The Value Of Pi
Humanoido
Posts: 5,770
The Value of Pi
The value of calculating pi is important for several reasons, including a benchmark for multi-core systems.
Someone beat me to it and calculated the value of pi to one trillion digits after the decimal point and posted the results in hundreds and hundreds of 57Mb files here. It was a high school project.
PI=3.14159265358979323846264338327950288419716939937510.....
I have not checked the accuracy. There are numerous methods to calculate pi and some are more accurate than others.
The site is really fantastic, setting the 5-trillion digit world record here.
You can download the program (y-cruncher - A Multi-Threaded Pi-Program) to run on PC or LINUX here.
The value of calculating pi is important for several reasons, including a benchmark for multi-core systems.
Someone beat me to it and calculated the value of pi to one trillion digits after the decimal point and posted the results in hundreds and hundreds of 57Mb files here. It was a high school project.
PI=3.14159265358979323846264338327950288419716939937510.....
I have not checked the accuracy. There are numerous methods to calculate pi and some are more accurate than others.
The site is really fantastic, setting the 5-trillion digit world record here.
You can download the program (y-cruncher - A Multi-Threaded Pi-Program) to run on PC or LINUX here.
Comments
Here you can find Pi and a number of constants calculated to far reaching decimals. These also make good benchmark tests.
- ［Statistics]
- ［Statistics for decimal digits(1 trillion)](Jul.16.2010 update)
- ［Statistics for decimal digits(5 trillion)](Aug.12.2010 update)
The original site is here with some interesting links.Meanwhile I have something else to do - study the Propeller Manual and Hydra programs. And maybe wash my hair.
Right. It would be useless as a benchmark for single-core systems.
You should share more of your calculations with us. What sorts of calculations are you presently working on?
the decimal representation of pi truncated to 39 decimal places is sufficient to estimate the circumference of any circle that fits in the observable universe with precision comparable to the radius of a hydrogen atom.*Ref*
yes it is cool to be able to say I build a computer that can compute the first trillion digits of pi. But what could these computers have been doing instead?
I got my copy of make magazine yesterday. Wish I had the $8000 it costs to launch your own satellite. Would be cool to have my own satellite up in orbit doing something.
My neighbor began putting little basa wood sticks together as a hobby. To outside eyes it may have seemed senseless and utterly ridiculous. Now he flies a model airplane. He will spend days just to get the trim perfect. It's his greatest enjoyment. He has automated the craft with robots and written the computer programs to fly it autonomously. He has become a master at robotics and programming. More of his hobbies. It can take off and land on its own. He knows a lot about aeronautics and celestial navigation. As a result he took up flying and enlisted in related courses at the university. He volunteered his time for the Life Services Rescue unit aboard helicopters and saved many lives. Last year he moved for the astronaut training program. I don't know what others think, but me, I think those little sticks in life are very important. Maybe it's just a piece of pie today, but you never know where it will lead to tomorrow.
http://scienceray.com/mathematics/the-search-for-pi-the-work-of-centuries/
There isn't a physical use for more than 40 digits of PI. In math, who knows? One could say there's no physical use for tiny little slices of numerical analysis being taken beyond some similar threshold, but take them to infinity, solve the resulting equation, and behold! You have Calculus, which reveals whole new ways to manipulate numbers -- and those seem to describe the real world too, with much greater utility than anyone might intuitively expect.
In the same way knowing pi is usefull. Knowing more then 40 digits isn't.
mctrivia wrote: The dice are not useless
If this were inline skating I would say you just did a 180. I think the dice are extremely useful, which is my original point, especially the ones that you spend 10 hours on designing, because, well, wow, look at those, they have more interesting and intricate shapes which are much more beautiful and aesthetically pleasing, mathematical in nature, puzzling, modern and artistically useful.
If you made these on a larger scale they would display well at art galleries and probably fetch thousands of dollars to adorn elitist futuristic homes. Even some murals would be totally fascinating especially in 3D. I'd say if you wear glasses, they must be on backwards to see everything in such a negative dim light, when in reality you're looking at the bright positive gems of the universe.
When you find such interesting things in this world, displaying the creative talent that you have with dice and capabilities to understand the deeper meaning of Pi, you just have to envision not only the positive but the usefulness as well. Look how you turned numbers into great works of admiration and value. The world is big. There's plenty of space for both. I also see something of great beauty and usefulness in Pi.
