Pi Definition and 504 Threads

can anyone provide me the proof of pi being a transcedental number

I am looking to work with a raspberry pi board to do some basic and eventually more complex things, what are the best types of things to attempt / what type of raspberry pi board is the best to purchase for a starter? As for the boards themselves I am aware that are quite powerful and I have...

Homework Statement Find the La Place transform of cos(x)*(u(x-\pi)) Homework Equations L{u(t-a)}(s)=(e^(-as))/s The Attempt at a Solution I don't think I can just multiply this by the La Place transform of cos (x), which is s/(s^2) ?

Watch this . . .\pi \;=\;3.141592645 . . = \;3 + 0.141592654 \;=\; 3 + \dfrac{1}{7.062573306} . [1] . . =\;3 + \dfrac{1}{7 + 0.062573306} \;=\; 3 + \frac{1}{7+ \dfrac{1}{15.99659441}} .[2] . . =\;3 + \dfrac{1}{7 + \dfrac{1}{15 + 0.99659441}} \;=\; 3 + \dfrac{1}{7 + \dfrac{1}{15 +...

New data from NASA's Cosmic Background Explorer (COBE), the Wilkinson Microwave Anisotropy Probe (WMAP), and Planck have found evidence that the composition of the universe: Matter - 4.9 % Dark Matter - 26.8 % Dark Energy - 68.3 % These numbers seem almost too coincidental to numbers...

As I am sure you know it was Pi day the other week and I found myself wondering how we know pi is constant. I decided it would be a fun problem for me to try and though I have spent a few nights awake in my bed thinking about it I cannot come up with a proof that pi is constant (although to be...

"Most people with a basic understanding of math probably knew that Thursday was 3.14 and therefore Pi Day, because that is the number of the ratio between a circle's circumference and its diameter." "But the actual number is much longer -- in fact, the decimals go on for at least 10 trillion...

(And Albert Einstein's birthday, too)

How comes \frac{\pi}{\pi}= 1 yet \frac{∞}{∞} is indeterminate? I mean \pi is infinite... so it's essentially just another type of infinity. If I said that \frac{3,4,5,6,7...∞}{3,4,5,6,7...∞} = 1 would I be correct? Or again would this be the same as \frac{∞}{∞} ?

I have everything correct, that is when I put in a value for n=10 I get the right results however I want to enter in more than one number at a time to give me three different results like a vector like [ 10 20 30] but I am just clueless as to how to go about this. the dots are there because i...

is there any sequnce which converges to \pi such that each term of it less than pi I know the sequnce related with the taylor expansion of the arctan \sum_{i=1}^\infty \frac{(-1)^{i+1}}{(2i-1)} but this sequnce first term is bigger than pi why I am looking for such a sequnce because I want to...

Hello, I am looking at the sigma and pi bonds and trying to understand them. I know that the bond is the overlap of the orbitals, in the case of sigma bonds two s-orbitals and the pi bonds is the p-orbitals. When you have the sp hybrid orbitals, how are there only the same number of hybrid...

Which of the following should occur at a greater rate: D0 to K(-) + (pi)(+) OR D0 to K(-) + positron + electron-flavor neutrino? I know that there are other decays that are Cabibbo supressed (or doubly so) but I can't see what would make one of these more likely than the other. Thanks

Homework Statement A ∏° meson moving with a velocity v in the z direction decays into two photons. One of the photons travels in the z direction and the other travels in the minus z direction. a) If one photon has an energy that is nine times greater than the other photon, calculate the speed...

I need to find the limit of. Ln (sinx) as x approaches pi-, that is, as x approaches pi from the left. I thought I should use the squeeze theorem, but I am not sure how to apply it. My teacher is not requiring us to use the delta/Epsilon method, so I am sure it is a squeeze method. But how do I...

If pi is infinite and nonrepetive and every number combination is in pi, somewhere, does that mean pi itself is in pi somewhere.. ? (that would make it periodic)

Back in 2008 I posted the same topic [thread now closed, due to age??: C:\Users\Owner\Documents\PHYSICS\What's the significance of pi.mht We missed a fascinating answer I just noticed: In natural units, commonly used in high energy physics, where the Coulomb constant is 1/4π and c = ħ = 1...

Homework Statement I have a project about pi. We are wanted to calculate pi in Fortran 90/95,without use intrinsic functions. For example, we must think like a computer. Homework Equations We must use formula of sin(x) and cos(x) for find 'pi'. When Sin(x)=cos(x) (and error is 10**-4)...

Today we switched the roster for lab duties up so that every person gets rotated to a new task in order to have the lab run smoothly. Normally we switch up the lab duties every quarter. Today, however, a lab co-worker decided to email everyone saying he thinks we shouldn't rotate the roster...

A question in my book says to prove that pi is irrational, I found a proof which I'm happy with and found a similar one on the web however on the solutions they have done: assume √π is rational i.e \sqrt{\pi} = \frac{p}{q} p,q \in \mathbb{Z} \pi = \frac{p^2}{q^2}, p^2,q^2 \in \mathbb{Z} ∴...

I was wondering about Lambert's proof of π's irrationality. Supposedly he was the first one to prove it in 1761 when he derived a continued fraction for the tangent function. Then I was reading through some of Euler's translated papers when I stumbled upon the same continued fraction in Euler's...

