Pi Definition and 514 Threads

Is it possible that the value of Pi is related to the properties of the spatial dimensions of our universe? Could another universe with different properties see circles differently and arrive at a different value for Pi? After all, Pi is determined based on ratios determined within our own...

So, I was working with the Fibonacci sequence this afternoon, and I stumbled onto something that maybe a major discovery to geometry, I don't know if it is or not. So, I began working with the golden spiral, and began drawing it. After drawing it, I noticed you could draw circles and more...

According to this link at Wolfram, the following formula can be used to calculate any digit of the base-16 representation of π: \pi = \sum_{n=0}^{\infty} \ \left( \frac{4}{8n+1} - \frac{2}{8n+4} - \frac{1}{8n+5} - \frac{1}{8n+6} \right) \cdot \frac{1}{16^n} But apparently it is not as...

Does anybody know of any good resources they can point me to for implementing PI control in an embedded system? I'm not necessarily looking for PID control - just PI. Books, websites, etc. - any suggestions are welcome.

I stumbled upon this infinite series that converges to \pi: 4\sum\frac{\sqrt{n^2-i^2}}{n^2} for i = 1:n as n{\rightarrow∞} I haven't been able to find any similar series online and I'm really curious how to prove this does indeed converge to \pi. Any insight would be greatly appreciated.

At least that's what the gentleman working the check-out at my local produce market said to me. I told him that there are an infinite number of digits in pi and he flatly said no. He went on to say that the newest supercomputer solved all the digits and until now, no computer could because it...

Help with Mobius Inversion in "Riemann's Zeta Function" by Edwards (J to Prime Pi) Can someone please add more detail or give references to help explain the lines of math in "Riemann's Zeta Function" by Edwards. At the bottom of page 34 where it says "Very simply this inversion is effected...

After being created in a high-energy particle particle accelerator, a pi meson at rest has an average lifetime of 2.60 x 10^-8s. Travelling at a speed very close to the speed of light, a pi meson travels a distance of 120m before decaying. How fast is it moving? Answer: 0.998c Could...

So I always wondered why you multiply by pi when you're finding an area of a circle, for a rectangle you multiply by length and width, I guess that makes sense... How I see multiplying a length and width is if you have a length of 5 cm and a width of 4 cm, I imagine you just stack 4, 5 cm...

Hi! I'm using MATLAB and I want to store or print some particular decimal digits of pi, from 9901 to 10000. I'm using the algorithm below (Brent-Salamin algorithm) to print the first 10000 digits but I can't find out a way to save and print only the decimal digits from 9901 to 10000. What...

pi+ + p --> Sigma+ + pi+ + K0 Dear forum readers; I have a simple question. Could someone tell me the isospin is conserved in the above reaction? This is the way i understood this. LHS possible Isospin values are 1/2, 3/2 RHS possible Isospin value is 5/2 5/2 is not in LHS. so...

When we say we know the value of Pi upto - say 1 billion position accuracy -, how exactly they calculate it? Is it as simple as Circumference / diameter and the whole accuracy of the value of Pi is completely dependent on the accuracy to measure circumference and diameter?

Homework Statement Let Arg(w) denote that value of the argument between -π and π (inclusive). Show that: Arg[(z-1)/(z+1)] = { π/2, if Im(z) > 0 or -π/2 ,if Im(z) < 0. where z is a point on the unit circle ∣z∣= 1 The Attempt at a Solution First, i know that Arg(w) = arctan(b/a)...

Hi , I only recently read the construction of reals from rationals. I could grasp that \sqrt{2} can be represented as the set of rationals given by {x\in Q : x2 < 2 } . As we know this set is defined purely in terms of Q. Is there a dedekind cut representation for pi as well ? I read...

This is being discussed in micromass's "Math stuff that hasn't been proven" thread, but I want to be particular about this topic. Essentially, I think I'm looking for a "proof" or derivation of pi from few first principles. Honestly I have no idea which is the "purest", most motivating question...

I'm not sure it's safe to post real theorems here. Is it?

Hey guys/gals, The block diagram attached is a PI controlled robotic joint system where: G(s)=Kp+(Ki/s) P(s)=48500/(s^2+2.89s) R(s)= joint’s desired angular position C(s)= joint’s angular position D(s)= external disturbance G(s)= PI controller ess= Steady State Error My...

hi i need help with some pi matching for the following cct shown below, i would usually approach this problem with X=sqrt(1000*50) where X is the reactance of L1,C2,C3 but since C1 is in this cct then i can't use this equation so could someone please help me solve this problem

What is the derivative of the pi function

I watched a few of the videos on line at the PI http://pirsa.org/C11008 Some thoughts: it seems to me Penrose did show some new material on observational evidence of CCC, in particular he argued that families of 3 or 4 concentric circles were observed more frequently than a Gausian analysis...

Homework Statement arctan(sin((3 / 4) * pi) * 2) = 0.955316618 I want to express that in terms of a fraction with reference to pi. The Attempt at a Solution I thought of first dividing that by pi itself, and then convert the resulting number into a fraction and tack pi on at the...

Some mathematicians suggest, that it would be better, if instead of pi we would use 'tau', as pi very often occurs with a 2 nearby. So tau = 2*pi What's your opinion about this...

I'm not asking a question of what is permeability, but rather why is pi involved in its definition of 4pi x10^-7? As far as I know, pi is generally only used whenever dealing with a circle. How does the idea of magnetism relate to a circle?

I have noticed something strange when you take the value of sin(pi*10^-n). It approaches pi*10^-n. I have attatched the file here.

