[Tanada]

DRESDEN, Germany – A German 16-year-old has become the first person to solve a mathematical problem posed by Sir Isaac Newton more than 300 years ago.

Shouryya Ray worked out how to calculate exactly the path of a projectile under gravity and subject to air resistance, The (London) Sunday Times reported.

http://www.foxnews.com/world/2012/05/27 ... z1wA5AL4OQ

Though the article is written as a human interest story by the reporter the data is there. This young man has solved a problem that has only had approximations as answers for 300 years. Being able to calculate differential air resistance will impact designs for anything moving through the air from ballistic projectiles down to automobiles and delivery trucks. Compared to how this is done now with empirical studies in wind tunnels/water tunnels for dynamic behavior analysis this will have a huge impact.

[Beery1]

Well done, kid!

And he's in Germany, where they tend to do schooling right, and not in the US or UK, where his genius might have been stifled by incompetent teachers or school officials.

[EnergyUnlimited]

Kid solved problem, but only corporations will see any money out of that.

[EnergyUnlimited]

Well done, kid!

And he's in Germany, where they tend to do schooling right, and not in the US or UK, where his genius might have been stifled by incompetent teachers or school officials.

For very bright children school is irrelevant
They will still get there.

[dissident]

DRESDEN, Germany – A German 16-year-old has become the first person to solve a mathematical problem posed by Sir Isaac Newton more than 300 years ago.

Shouryya Ray worked out how to calculate exactly the path of a projectile under gravity and subject to air resistance, The (London) Sunday Times reported.

http://www.foxnews.com/world/2012/05/27 ... z1wA5AL4OQ

Though the article is written as a human interest story by the reporter the data is there. This young man has solved a problem that has only had approximations as answers for 300 years. Being able to calculate differential air resistance will impact designs for anything moving through the air from ballistic projectiles down to automobiles and delivery trucks. Compared to how this is done now with empirical studies in wind tunnels/water tunnels for dynamic behavior analysis this will have a huge impact.

Reminds me of the KdV equation where the nonlinear term is balanced by the diffusive term in such a way as to get an exact mathematical solution. Nonlinear systems cannot in general be solved explicitly and require numerics. The Fox News piece is lacking in any serious detail so I am guessing that he is solving the nonlinear equation created when you add the velocity squared air drag term. It is not accurate to say that all we have are "approximations" which can be interpreted to mean that we have no precision. Numerical solutions can be made as precise as you want. Analytical solutions are rare in reality since the interesting problems are nonlinear and numerics is all that we will ever have unless there are exceptional circumstances like in the KdV and apparently this case.

As for hyping up the kid's analytical solution. Don't get carried away. He has included the v^2 "generic" projectile air drag term but obviously has not included any ambient flow. He would not have a solution if he had to deal with wind and turbulence, which is obeying the Navier-Stokes equations, a set of partial differential equations that does not have analytical solutions aside from some idealized cases. The claim that this analytical solution will improve projectile design is rather silly. Newton's problem hardly pertained to projectile shape and its interaction with a fluid medium but to the motion of some mass, in all likelihood spherical like a cannon ball, through the air. You have to at the very least to do asymptotic perturbation expansions to deal with projectile design (think of the applied math used for wing design) and ultimately it is back to numerics.

[ohanian]

An ode to Ordinary Differential Equations....

This is one of my favourite book

http://www.amazon.com/Introduction-Ordinary-Differential-Equations-Mathematica/dp/0387944818

If you can understand the below, please let me know

http://www.reddit.com/r/worldnews/comments/u7551/teen_solves_newtons_300yearold_riddle_an/c4sxd91

[Cog]

Its obvious from dissident's statement that he could have solved this simple 300 year old calculus problem in an afternoon over a few beers. The German kid should be condemned as unworthy to walk in dissident's large intellectual shadow.

[AgentR11]

For very bright children school is irrelevant
They will still get there.

Not completely irrelevant, you get to play with lab gear that someone else payed for.

[EnergyUnlimited]

For very bright children school is irrelevant
They will still get there.

Not completely irrelevant, you get to play with lab gear that someone else payed for.

But lab gear worth more than few dollars only begins in university and said kid is only 16.

There is nothing in secondary school lab what science dedicated kid with parents not relying on food stamps cannot do on its own.

[Cog]

Its a pure mathematical problem. You don't need lab equipment. Just a pencil and a piece of paper. You think Newton had a computer?

[AgentR11]

I wasn't saying that the lab gear was necessary for the math, I was saying school isn't a complete waste for the very bright, cause they let you play with the expensive toys mostly unsupervised. "Chem III" in high school for me was "here's the lab room, go do something.... quietly." Disagree with EE, high schools often have some pretty good gear, but its spotty, random pieces, so its mostly a think of something fun to do with the toys you have.

