange.com/question ... metic?rq=1 about the structural problems and limitations of doing arithmetic in weaker axiomatic systems. These seem more indicative of what is taught at university level.

scherado wrote:

scott1328 wrote:... God created the Natural Numbers, all the rest are the work of man.

What's the reason God did not create circular orbits? (This question assumes that there is NOT one circular orbit in the Universe, which, I'm certain, we can "count" on.)

The reason I asked will be revealed [in] a new thread. Oy.

Please, no.

scherado wrote:

scherado wrote:

scott1328 wrote:... God created the Natural Numbers, all the rest are the work of man.

What's the reason God did not create circular orbits? (This question assumes that there is NOT one circular orbit in the Universe, which, I'm certain, we can "count" on.)

The reason I asked will be revealed a new thread. Oy.

Don't forget that ellipses in 3-D space may be represented by the projection of a circular orbit in 4-D space, as shown by John Baez here.

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.

scherado wrote:

scherado wrote:

scott1328 wrote:... God created the Natural Numbers, all the rest are the work of man.

What's the reason God did not create circular orbits? (This question assumes that there is NOT one circular orbit in the Universe, which, I'm certain, we can "count" on.)

The reason I asked will be revealed [in] a new thread. Oy.

No more "challenges" until you attempt to answer my challenge. Prove you can take it as well as you dish it out.

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.

Do you want to reconsider...when you've sobered up?

scott1328 wrote:

scherado wrote:

scherado wrote:

scott1328 wrote:... God created the Natural Numbers, all the rest are the work of man.

What's the reason God did not create circular orbits? (This question assumes that there is NOT one circular orbit in the Universe, which, I'm certain, we can "count" on.)

The reason I asked will be revealed [in] a new thread. Oy.

No more "challenges" until you attempt to answer my challenge. Prove you can take it as well as you dish it out.

Uhhhhh, I'm ready! Give me the linky dinky!!

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.

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.

If you insist.

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.

Is this the challenge?

Yes.

newolder wrote:Do these circles live solely in the Platonic world or do the approximations found in nature suffice?

And are they poof of god? (tee hee)

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.

Don't you need to start a new thread? Yes.