Please help, I am confused with part c and d. 1. Doug in a lab on Earth observes a π-meson is created 2.8 km from the surface of the Earth. It has a rest decay time is 9.0 x 10-6 s and it travels straight down to the Earth at 0.95c. a) What distance would the π-meson measure to the lab...

Hello, I am trying to figure out at some level(not fully) Hybrid PI model BJT. Only one thing bothers me. Does it matter if the v0 is + or -. Is for npn transistor v0 -ive and for pnp +ive? How do I figure that out and does it really matter, and if not why?

Homework Statement The volume of a fixed mass of an ideal gas is doubled while the temperature is increased from 100 K to 400 K. What is the final pressure in terms of its initial pressure pi? Homework Equations in terms of pi? what?? does that stand for ' pressure initial or...

I was playing around with an infinite series recently and I noticed something peculiar, I was hoping somebody could clarify something for me. Suppose we have an infinite series of the form: \sum^_{n = 1}^{\infty} 1/n^\phi where \phi is some even natural number, it appears that it is always...

Homework Statement I wrote a code that calculates pi using accept&reject monte carlo integration. It picks -1000000000 pseudo-random points (x,y), and counts the number of points that fall within a unit circle (let's call that number k). The ratio of k/ N (N = Number of trials = 1000000000)...

[PLAIN]http://blog.bfg9000.co.uk/wp-content/uploads/2010/11/pi_equals_4.png Could someone explain the error here?

how to measure perimeter without pi? [before they knew about the pi ratio]

does pi over infinity equal .00000...314159...? if not please post opinions. :(

Hi! I've been looking to simulate a PI controller in SIMULINK without much success. You will be able to find a description of the above in the images located here: https://picasaweb.google.com/102197309611185157885/PIControlWithMatlabAndSIMULINK?authkey=Gv1sRgCOCnzvbm5PuNJA&feat=directlink. I...

Suppose you have a circle with a diameter of 1. If you draw a square with all four sides touching the circle, the perimeter of the square is 4. Now suppose you indent each corner of the square so that they all touch the circle-this will make a cross shape, and the perimeter of it is still 4. Now...

Whyyyyyy??! Whhhhhy?!?

Homework Statement Explain in words the importance of pi(x) and phi(x) for the canonical quantisation programme. Homework Equations none The Attempt at a Solution This is a past paper exam question, which I would appreciate some clarity on. As a proposed suggestion: pi(x) and...

Hi I feel I am competent enough at the Buckingham Pi theory regarding both Pipe flow and for Propeller analysis. Derive a relationship between the volume flow rate and rotational speed of propeller in terms of the diameter of the pipe and propeller and also fluid characteristics density and...

I've never really thought about this before, but today it hit me: Why do we define the Fourier transform of a function to be \hat f(k) = \frac{1}{\sqrt{2 \pi}} \int_{-\infty}^\infty f(x) e^{ikx} dx What do we lose if we just define it to be \hat f(k) = \int_{-\infty}^\infty f(x) e^{ikx} dx

Hi all, very new here, sorry if this is in the wrong place, my question is related to gravity/spacetime warping and all that good stuff, so maybe general relativity My knowledge only goes as far as 5 TTC lecture series on particle physics, quantum mechanics etc, and my maths only goes as far...

Curious on people's thoughts. Especially since most people here are a lot better at math than me! https://www.youtube.com/watch?v=jG7vhMMXagQ

As far as I can tell from googling, pi has been calculated to over 3 trillion decimal places. I'm curious whether a string of 100 2's has been found. It has to happen, right? As I understand it, we should be able to find a string of 3 trillion consecutive 2's. Am I wrong in my thinking?

Couldnt we just use whole numbers to graph on the x-axis instead of labeling them pi/2, pi, 3pi/2 ? Because it gets confusing having to memorize which pi fraction goes in order. Is there a better way to memorize these? Thanks

Not sure if this interests anyone (maybe it's too basic?), but pi = (5^1.25/2) * (2/sqrt(5)) * (3/sqrt(10)) * (5/sqrt(25)) * (7/sqrt(50)) * (11/sqrt(120)) * ... Each radicand is the square of the corresponding prime number numerator, but rounded to the nearest mutliple of 5. I derived...

hi. I've been working on a project lately about pi. and its unconstructiveness doesn't make sense. can you think of a way to possibly do this?

The plot of x^(pi) looks like an odd function, does that make pi an odd number? http://www.wolframalpha.com/input/?i=x^pi same goes for x^e http://www.wolframalpha.com/input/?i=x^e

Homework Statement The cation [CH2=CH-CH2]+ has a delocalized pi network that can be described using Huckel Molecular Orbital Method. Calculate the pi bonding formation energy 2. The attempt at a solution Using matrix, energy = alpha, alpha + root2 beta , alpha-root2 beta The pi...

"A high-energy photon creates a pi+ pi- pair." ? Homework Statement "A high-energy photon creates a pi+ pi- pair. What is the minimal frequency of the photon?" (+ other side questions) Homework Equations E = hf E = mc² The Attempt at a Solution Well superficially it looks very easy...

If pi is the ratio of its circumference to its diameter , But it cannot be written as a fraction then how is it a ratio ?

I would like to know how confident I can be in my Monte Carlo estimate of Pi, plus/minus a specified margin of error. I know the locations of the "pins" are uniformly distributed, thus P(pin being within circle's radius) = P(x <= radius) * P(y <= radius)

http://www.lolblog.co.uk/wp-content/uploads/2010/11/1290616506315.jpg Just thought I'd share this. Don't know if anyone has seen it, but I found it rather amusing. Disclaimer: I know why it doesn't work and am not trying to push this as some "new" maths.