Pi Definition and 514 Threads

Homework Statement can someone explain why we are interested in forming dimensionless products and why only n-j of them should be formed from the problem's variables? Homework Equations Step 1: List the variables in the problem Step 2: Express each of the variables in terms of basic...

Homework Statement Hi Guys, I am a bit confused concerning one part of this topic. Specifically when trying to find non dimensional groups. My problem is a small thing in the finding of the indices. So, for example, your are trying to find a pi group when finding the drag on a car. so you...

Hi everyone. I am starting to study transisors at Uni. and I am confuse in some main concepts. i thought about posting it here so someone can help me up. are pi hybrid signals equivalent circuits used with the same porposes as small signals equivalent circuits? or are pi hybrid signals, small...

I have recently taken apart a few old DVD drives to see if there were any stepper motors available for a Raspberry Pi project I am currently working on. When I opened one of the older drives I found a motor which was unlike the others as it only seemed to have two wires going directly to the...

Background: I am trying to write a program for Buckingham Pi Groups. I need to find a way to list all the input varialbes as different sets. For example if I have 4 variables [V D p u] and I want to distribute them 3 ways I get 4 sets. Number of Sets = Binomial(Number of Variables...

Homework Statement The UV/visible spectroscopy of linear conjugated molecules, particularly 1,3-butadiene in this problem, can often be modeled with the Particle-in-a-box of the electrons. Assume that we are interested in the pi electrons ONLY. A molecule with N double bonds = 2N pi electrons...

Hi everybody! I am trying to implement current control of a DC motor using a PI controller and was having a few questions. I am supplying 19V as input voltage (and capable of supplying current upto 2A) to the H- bridge and the controlling is done via a microcontroller using PWM. When I connect...

How do you solve when an exponent is pi? And a cube root. Thanks, sorry I'm slow.

Lets say that "d" is diametr of a circly,and C is the perimetr(length). Why C/d = pi (3.14) is a constant?? I know the proof of archimides with poligons,from which found the value of pi,but how we know that C/d is always equal with a constant that we named as π=3.14; Thanks !

http://pirsa.org/14070033/ Physical Hilbert space for the affine group formulation of 4D, gravity of Lorentzian signature. Eyo Ita The authors have revealed a fundamental structure which has been hidden within the Wheeler-DeWitt (WDW) constraint of four dimensional General Relativity (GR) of...

Iam reading Julian Havil's book, The Irrationals: A Story of the Numbers You Can't Count On. In Chapter 3 Havil is writing about progress in the eighteenth century in determining the nature of \pi and e through the use of continued fractions. He writes (pages 92 - 93): Can someone please...

after it was found out that the first 9 pi digits 141592653 result in the end sum of 9, i searched for its iteration in the large digit chain of pi. after scanning stuff.mit.edu/afs/sipb/contrib/pi/pi-billion.txt it was found that .141592653 occurs at the 427238911 place and ends on the...

Hello, I'm trying to learn C and am only a couple weeks into it. Suppose I want to write a simple code for Trapezoidal integration and want to have the user input the integration limits via use of scanf. Also, suppose I want to focus on only trig functions such that a common limit is pi. How...

or is it all random? thanks :approve:

One of my interests in pi, and this is all purely recreational, is locating unique integers/relationships, looping numbers ( " orbits " ) etc. In pi, certain integers are located with a position number that when multiplied, by single integers, will return the number itself as a product...

Perimeter conference http://pirsa.org/C14020 Here are links to the talks' videos and slides PDF Recent developments in asymptotic safety: tests and properties Tim Morris http://pirsa.org/14040085/ What you always wanted to know about CDT, but did not have time to...

hi! i have a doubt, how can i know the total number of bonding and antibonding electrons given a diatomic molecule's electronic configuration in therms of sigma and pi orbitals? I have to add these σ and π orbitals are of the type gerade and ungerade. does anyone can help me?

Let's say we randomly select integers to construct a potentially infinite number, for example 3588945... There is a non-zero chance that eventually we will obtain any possible finite series of numbers, say a billion 3's in a row. It is known that pi is indistinguishable from a random series of...