[MD]

Its obvious from dissident's statement that he could have solved this simple 300 year old calculus problem in an afternoon over a few beers. The German kid should be condemned as unworthy to walk in dissident's large intellectual shadow.

It's obvious from cog's statement that he could find no no error with dissidents expression of fact.
Additionally his response smells of sour grapes, which makes me suspect he was unable to parse it at all.

[PrestonSturges]

DRESDEN, Germany – A German 16-year-old has become the first person to solve a mathematical problem posed by Sir Isaac Newton more than 300 years ago.

In a perfect world, this would make women want to have sex with him.

[AgentR11]

LOL. math geeks getting girls. Outrageous.
Girls say they want smart, sensitive, funny.

What they want are biceps.

[dissident]

Its obvious from dissident's statement that he could have solved this simple 300 year old calculus problem in an afternoon over a few beers. The German kid should be condemned as unworthy to walk in dissident's large intellectual shadow.

This is media hype and not mathematics. Clearly you can't tell the difference.

Nowhere in my statement was there any knocking of the 16 year old's achievement. I compared it to the solution of the Korteweg-de Vries equation, which is a compliment. He should get his work published. But you won't be flying to the stars with his solution.

[PrestonSturges]

LOL. math geeks getting girls. Outrageous.
Girls say they want smart, sensitive, funny.

What they want are biceps.

I like them big and stupid.
I like them big and real dumb.
-Julie Brown

[dinopello]

The founder of the first company I worked for made his mark by developing a machine learning algorithm that was applied to estimating real-time solutions to boundary-value problems in ballistic flight applications. I think there are a lot of factors that will still require the numerical approach for real-world applications.

[SeaGypsy]

Without seeing the data maybe hard to say, but likely similar to fluid dynamic equations also, meaning new solutions in all kinds of hull design. If this kid's formula really works, it could make designing an aircraft, a ship, a projectile, child's play. Just put in the approximations/ dimensions, variable mass etc. & out pops your ideal configuration. For this reason, plus the massive number of people working in industrial design who are likely to become redundant, it would not surprise me if the formula disappears into a vault somewhere.

[MD]

Its obvious from dissident's statement that he could have solved this simple 300 year old calculus problem in an afternoon over a few beers. The German kid should be condemned as unworthy to walk in dissident's large intellectual shadow.

This is media hype and not mathematics. Clearly you can't tell the difference.

Nowhere in my statement was there any knocking of the 16 year old's achievement. I compared it to the solution of the Korteweg-de Vries equation, which is a compliment. He should get his work published. But you won't be flying to the stars with his solution.

He simply managed to define a relationship with additional precision. Math geeks are apparently the only ones that truly appreciate the accomplishment.

It's always been that way.

[ohanian]

Without seeing the data maybe hard to say, but likely similar to fluid dynamic equations also, meaning new solutions in all kinds of hull design. If this kid's formula really works, it could make designing an aircraft, a ship, a projectile, child's play. Just put in the approximations/ dimensions, variable mass etc. & out pops your ideal configuration. For this reason, plus the massive number of people working in industrial design who are likely to become redundant, it would not surprise me if the formula disappears into a vault somewhere.

It's not that useful..

First there is already a numerical solution, the kid only found the analytical solution. Two the drag is proportional to the velocity square. But in the real world, the drag is proportional to "a v + b v^2 + c v^3 + d v^4". So as you can see it's only an approximation to the real world..

* * *


The problem he solved is as follows:
Let (x(t),y(t)) be the position of a particle at time t. Let g be the acceleration due to gravity and c the constant of friction. Solve the differential equation:
(x''(t)2 + (y''(t)+g)2 )1/2 = c*(x'(t)2 + y'(t)2 )
subject to the constraint that (x''(t),y''(t)+g) is always opposite in direction to (x'(t),y'(t)).
Finding the general solution to this differential equation will find the general solution for the path of a particle which has drag proportional to the square of the velocity (and opposite in direction). Here's an explanation how this differential equation encodes the motion of such a particle:
The square of the velocity is:
x'(t)2 + y'(t)2
The total acceleraton is:
( x''(t)2 + y''(t)2 )1/2
The acceleration due to gravity is g in the negative y direction.
Thus the drag (acceleration due only to friction) is:
( x''(t)2 + (y''(t)+g)2 )1/2
Thus path of such a particle satisfies the differential equation:
( x''(t)2 + (y''(t)+g)2 )1/2 = c*(x'(t)2 + y'(t)2 )
Of course, we also require the direction of the drag (x''(t),y''(t)+g) to be opposite to the direction of the velocity (x'(t),y'(t)). Once we find the intial position and velocity of the particle, uniqueness theorems tell us its path is uniquely determined.