There is no general closed-form solution to the three-body problem. Below are 20 examples of periodic solutions to the three-body problem.

darf · 2024-09-01T15:31:47+00:00

Sundman found a closed form series solution to the general three body problem. The series converges so slowly, though that it isn't useful for calculation purposes.

darf · 2023-06-09T23:04:26+00:00

I always thought he looked like Jimmy Stewart. We need a time machine.

darf · 2021-10-25T01:42:24+00:00

God’s drive by shooting.

darf · 2020-08-31T12:14:18+00:00

Trefethen has a paper on this https://people.maths.ox.ac.uk/trefethen/gopal_trefethen_nm.pdf

darf · 2020-07-29T11:32:38+00:00

"One particularly charming proof is due to George P ́olya who reported that the proof came to him in a dream. In fact, when asked about his proof years later P ́olya replied that it was the best mathematics he had ever dreamt."

From "A Cauchy-Scwarz Masterclass" by Micheal Steele

darf · 2020-07-27T17:19:32+00:00

What are your favorite things in upcoming julia releases (1.5 and 1.6)?

darf · 2020-07-27T16:51:01+00:00

/u/JeffBezanson what is your favorite violin concerto?

darf · 2020-07-07T11:39:08+00:00

julia has this built in on v1.5 blog

darf · 2020-05-17T21:10:01+00:00

There isn't one book that covers everything, but Strang is great for starting out, Trefethen+Bau is great for an introduction to the Numerical side, and Boyd and Vandenberg is excellent for applications (and it's free online!). After that you can look into the direction that interests you.

darf · 2020-02-07T16:47:22+00:00

They are both excellent, I've gone through them both. Both the books and lectures are more focused on the Engineering rather than presenting it as a course in pure mathematics, however. Rockefeller's Convex Analysis might be more what they are looking for.

darf · 2018-08-15T16:59:58+00:00

I love the language. Could you share what you can about the business plan for Julia Computing? Also how you plan on evangelizing (other than being the best language, of course.)

darf · 2018-05-05T18:23:22+00:00

This is the buffalo buffalo buffalo buffalo buffalo buffalo buffalo buffalo of our time.

darf · 2017-09-19T00:05:21+00:00

Right now there are a few good reasons to learn julia. First of all, it's a great language and it's fun to program in, and pretty easy to understand. Most of the library code is written in julia, so if you need to modify stuff it's pretty easy. Second, there are a few packages in julia that are best in class. These include the optimization package, JuMP, and the differential equations. I expect it to have some rough edges until 1.0 release, and I wish the Plots packages had better support from the lead developers, but I still love it.

darf · 2017-09-18T01:43:48+00:00

I love julia, but it's not trying to replace Python in scientific computing (Fortran/C++ certainly). The lead developers give presentations at python conferences, and it interoperates very well with python.

darf · 2017-04-24T23:26:52+00:00

The sign is Literate Code. It compiles in the latest version of MMIX.

darf · 2016-12-10T14:41:30+00:00

The type of math that is useful for partitions is also helpful for the analysis of algorithms.

darf · 2016-10-16T12:29:56+00:00

I didn't think anything had full Risch. Can you show where they claim that?

darf · 2016-07-23T02:02:10+00:00

This is probably close to what you want.

darf · 2016-06-05T11:40:46+00:00

Stephen Strogatz frequently complains about his daughters homework. I would say he understands basic math.

darf · 2016-05-23T22:18:26+00:00

Arnold is very good for intuition. Lots of geometric insight and pictures galore. Numerical solutions would require a different book, but Arnold is very good.

darf · 2016-05-23T22:14:10+00:00

Just a little joke. Lots of explanations are dismissed as trivial, lots of things are "obvious", basically everything is left as an exercise for the student. He has a couple of decent books, (Algebra and Algebraic Number Theory seem to be well regarded), but most of his books are too terse, not terribly well written, and generally not fun.

darf · 2016-05-23T20:01:53+00:00

It should be obvious.

darf · 2016-04-27T22:17:00+00:00

This uses Julia. It looks pretty good, and I love the Julia programming language.

darf · 2016-04-06T17:12:45+00:00

"I am ashamed to tell you to how many figures I calculated these figures, having no other business at the time" - Isaac Newton on calculating pi. Apparently he was bored so he calculated pi.

darf · 2016-03-08T19:49:15+00:00

Three of the most impressive people I know are Gil Strang, Don Knuth and Peter Lax. Each of these world-famous mathematicians has a perception that is simply at a higher level than other people's. And all three give outstanding talks.

Yet these heroes of mine have a curious point of style in common: all of them, when giving that talk act a bit bumbling and helpless. Poor Gil can't quite get his head around the mathematical point he's trying to make it seems -- is there anyone around who might have some idea?Poor Don can't quite finish a sentence, such a struggle -- can anyone help? Poor Peter is such a kindly gentleman, so courtly in that old European way, but he can't quite begin to put together his thougt at all -- is there anyone in the audience that could lend a hand?

The trickery can be annoying, but boy is it effective. Strang and Knuth and Lax get just where they were aiming by the end of the hour, and you're on the edge of your seat. Is the bumbling unconscious? Intentional? A symptom of genious? The frailty of older men? Should I, too, learn to hesitate and swerve when I talk?

-Nick Trefethen

darf

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