Partial Differential Equations!

[New Genoa]

Why do you guys love maths so much?

It's just an abstract.

a million plus a million equals two million, yeah, great, what next?

It's an abstract with a great number of physically useful applications. Also, arithmetic =/= all of math.

and even the ones that aren't physically useful now somehow end up getting used in the physics of the future.

[United Technocrats]

You know, you could model a stream of urine using a few partial differential equations.

That would really be useful! I cannot understand how I managed to get so far without familiarizing myself with that model!

Navier-Stokes and the equation of continuity for mass come to mind.

I'm sure Navier and Stokes would be proud of their names appearing in such an important application of hydrodynamics!

Just joking!

[UnhealthyTruthseeker]

and even the ones that aren't physically useful now somehow end up getting used in the physics of the future.

The theories of groups and rings is one such field (no pun intended) which has a great many number of applications. This same field was thought to be purely mathematician's math with no real use whatsoever not so long ago.

[United Technocrats]

UhTruthseeker,

Reading through this thread I suddenly remembered an interesting problem that I heard about loooong ago. I can't remember it's exact formulation, let alone the solution, but perhaps you've heard of it. It goes something like this: there are two points in space, A and B. There are two bodies, say Alpha and Beta (which can be modeled as points). Alpha is travelling from A to B, on an arbitrary trajectory. Beta is following Alpha at a constant speed in a way so that its velocity vector always points exactly at Alpha. The task is to formally prove that, no matter what the trajectory of Alpha is, and no matter how it changes its velocity, the trajectory of Beta is shorter or equal than that of Alpha. Have You heard of such a problem? I hope I remembered it correctly ... I'm not sure if Beta starts out at the same time as Alpha, but let's suppose it does.

[UnhealthyTruthseeker]

UhTruthseeker,

Reading through this thread I suddenly remembered an interesting problem that I heard about loooong ago. I can't remember it's exact formulation, let alone the solution, but perhaps you've heard of it. It goes something like this: there are two points in space, A and B. There are two bodies, say Alpha and Beta (which can be modeled as points). Alpha is travelling from A to B, on an arbitrary trajectory. Beta is following Alpha at a constant speed in a way so that its velocity vector always points exactly at Alpha. The task is to formally prove that, no matter what the trajectory of Alpha is, and no matter how it changes its velocity, the trajectory of Beta is shorter or equal than that of Alpha. Have You heard of such a problem? I hope I remembered it correctly ... I'm not sure if Beta starts out at the same time as Alpha, but let's suppose it does.

It sounds similar to the idea that you can never have a higher average speed than the guy in front of you on the highway. In fact, it really is the same thing but formulated in different terminology.

[United Technocrats]

UhTruthseeker,

Reading through this thread I suddenly remembered an interesting problem that I heard about loooong ago. I can't remember it's exact formulation, let alone the solution, but perhaps you've heard of it. It goes something like this: there are two points in space, A and B. There are two bodies, say Alpha and Beta (which can be modeled as points). Alpha is travelling from A to B, on an arbitrary trajectory. Beta is following Alpha at a constant speed in a way so that its velocity vector always points exactly at Alpha. The task is to formally prove that, no matter what the trajectory of Alpha is, and no matter how it changes its velocity, the trajectory of Beta is shorter or equal than that of Alpha. Have You heard of such a problem? I hope I remembered it correctly ... I'm not sure if Beta starts out at the same time as Alpha, but let's suppose it does.

It sounds similar to the idea that you can never have a higher average speed than the guy in front of you on the highway. In fact, it really is the same thing but formulated in different terminology.

I don't think so. You see, on a highway, both of you share the same trajectory (the highway). However, in this problem, the two bodies almost always have different trajectories. Take a better look, it's not trivial. Although, as far as I can remember, the solution starts out by examining the trivial case (straight A-B trajectory).