Proof that Pi is irrational, From Wikipedia
Although the mathematical constant known as π (pi) has been studied since ancient times, and so has the concept of irrational number, it was not until the 18th century that Johann Heinrich Lambert proved that π is irrational. In the 20th century, proofs were found that require no prerequisite knowledge beyond integral calculus. One of those, due to Ivan Niven, is widely known. A somewhat earlier similar proof is by Mary Cartwright.[1]
Pi is Irrational, Projects by Students for Students
For many centuries prior to the actual proof, mathematicians had thought that pi was an irrational number. The first attempt at a proof was by Johaan Heinrich Lambert in 1761. Through a complex method he proved that if x is rational, tan(x) must be irrational. It follows that if tan(x) is rational, x must be irrational. Since tan(pi/4)=1, pi/4 must be irrational; therefore, pi must be irrational.
Why is Pi irrational, from Ask
Pi can't be expressed as a fraction (a ratio of two integers), which makes it irrational. Pi (π) is an irrational number; it's trancendent. The mathematical proof that pi is irrational can be viewed by using the link to the Wikipedia article on exactly this topic. The challenge is that to understand the proof, one needs some familiarity with integral calculus. Short of that, one would probably have to just accept the fact that pi is transcendent and that it has been proved. (Pi was suspected to be irrational from ancient times, but it was actually proved to be in the 1700's.)
I like the way you describe my dice. I just want to point out the following:
mctrivia wrote: My designing dice is useless
mctrivia wrote: The dice are not useless
these are not opposing statements. one is talking about the act of creating the other is talking about the actual physical object(even if most of them are really just 50,000-500,000 triangles stored on a computer. They definitely have a lot to do with pi since the formulas used to define the circles is
d=2*sqrt(V/(n*PI)) where n is the side number and V is a constant chosen to make sides 2 and 3 possible. Though I usually chose a value of V that is a multiple of PI to simplify the formula.
"Despite much analytical work, and supercomputer calculations that have determined over 1 trillion digits of the decimal representation of π, no simple base-10 pattern in the digits has ever been found."
... could it be we've been searching all this time for a 'pi pattern' to emerge in the wrong base numbering system. :-) ... how daft we must be.
355/133 = 2.669172932330827
355/113 = 3.141592920353982
Here are some algorithms for Pi approximations at the Wolfram Mathworld site. Some are quite involved to remember.
Two other simple approximations are 3 and 22/7.
Or remember more digits for more accuracy.
103993/33102 = 3.141592653011903
For Pi accuracy comparison,
here are the first 50 decimal places found at Wikipedia.
3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510
patterns in pi have been found in base 16
Pi Hex was a project to compute three specific binary digits of π using a distributed network of several hundred computers. In 2000, after two years, the project finished computing the five trillionth (1012), the forty trillionth, and the quadrillionth (1015) bits. All three of them turned out to be 0.
Beau, take a look at Stu's page for Pi in base 3. Definitely lots of patterns in this small clip. See also other base systems such as base 9, base 16 and base 36.
Pi in Base 3 (trinary)
10.010211012222010211002111110221222220111201212121200121100100101222022
212012012111210121011200220120210000101022010020111120002221022201100101
110121101201010001000222021220110022122210112222212102022011020121022202
201202222120121200201112210000112022001212201101110122210211002112122121
211222122110212212110100221202121011001210210011011102222020021111121010
210000020112212201001211102202212200120020020010012100101122200022202110
211210122110122112120220000111101200101111122000201122111122201010211221
111022122212101200222102212122011001202022112000020111212020200000020222
210021220021011101201122121102000010102101100200202220202100122000010000...
Perhaps the real debate is do you see a pattern for Pi in base Pi?
The formula sure beats looking at the actual numbers, or can you spot the patterns?
Pi in Base 16 from Stu's web site
3.243F6A8885A308D313198A2E03707344A4093822299F31D0082EFA98EC4E6C89452821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... The base numbering systems that we try to throw at pi are all flat or 2d representations (conversions from one base to another basically)
... When/if we ever hit on the right formula to 'unravel' pi, it will be like tuning in a crystal clear radio station and there will absolutely be no doubt to the solution. Until then ... well...
-Phil