The title pretty much says it all, what do we have today that is better than Archimedes 'method of exhaustion' (although I would argue it is quite beautiful) for deriving Pi?

According to the Molecular orbital theory, diatomic oxygen should have σ2px (internuclear axis) and \pi2py and \pi2pz orbitals filled with two unpaired electrons, one at antibonding \pi2py and the other at antibonding \pi2pz. And of course, the 2s bonding and antibonding orbitals as well...

Here's something that has been bugging me for decades. Well I keep forgetting about it thankfully, but I've never really been able to answer it. Why is Pi actually the value that we have for it and not some other number? If the ratio of a circle's circumference to its diameter was any...

Hi all. This is my first time posting so forgive me If I am doing something wrong. I am a year 7 student interested in all types of physics and my question is, if nothing can be smaller than Planck length then wouldn't past a certain point the digits of pi become obsolete? Simply because the...

Happy Pi day folks ! Heres a general misconception I am having. It might turn out to be a pretty easy question so please do help me. If i pull out my compass to a radius of 7 cm and draw a circle on a paper. Then i'll take a piece of thread and cut it such that it matches exactly with the...

Now I'm hungry. What is your favorite pie? Country apple for me :)

Hello all, Sorry about the crappy title. I'm actually not sure what the call the thing I'm here to ask about, which is why I'm here. In the process of reading about gravitational lensing, I've run across an odd mathematical thing that I just don't know how to handle. When a spherical...

Homework Statement Here is the example along with the solution: What I don't get is what happened to the R_E value. So in this model does it neglect this value? It seems like R_E could be anything and you would still get the same model.I have another question, for this same example, it asks...

Wiki defines a real number as But then it turns out that that definition is not rigorous: Since we don't have a rigorous definition of a real number it is hard to justify that pi is a real number. Let's discuss what it means to 'represent a quantity'. Say I were to ask you what is the...

I noticed that there are some odd looping numbers in pi Following the rule that : the string becomes the position which becomes the string ( I'll use " Sn " for string number and " Pn " for position number, ( after the decimal ) becomes the next string to locate ( Sn → Pn → Sn ) The process is...

Show that for $|a| \le \frac{\pi}{2}$, $$\int_{0}^{\infty} \frac{\cos (\frac{\pi x}{2}) \cos(ax)}{1-x^{2}} \ dx = \frac{\pi}{2} \cos a$$Similarly, show that for $|a| \le \pi$, $$ \int_{0}^{\infty} \frac{\sin (\pi x) \sin(ax)}{1-x^{2}} \ dx = \frac{\pi}{2} \sin a $$

In mathematics, a normal number is a real number whose infinite sequence of digits is distributed uniformly in the sense that each of the digit values has the same frequency, also all digits are equally likely. Wikipedia says that it is widely believed that pi is normal, but a proof remains...

Interesting take on solving the Squaring the Circle problem enshrined in law: http://pulse.edf.com/en/day-pi-became-3-2-instead-3-14159/?utm_source=OutbrainInter&utm_medium=cpc&utm_campaign=Trafic

So \sqrt[5]{306} is a pretty good approximation for Pi (=3.14155). If you add 1/51, so that you have \sqrt[5]{306+1/51} you get 3.1415925 (last digit is 6 for actual Pi.) If you add 1/12997, \sqrt[5]{306+1/51+1/12997} you get 3.141592653587 (vs 3.141592653589 for actual Pi.) And so on. As you...

I'd like to understand better the connection between Hal Haggard's September ILQGS talk http://relativity.phys.lsu.edu/ilqgs/ http://relativity.phys.lsu.edu/ilqgs/haggard091713.pdf http://relativity.phys.lsu.edu/ilqgs/haggard091713.wav and the talk he gave at PI two days ago...

