Teen solves Newton’s 300-year-old riddle

[LargoWinch]

An Indian-born teenager has won a research award for solving a mathematical problem first posed by Sir Isaac Newton more than 300 years ago that has baffled mathematicians ever since.


The solution devised by Shouryya Ray, 16, makes it possible to calculate exactly the path of a projectile under gravity and subject to air resistance.


Shouryya, who lives in Dresden, eastern Germany, came up with the solutions to this and a second mathematical riddle while working on a school project.


He is being hailed as a genius in the German press, but attributes his achievement to “curiosity and schoolboy naivety.”


Continued here.

[Shakespear]

Re: Teen solves Newton’s 300-year-old riddle

Yes, amazing what the mind can do if pointed in the right direction.

(Reuters) - German solar power plants produced a world record 22 gigawatts of electricity per hour - equal to 20 nuclear power stations at full capacity - through the midday hours on Friday and Saturday, the head of a renewable energy think tank said.

http://uk.reuters.com/article/2012/0...84P0FI20120526
While the US wastes billions dropping bombs.

[lektrode]

Re: Teen solves Newton’s 300-year-old riddle

Yes, amazing what the mind can do if pointed in the right direction.



http://uk.reuters.com/article/2012/0...84P0FI20120526
While the US wastes billions dropping bombs.

can hardly wait for the discussion on this one = not sure if i want to cheer or cry (about the futileness of all that infrastructure and expense - for 4% ?.... sniff....


BARTENDER!!!

The German government decided to abandon nuclear power after the Fukushima nuclear disaster last year, closing eight plants immediately and shutting down the remaining nine by 2022.
They will be replaced by renewable energy sources such as wind, solar and bio-mass.
Norbert Allnoch, director of the Institute of the Renewable Energy Industry (IWR) in Muenster, said the 22 gigawatts of solar power per hour fed into the national grid on Saturday met nearly 50 percent of the nation's midday electricity needs.
"Never before anywhere has a country produced as much photovoltaic electricity," Allnoch told Reuters. "Germany came close to the 20 gigawatt (GW) mark a few times in recent weeks. But this was the first time we made it over."
The record-breaking amount of solar power shows one of the world's leading industrial nations was able to meet a third of its electricity needs on a work day, Friday, and nearly half on Saturday when factories and offices were closed.
Government-mandated support for renewables has helped Germany became a world leader in renewable energy and the country gets about 20 percent of its overall annual electricity from those sources.
Germany has nearly as much installed solar power generation capacity as the rest of the world combined and gets about four percent of its overall annual electricity needs from the sun alone.

alone?
what they get from their nukes?
and their gonna close em all? tween them and japan? IT WONT BE PEAK CHEAP OIL THAT CAUSES THE NEXT ENERGY-PRICE-INDUCED 'slowdown'

[Chomsky]

Re: Teen solves Newton’s 300-year-old riddle

http://math.stackexchange.com/questi...e-is-the-paper

[c1ue]

Re: Teen solves Newton’s 300-year-old riddle

Yes, amazing what the mind can do if pointed in the right direction.

(Reuters) - German solar power plants produced a world record 22 gigawatts of electricity per hour - equal to 20 nuclear power stations at full capacity - through the midday hours on Friday and Saturday, the head of a renewable energy think tank said.

http://uk.reuters.com/article/2012/0...84P0FI20120526
While the US wastes billions dropping bombs.

Yes, and they only had to spend how many billions to do so? $130 billion.

And the result? The numbers I see are far lower than what lektrode posted:

http://www.project-syndicate.org/com...shine-daydream

One of the world’s biggest green-energy public-policy experiments is coming to a bitter end in Germany, with important lessons for policymakers elsewhere.

Illustration by John Overmyer

Germany once prided itself on being the “photovoltaic world champion”, doling out generous subsidies – totaling more than $130 billion, according to research from Germany’s Ruhr University – to citizens to invest in solar energy. But now the German government is vowing to cut the subsidies sooner than planned, and to phase out support over the next five years. What went wrong?

There is a fundamental problem with subsidizing inefficient green technology: it is affordable only if it is done in tiny, tokenistic amounts. Using the government’s generous subsidies, Germans installed 7.5 gigawatts of photovoltaic (PV) capacity last year, more than double what the government had deemed “acceptable.” It is estimated that this increase alone will lead to a $260 hike in the average consumer’s annual power bill.

According to Der Spiegel, even members of Chancellor Angela Merkel’s staff are now describing the policy as a massive money pit. Philipp Rösler, Germany’s minister of economics and technology, has called the spiraling solar subsidies a “threat to the economy.”

Germany’s enthusiasm for solar power is understandable. We could satisfy all of the world’s energy needs for an entire year if we could capture just one hour of the sun’s energy. Even with the inefficiency of current PV technology, we could meet the entire globe’s energy demand with solar panels by covering 250,000 square kilometers (155,342 square miles), about 2.6% of the Sahara Desert.