Homework Statement The proper mean lifetime of a \pi^{+} mesons is 26ns. (a) (i) What is the mean lifetime of \pi^{+} mesons traveling with \beta=\frac{v}{c}=0.73? (ii) What distance is traveled at this velocity during one mean lifetime? (iii) What distance would be traveled in the...

I'm doing my homework, and encountered a problem. The problem is the one as attached. It includes a part of solution that I don't understand. I've known that when designing the PI controller, we start from D(s) = (Kp + Ki/S) The condition of the PI controller is, firstly, unity DC gain. So...

hello! why a cyclic aromatic molecule forms pi interactions, while a cyclic aliphatic (with single only carbon bonds) doesnt? thanks!

... and for a long time, I took this for granted, but now I'm starting to wonder how it is doing this. From my knowledge, the only way one could calculate pi is to measure the diameter and radius of a circle, and find the ratio, but to calculate an irrational decimal as thoroughly as we have...

Homework Statement find total sigma and pi bonds in c6h6 Homework Equations Benzene structure The Attempt at a Solution if i consider benzene structure, then total will be 12σ and 3∏ but according to the random structure that i managed to draw, it showed, 11σ and 4∏, was i wrong...

I am trying to label the y-axis with pi and -pi. How can I do that? \begin{tikzpicture} \draw[->] (0,0) -- (3.5,0) coordinate (x axis); \draw[->] (0,-3.5) -- (0,3.5) coordinate (y axis); \end{tikzpicture}

I have to write a MATLAB function that estimates the value pi based on the fraction of a collection of random points in the square [1; 1] that are within the circle of radius 1 centered at the origin. I am very new to MATLAB and computer science in general and I've been having a great deal of...

Hi everyone, About 15 minutes ago I came up with a problem... What whole number multiple of pi would result in a number closest to a whole number? Does a single whole number multiple exist, and can we... prove it? Thanks for help in advance! -Daniel

I think it's the first 1000 digits. wish I could have been there https://www.youtube.com/watch?v=4iALEU1dD1A

I have a single phase DC-AC inverter (or H-Bridge) with an inductive load I want to design a controller that controls the PWM signals to the control side switches that will ensure there is a sinusoidal current through the load. I need to use PI control and implement into a DSP so it has to be...

Does anyone know if it has ever been proved that pi divided e, added to e, or any other mathematical operation combining these two irrational numbers is rational. Another thing does anybody know of any other irrational numbers that is not some derivative of pi and e.

Here is a petition about supporting pi against tau. So if you think that pi should not be changed, please sign this petition: http://www.change.org/petitions/khan-academy-withdraw-the-support-for-tau. I'm not sure if the petition will help, but... P.S. If this petitions are not allowed, by...

Hi, recently I have being thinking about math in different bases, and I was wondering if there is a relationship between ∏ from different bases. Also is there mathematics related books that discusses math in different bases? Thanks in advance

Whilst messing around with some geometry pertaining to the n-sided regular polygon, I stumbled upon this equation which I could not find anywhere on the internet. \pi = \lim_{n \to \infty} n \sin \frac{\pi}{n} But if we take this to be true then, by substitution, this is also true: \pi =...

Here's a question. Pi is said to be the ratio of a circle's circumference to its diameter. If this is the case, what does it say about the circumference of a circle that pi is still irrational. I get that pi is also used in the calculation of a circumference in the first place. Since this is...

good day all.i've just written a program in fortran77 for the model of a binary distillation column.i included a PI controller in my program.To obtain the integral term of the PI,I used the explicit euler to numerically integrate the error.i would love to compare my results using another method...

Conformal Nature of the Universe (at PI) "Is nothing sacred?" Starting Wedesday 9 May at PI will be an unusual conference at Perimeter. Some topics of talks include: Shape Dynamics (Barbour, Koslowski, Gryb, Gomes...) Relationalism (Edw. Anderson...) Horavaism :smile: 't Hooftism :biggrin...

How would i write 1.047 rad in terms of pi? I know the answer i will get is Pi/3 rad, but HOW do i get this answer? I know how to convert degrees to radians and vice versa in terms of pi but this particular question is in radians. Help?

When I'm using formulas such as T = 2(pi) / w I thought Pi should be in Radians as w is in rad/sec yet when I look at an example it uses 3.14. Why is it 3.14 instead of 180?

we all know the PI crops up everywhere.. why for example would PI be found in the equation for the density parameter of the cosmological constant etc.. is there a book that can explain why PI rears its head up in all types os studies... cheers

Hello! I am taking a computational physics class this semester and just got out of a test. One of the questions provided us with 10 random numbers and asked us to approximate pi. The method I came up with was realizing that \int_0^1 \sqrt{1-x^2} dx = \frac{\pi}{4}, and then performing this...

Hi. I was just wondering about when I'm doing small singla analysis with Bipolar Junction Transistor (BJT) is there a basic rule on which model to use, the Hybrid Pi or the T-model?

Happy Pi Day everyone! Happy Pi day, everyone! Europeans, sorry, but you're going to have to wait till July...

Inspired by http://www.mathhelpboards.com/showthread.php?560-integrals thread: By considering the integral $\displaystyle \int_{0}^{\infty} \frac{\ln(1+x^2)}{1+x^2}\;{dx}$ or otherwise, show that $\displaystyle \sum_{k \ge 0}~\sum_{0 \le j \le k}\frac{(-1)^k}{(2k+3)(j+1)} =...

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 [FONT="Times New Roman"]π[/size]: \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}...

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.