\(\DeclareMathOperator{\Ima}{Im}\) \(\DeclareMathOperator{\Res}{Res}\) Given \[ \Ima\left[\int_{-\infty}^{\infty}\frac{e^{iz}}{z(\pi^2 - z^2)}dz\right]. \] I know the integral is equal to \[ 2\pi i\sum_{\text{UHP}}\Res(f(z); z_j) + \pi i\sum_{\mathbb{R}\text{ axis}}\Res(f(z); z_k). \] However...

Hello everyone, I have trouble understanding how to apply the BBP formula, i.e. actually compute the n-th digit of pi. \pi=\sum\frac{1}{16^{k}}(\frac{4}{8k+1}-\frac{2}{8k+4}-\frac{1}{8k+5}-\frac{1}{8k+6}) where the sum uses k from 0 to ∞. I've read a few explanations how to adapt it...

Homework Statement (a) Design a π section symmetrical attenuator to provide a voltage attenuation of 15 dB and a characteristic impedance of 600 Ω. (b) Construct and test the π section attenuator. Measure and record the input & output voltages of the attenuator and determine the...

Integral of ... Homework Statement Hi, no directions were given it just says ∫(tan(x/2))^2 dx between 0 and pi. You will get for the integral (1/2 (sin(2x)) - ((1/6)sin(2x))^3 I think that this is OK. Part of the graph of the origonal function dips below the axis so it end up being 0. I...

from this equation i get the amplitude is 8 cm, it's a sine function so i guess it has to be a harmonic oscillation i haven't had physics in a while so not really getting anywhere -i need to know T (time for one oscillation) -the frequency f which is 1/T -Vt and At equations, i know i...

A question in regards to nomenclature. I am curious as to the significance of using the symbol π for a time-independent distribution. Does it have any relation to the number π or circular geometry? Or does it come maybe from the invariance of i in the P Matrix such that Pi,j → πj? I don't like...

Was just watching an episode of person of interest and the student asks the teacher what pi is good for and he tells her that contained in pi lies every possible combination of words, every conversation that has ever taken place on Earth is located somewhere in pi. Every shakespear play, every...

Why is the value of PI not absolute mathematically?

I'm wondering if Pi is a rational number in any other base besides base Pi. Also is there a formula or function to figure this out? I'm not what the relevance would be if we could find one since the integers might be irrational if we did but I am just curious if indeed Pi is only a rational in...

Homework Statement Perform a T to ∏ conversion on the components marked with an asterix (see attachment) The Attempt at a Solution I believe the answer is 6. Zab = sum of the two impedances connected to terminals "A and B" + product of T impedance connected to terminals...

I just heard about this thing called raspberry pi. It's a credit-sized computer made by raspberry pi foundation. I heard of many projects you can do with this. There are sites with top 10 things you can do with the computer etc. What makes this computer special which allows us to do so many...

Me and my friend are looking to do a project for our science research class in high school. My friend said he is allowed to use his Rasperry Pi for a project and I am interested in physics while he is a big computer and technology guy, I'm looking for ideas for projects either using the software...

I know a Pi is 3.14159265359 or 22/7. Or Pi is a ration between a circle's circumference and its diameter. Why Pi = 180 deg and 2 pi = 360 deg? Please explain.

Hi folks, can someone help explain this in words of one syllable or less? I am looking at a text that compares flux and intensity of a distant source, and it states that ∫∫dΩ = ∏ I know that dΩ = sinθ dθ d∅ but I don't understand where the given result comes from. What are the...

So I heard someone say that the cube root of 31 is a good approximation for ∏. This led me to thinking about higher roots and approximations. ψ denotes the nearest whole number \pi^{2} \approx 9.86960440109 ψ=10 \sqrt[2]{10}=3.16227766017 \pi^{3} \approx 31.00627668029 ψ=31...

Dirichlet's Approximation Theorem not working for n=8 and α= pi? I am reading a number theory textbook that states Dirichlet's Approximation Theorem as follows: If α is a real number and n is a positive integer, then there exists integers a and b with 1≤ a ≤ n such that |aα-b|< 1/n . There...

calculate "pi" How do you calculate "pi"? pi~3.141592654