Unfortunately, Germany – like most of the world – is not as sunny as the Sahara. And, while sunlight is free, panels and installation are not. Solar power is at least four times more costly than energy produced by fossil fuels. It also has the distinct disadvantage of not working at night, when much electricity is consumed.

In the words of the German Association of Physicists, “solar energy cannot replace any additional power plants.” On short, overcast winter days, Germany’s 1.1 million solar-power systems can generate no electricity at all. The country is then forced to import considerable amounts of electricity from nuclear power plants in France and the Czech Republic. When the sun failed to shine last winter, one emergency back-up plan powered up an Austrian oil-fired plant to fill the supply gap.

Indeed, despite the massive investment, solar power accounts for only about 0.3% of Germany’s total energy. This is one of the key reasons why Germans now pay the second-highest price for electricity in the developed world (exceeded only by Denmark, which aims to be the “world wind-energy champion”). Germans pay three times more than their American counterparts.

Moreover, this sizeable investment does remarkably little to counter global warming. Even with unrealistically generous assumptions, the unimpressive net effect is that solar power reduces Germany’s CO2 emissions by roughly eight million metric tons – or about 1% – for the next 20 years. When the effects are calculated in a standard climate model, the result is a reduction in average temperature of 0.00005oC (one twenty-thousandth of a degree Celsius, or one ten-thousandth of a degree Fahrenheit). To put it another way: by the end of the century, Germany’s $130 billion solar panel subsidies will have postponed temperature increases by 23 hours.

Using solar, Germany is paying about $1,000 per ton of CO2 reduced. The current CO2 price in Europe is $8. Germany could have cut 131 times as much CO2 for the same price. Instead, the Germans are wasting more than 99 cents of every euro that they plow into solar panels.

It gets worse: because Germany is part of the European Union Emissions Trading System, the actual effect of extra solar panels in Germany leads to no CO2 reductions, because total emissions are already capped. Instead, the Germans simply allow other parts of the EU to emit more CO2. Germany’s solar panels have only made it cheaper for Portugal or Greece to use coal.

Defenders of Germany’s solar subsidies also claim that they have helped to create “green jobs”. But each job created by green-energy policies costs an average of $175,000 – considerably more than job creation elsewhere in the economy, such as infrastructure or health care. And many “green jobs” are being exported to China, meaning that Europeans subsidize Chinese jobs, with no CO2 reductions.

Germany’s experiment with subsidizing inefficient solar technology has failed. What governments should do instead is to focus first on increasing research and development to make green-energy technology cheaper and more competitive. Production should be ramped up later.

In the meantime, Germans have paid about $130 billion for a climate-change policy that has no impact on global warming. They have subsidized Chinese jobs and other European countries’ reliance on dirty energy sources. And they have needlessly burdened their economy. As even many German officials would probably attest, governments elsewhere cannot afford to repeat the same mistake.

[lektrode]

Re: Teen solves Newton’s 300-year-old riddle

http://www.project-syndicate.org/com...shine-daydream

Using solar, Germany is paying about $1,000 per ton of CO2 reduced. The current CO2 price in Europe is $8. Germany could have cut 131 times as much CO2 for the same price. Instead, the Germans are wasting more than 99 cents of every euro that they plow into solar panels.

It gets worse: because Germany is part of the European Union Emissions Trading System, the actual effect of extra solar panels in Germany leads to no CO2 reductions, because total emissions are already capped. Instead, the Germans simply allow other parts of the EU to emit more CO2. Germany’s solar panels have only made it cheaper for Portugal or Greece to use coal.

Defenders of Germany’s solar subsidies also claim that they have helped to create “green jobs”. But each job created by green-energy policies costs an average of $175,000

and i double-dead-dog-DARE ANYbody to FIND ME A SOLAR JOB THAT PAYS even 1/2 that (hell, a third of it)
the diff is siphoned-off by the buracracy and the political class in crony-capitalist backroom subsidy deals!

the most 'inconvenient truth' ?

al gore prolly aint makin a dime off any of it...
poor al, i almost feel sorry for him, it'll get pricey keepin his 20000sqft mansion cool this summer...

[cbr]

Re: Teen solves Newton’s 300-year-old riddle

The solution devised by Shouryya Ray, 16, makes it possible to calculate exactly the path of a projectile under gravity and subject to air resistance.

does no one find this statement slightly odd, in that we can land a projectile under gravity and subject to air resistance to within millimeters from miles away, and obviously have FULLY understood these physics since at least the 19th century? I would actually wager that we have fully understood these physics since the near the dawn of mathematics, frankly since the physics of hitting things with projectiles was the REASON mathematics were created in the first place....

[leegs]

Re: Teen solves Newton’s 300-year-old riddle

does no one find this statement slightly odd, in that we can land a projectile under gravity and subject to air resistance to within millimeters from miles away, and obviously have FULLY understood these physics since at least the 19th century? I would actually wager that we have fully understood these physics since the near the dawn of mathematics, frankly since the physics of hitting things with projectiles was the REASON mathematics were created in the first place....

