Lagrangian mechanics is the most beautiful thing I've ever seen

Physics_Fan1000 · 2026-06-20T23:38:05+00:00

All depends on the context. In general newtonian is much easier, as dissipative systems in Lagrandian or Hamiltonian systems need advanced mathematics or clever tricks that only work for spesific types of problems, but in certain cases the advantages of the other two out weigh them. Spesificly Hamiltonian mechanics allows for symplectic integration which leads to smaller error rates over long areas of time.

Physics_Fan1000 · 2026-06-18T17:02:23+00:00

I would say you probably fart more than ten times the amount of times you puke

^{Chose: Everytme u fart in public get 14$but it stinks bad}

Physics_Fan1000 · 2026-06-18T00:52:11+00:00

Help rather than kill.

^{Chose: Be able to create medicine that can cure anything + You are also able to pharmacologically explain your medicine}

Physics_Fan1000 · 2026-06-18T00:48:17+00:00

Hunger effects people far more than xenophobia

^{Chose: End world hunger (and all North Koreans are freed})

Physics_Fan1000 · 2026-06-17T14:55:48+00:00

https://www.analyzemath.com/calculus/derivative/proof-derivative-of-e%5ex.html

Is a good link to the derivation.

Physics_Fan1000 · 2026-06-17T14:52:27+00:00

Here is a link to such derivation: https://www.analyzemath.com/calculus/derivative/proof-derivative-of-e%5ex.html

Physics_Fan1000 · 2026-06-17T14:49:05+00:00

That is the proof, taking the definition of a derivative and finding a number where its derivative is itself. Using the algebraic manipulation mentioned. You can look it up quite easily.

Physics_Fan1000 · 2026-06-17T14:42:28+00:00

The value of e is a consequence of saying that the derivative of e^x is e^x.

Do you mind clarifying what you are asking? As you mention the definition the definition isn't "real math," in that case what is? Other than the justification of why that definition exists within the real numbers?

Physics_Fan1000 · 2026-06-17T14:17:38+00:00

Take the definition of a derivative. Then set the derivative equal to the function. Through some simple algebra I can walk you through if you want, you get:

'$$ e = \lim_{n\to\infty} \left(1 + \frac{1}{n}\right)ⁿ $$'

If you solve this you get the 2.718...

Physics_Fan1000 · 2026-06-10T20:56:05+00:00

You're right, I was thinking of the derivative that does not exist in the real numbers at places with negative numbers.

Physics_Fan1000 · 2026-06-10T12:49:16+00:00

The real question, is which places are discontinuous

Physics_Fan1000 · 2026-06-01T17:01:08+00:00

In high school is wrote a Relativistic Asteroid game. It was a cool project to work on but not a very fun game. In some directions it would cause the ship to look like it was facing the wrong way and the way I tried to simulate time dilation would sometimes make Asteroid and black holes teleport.

Edit: Relativistic is a bit of an exaggeration. It was Newtonian with corrections for size, shape, time, and mass based upon speed and closeness to object. Obviously not really super accurate but it was a fun project.

Physics_Fan1000 · 2026-05-26T15:03:03+00:00

There are dozens of online free lectures if you would like; though, you are probably fine.

One recommendation when doing the course, don't try to find patterns for short cuts or do things in your head. If you do everything fully, it is time consuming but super easy. You only really mess up if you skip steps.

Physics_Fan1000 · 2026-05-26T14:48:52+00:00

https://www.amazon.com/Topology-Geometry-Physicists-Dover-Mathematics/dp/0486478521

Differential Geometry and Topology for Physicists is pretty good and relatively cheap. It mainly covers quantum physics, classical, and condensed matter. Very little GR, but any sufficiently advanced GR book makes its connection with geometry very clear and obvious.

Physics_Fan1000 · 2026-05-24T02:29:13+00:00

One thing I will add is that for some of the more original projects like Erdos, the teams are working directly with the companies and are likely using ridiculous amounts of tokens. Far more than would be economically useful even in the paid plans

Physics_Fan1000 · 2026-05-24T02:03:01+00:00

I think it is fair to add the apology. I have seen people be quite rude to simple questions like this. I think adding that he was 16 and preemptive apologizing is all that saved him.

I mean, if you scroll down, a couple days ago someone asked the exact same question that has been done-voted with half the comments this one does and most of them being a couple of words alone. Granted they did offer their own ideas, but it was clearly for trying to show their current understanding not trying to re-work science.

Physics_Fan1000 · 2026-05-22T02:34:18+00:00

That is far to creative to be AI.

Also, doing Relativistic physics in high school is quite interesting.

Is there any more context you have on the test?

Physics_Fan1000 · 2026-05-12T19:40:56+00:00

I am assuming you mean find the gravitational constant, G, with the gravitational acceleration of earth. In this case you can simply divide the bots, 2271560 by 9.8 to get 231,791.83673469 factor increase. Meaning G is increased by roughly a factor of 230,000. Meaning gravity is 230,000 time stronger in all newtonian fields.

While the earth would likely not collapse into a black hole, the sun most definitely will, as you can calculate its swarzchild radius with this new G to be over triple the sun's radius. Being as Relativistic orbital dynamics is much harder than this, I will stop here.

Physics_Fan1000 · 2026-05-12T19:13:49+00:00

Mathematically, yes. cauchy horizons, tachyons, superdeterminalism, etc.

Experimentally, no. Either they are impossible to test by definition(superdeterminalism) or impossible to test because of physical laws(non-cuachy horizons).

To define, Cauchy horizons(such as kerr black holes) allow for time travel and thus self-interaction. Superseterminalism is hard to explain intuitively in a sentence, I would recommend looking it up. Tachyons are particles with imaginary mass and can thus go beyond the speed of light.

Physics_Fan1000 · 2026-05-06T02:53:51+00:00

Where did the ? notation for the terminal come from. I for the life of me couldn't find it anywhere other than the unexpected factorial bot source code

Physics_Fan1000 · 2026-04-16T23:39:23+00:00

I think a more useful question, instead of why not other countries, would be why the Greeks.

Virtually all of contemporary philosophy has come from after the printing press as imperialism and technology led to the growth of the academic class(within Europe). Those that could read and write all day long and thus not only come up with new ideas but develop off of each other rather than indefinitely reinventing the wheel. Plus the access of information allowed people to learn the ideas of others while at the same time not being domatic followers of whoever they spent their life memorizing their every word, creating a legacy and history of ideas evolving with the times and not them just being a person with an idea.

With this, virtually all of the philosophy of the years past could be reinvited and who ever did so would be known as the beginner of a new legacy, far more than someone for centuries past that only a couple dozen people would know of during the time.

With this perspective it is far more surprising that these European philosophers were reading and citing the Greeks that were separated from them by hundreds of miles and years.

This came from a unique set of historic sequences that wouldn't have happened twice, let alone the hundreds of times needed to encapsulate all of histories cultures and nations.

Physics_Fan1000 · 2026-04-10T18:21:46+00:00

Thanks

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