[UnhealthyTruthseeker]

UhTruthseeker,

Reading through this thread I suddenly remembered an interesting problem that I heard about loooong ago. I can't remember it's exact formulation, let alone the solution, but perhaps you've heard of it. It goes something like this: there are two points in space, A and B. There are two bodies, say Alpha and Beta (which can be modeled as points). Alpha is travelling from A to B, on an arbitrary trajectory. Beta is following Alpha at a constant speed in a way so that its velocity vector always points exactly at Alpha. The task is to formally prove that, no matter what the trajectory of Alpha is, and no matter how it changes its velocity, the trajectory of Beta is shorter or equal than that of Alpha. Have You heard of such a problem? I hope I remembered it correctly ... I'm not sure if Beta starts out at the same time as Alpha, but let's suppose it does.

Now that I think about it, there has to be more to the problem than this, because, as it is written now, I can think of counterexamples. Say A and B are right next to each other and alpha runs straight from A to B. Next suppose that beta starts really far away from A. There need to be more restrictions that just the ones you've thus far given me.`

[United Technocrats]

UhTruthseeker,

Reading through this thread I suddenly remembered an interesting problem that I heard about loooong ago. I can't remember it's exact formulation, let alone the solution, but perhaps you've heard of it. It goes something like this: there are two points in space, A and B. There are two bodies, say Alpha and Beta (which can be modeled as points). Alpha is travelling from A to B, on an arbitrary trajectory. Beta is following Alpha at a constant speed in a way so that its velocity vector always points exactly at Alpha. The task is to formally prove that, no matter what the trajectory of Alpha is, and no matter how it changes its velocity, the trajectory of Beta is shorter or equal than that of Alpha. Have You heard of such a problem? I hope I remembered it correctly ... I'm not sure if Beta starts out at the same time as Alpha, but let's suppose it does.

Now that I think about it, there has to be more to the problem than this, because, as it is written now, I can think of counterexamples. Say A and B are right next to each other and alpha runs straight from A to B. Next suppose that beta starts really far away from A. There need to be more restrictions that just the ones you've thus far given me.`

Yes, I'm sorry. I forgot to mention both Alpha and Beta travel from A to B. Also, technically, if Beta starts moving at the same time as Alpha, its velocity at t=0 cannot be anything other than zero; so, should Beta catch up with Alpha at any given moment, you can define its velocity vector to be identical to Alpha's in any such moment. Anyway, think of it as a real life problem that you need to model. It's really simple to simulate, though, and somewhat intuitive, but a real pain to formally prove...

[UnhealthyTruthseeker]

Navier-Stokes equation:

rho*(dv/dt + (v*del)v) = grad(P) + div(T) + F

[Tunizcha]

I got 5th place in the SF Science Fair. They took my model.

[UnhealthyTruthseeker]

I got 5th place in the SF Science Fair. They took my model.

Our schools never had a real science fair to speak of. What did you make a model of?

Also, as an aside, the coolest science fair project ever has to be the one Michio Kaku made in high school. In high school, he made A FUCKING 2.3 MEGAVOLT PARTICLE ACCELERATOR IN HIS PARENTS' GARAGE!

[Tunizcha]

I got 5th place in the SF Science Fair. They took my model.

Our schools never had a real science fair to speak of. What did you make a model of?

Also, as an aside, the coolest science fair project ever has to be the one Michio Kaku made in high school. In high school, he made A FUCKING 2.3 MEGAVOLT PARTICLE ACCELERATOR IN HIS PARENTS' GARAGE!

I know, right? Insane. He had his parents help him lay out the piping on his highschool football field and he used the accelerator to try and accelerate atoms. His original tests with the Particle Accelerator blacked out his house and the rest of the block.

I made a model of the "foam" described by quantum theory in vacuums required for Planck energy, along with parallel universe "bubbles" connected by wormholes.
It took me a couple weeks to build, and I only got $50 as the 5th place prize.
The judges are incredibly dense. It took me 20 minutes to explain to them what it was. And 1st place was a primitive superconductor-esque machine.