I thought exactly the same thing, since I have software on my iphone that will zero my 308 in with pretty good accuracy.

[lakedaemonian]

Re: Teen solves Newton’s 300-year-old riddle

I thought exactly the same thing, since I have software on my iphone that will zero my 308 in with pretty good accuracy.

Same.....I use old school ballistic tables, and adjust for wind, angle, altitude.

I know there are much larger systems with automated range finding, and a bunch of sensors like barometric pressure/wind/etc that allow you to hit rabbits from several kilometers away

It would be interesting to know the difference between his maths and the maths used to slave a ballistic weapon system on target.

I'm guessing what was used up until now(the math behind the ballistic charts and computer slaving systems) were just "good enough for government work"?

[LargoWinch]

Re: Teen solves Newton’s 300-year-old riddle

does no one find this statement slightly odd, in that we can land a projectile under gravity and subject to air resistance to within millimeters from miles away, and obviously have FULLY understood these physics since at least the 19th century? I would actually wager that we have fully understood these physics since the near the dawn of mathematics, frankly since the physics of hitting things with projectiles was the REASON mathematics were created in the first place....

Same.....I use old school ballistic tables, and adjust for wind, angle, altitude.

I know there are much larger systems with automated range finding, and a bunch of sensors like barometric pressure/wind/etc that allow you to hit rabbits from several kilometers away

http://math.stackexchange.com/questi...e-is-the-paper

Guys, unfortunately it is not that simple and it appears that Ray's solution has now been confirmed (knock yourselves out! - I have dropped the towel at line 1):

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.



Also, someone used Maple [a Waterloo Canada engineered mathematical software] to verify Shouryya Ray's solution. It checks out! Here's the maple program.

[dropthatcash]

Re: Teen solves Newton’s 300-year-old riddle

Yes, amazing what the mind can do if pointed in the right direction.



http://uk.reuters.com/article/2012/0...84P0FI20120526
While the US wastes billions dropping bombs.

A little cold water on that 180 billion dollar euphoria;
"...despite the massive investment, solar power accounts for only about 0.3 percent of Germany’s total energy. This is one of the key reasons why Germans now pay the second-highest price for electricity in the developed world (exceeded only by Denmark, which aims to be the “world wind-energy champion”). Germans pay three times more than their American counterparts.>

http://joshuapundit.blogspot.com/201...wer-after.html

[Jam]

Re: Teen solves Newton’s 300-year-old riddle

Here is a solution--reverse-engineered by someone way smarter than me
http://www.reddit.com/r/math/comment...lating/c4szzld

Consider a projectile moving in gravity with quadratic air resistance. The governing equations are
u' = -a * u * sqrt( u² + v² )
v' = -a * v * sqrt( u² + v² ) - g
where a is the coefficient of air resistance defined by |F| = ma|v|² .
Cross-multiply and rearrange to find
a * sqrt( u² + v² ) * (uv'-vu') = gu'
Substitute v = su and separate variables:
a * sqrt( 1 + s² ) * s' = g*u'/u³
Integrate both sides to get the answer:
g/u² + a(v * sqrt( u² + v² )/u² + arcsinh|v/u|) = const

(Note: u is the horizontal component of the velocity, and v is the vertical component of the velocity.)

[thriftyandboringinohio]

Re: Teen solves Newton’s 300-year-old riddle

Here is a solution--reverse-engineered by someone way smarter than me
http://www.reddit.com/r/math/comment...lating/c4szzld

(Note: u is the horizontal component of the velocity, and v is the vertical component of the velocity.)

Just at a glance, that solution does not look correct to me.

I don't expect "m" in the expression for drag forces in the third line.
I presume "m" is mass, which plays no role in classic aerodynamic drag. That force depends only in the shape of the body, the velocity of flow, and the properties of the fluid (i.e. air).

The whole thing looks off the mark (though I admit to only spending 90 seconds looking at it, and its been many years since I've worked any problems in fluid dynamics or Newtonian motion).
.
.
.

[Jam]

Re: Teen solves Newton’s 300-year-old riddle

Well, it actually depends on how you define your a (may not be necessarily the conventional definition). Note that (s)he uses |F| = ma|v|² to define a. And it's consistent with the definition Ray used https://www.jugend-forscht.de/images...7_download.jpg. I checked the rest of the math, and it seems to work out--except for the absolute value under the arcsinh that I couldn't recover.

[cbr]

Re: Teen solves Newton’s 300-year-old riddle

I'm not going to get into the equations, I have not done that since college. But riddle me this: what is new here? Are we concluding that this is a mathematical expression of known empirical results that has never been quantified in a short equation in this manner? I am going on a limb and saying this finding will not revolutionize applied ballistics in any way. Or please correct me if I am wrong.