Pi Definition and 514 Threads

Pi. An infinite number. INFINITE. People have been memorizing the digits of pi to a certain number of decimal places. A challenge for you: how many can YOU remember? I hold the world age record(i actually don't, because i haven't told anyone except my friends about it) for memorizing 1500...

Approximating PI Show that \int\stackrel{1}{0}\frac{x^{4}(1-x)^{4}}{1+x^{2}}dx=\frac{22}{7}-\Pi Why does this imply that \Pi\triangleleft\frac{22}{7} I have no clue where to begin with this, I'm at a loss, this is one of the questions for in my university project, first year. Any help is...

Hey all we doing some work with integrals and Our lecturar mentioned that one can get a answer for pi using integrating, my question is what would that integral be, and wot is the most accurate? I've gotten it till 3 decimal places.

What is Pi? I just want to know!

I'm relatively new to calculus, and this question was bugging me, so I have decided to ask it. We have the function y=1/x with domain x\geq1 and we rotate the curve around the x-axis in order to form a solid of revolution. (Gabriel's Horn) The integral is V=\pi\int^{z}_{1}1/x^2 dx and we...

I was thinking about how to approximate pi accurately and came up with something and all the calculations i did seem to show that its true and I am wondering if its used often for calculating pi or if there is something better? radius of this circle equals 1 and therefore calcualting a...

I'm 16 and in high school. I've never taken physics or anything before. I have this equation that shows that pi = infinity times zero Ok. So if u take a circle with a diameter of 1 and draw equal spaced radius' and connect them you get a polygon with all equal sides. the more...

Homework Statement Find the Fourier cosine series for f(x) = cos x, 0 < x < Pi EDIT: I believe we are talking about a half-range extension.. Homework Equations Fourier cosine series: f(x) = a0/2 + Sum(n = 1 to infinity) (an * cos (nx)) where a0 = 2/L * integral (x = 0, x = L)...

Is it possible to design a cable with properties (Capacitance and Inductance) to reduce the number of components needed for the PI filter? I know I can design a cable to have a specific capacitance and specific inductance, but I am not sure if or how i would get these to work with the pi...

Howdy folks. The Gelfond-Schneider Constant 221/2 is transcendental. Of my understanding, transcendental numbers are a special case of irrational numbers in the sense of how they may or may not be derrived. This being the case, how is it that many infinite series are stated with such...

Homework Statement Hello, I am trying to draw a Feynman Diagram at quark level for the decay sigma+ -> neutron + pi+.Homework Equations sigma+ -> neutron + pi+ uus -> udd + udbarThe Attempt at a Solution Well, the attachment is what I came up with. I have no idea if it's right to be honest...

Homework Statement \int_{0}^{\pi} \cos ( \sin x ) \mbox{d}x The Attempt at a Solution If I use u = \pi-x I get : \int_{0}^{\pi} \cos ( \sin x ) \mbox{d}x = \int_{0}^{\pi} \sin ( \cos x ) \mbox{d}x but then what?

Homework Statement Solve for 0 ≤ θ ≤ 2π (pi). Give the exact values. tan^2θ=2tanθsinθ I'm not sure how to go about this one =/

Good day everyone I'm implementing a speed controller for a DC motor 220 v 2.7 A 1500 rpm. I've already made and tested the firing circuit and the motor works fine in an open loop. Now big problem the parameters of the motor are unknown and impossible to find. No time for mechanical...

Hi, I have the following equation: \Theta = log \left(\frac{\Pi}{1-\Pi}\right) I want to re-arrange it for \Pi Here's my attempt: \Theta = log \left( \frac{\Pi}{1-\Pi}\right) \Theta = log \left( \Pi \right) - log \left(1-\Pi \right) exp^{\Theta} = \Pi - (1-\Pi)...

Homework Statement Find all angles x, -pi <= x <= pi which satisfy sin4x = 1Homework Equations The Attempt at a Solution Solved x, ie 4x = sin^-1(1) 4x = pi/2 x = pi/8 Sine is positive for angles in quadrants one and two, so there's one other angle which is in quadrant two? x = pi - pi/8 x...

Hoo-Ray, to all us math-science geeks! It's PI day...3-14! Um, well, maybe only for those of us who use mm-dd format :-p ...

In "http://users.info.unicaen.fr/~karczma/arpap/lazypi.ps.gz " Jerzy Karczmarczuk develops some functions for computing pi lazily. http://www.haskell.org/haskellwiki/Libraries_and_tools/Mathematics This thread is motivated by the following response by Hurkly in the thread...

I am interesting for mathematical background od fast algorithms for computing number \pi with complete proofs only. More specific, I am interesting for Gauss Legendre algorithm, Borwein algorithm, Ramanujan formulas and Chudnovsky formula.

That's what my Precal teacher said, and so far I agree with him (though that's not saying much as I've only been exposed up to Precal mathematics). Do all of you mathematicians agree?

Who is pi derived, and what exactly is pi.

My first topic here. Here goes I've written a small program that first calculates pi in decimal and then changes it into binary. But as you know there's no accurate binary presentation even for 0.1 so I just can't change the whole 20000 decimal representation of pi into binary. I there for...

hi are all answer are correct ? help please http://img73.imageshack.us/img73/2421/10267725rs8.png

Homework Statement y = sin \pix Using arc length and surface revoultion on x-axis 0 <= x <= 1 The Attempt at a Solution d/dx sin \pix = \pi cos \pix (\pi cos\pix)^2 = \pi^2 cos^2\pix \int sin pi * x * 2 * pi * \sqrt{1 + pi^2 * cos^2 (pi*x)} u = pi cos (pi * x) du = -pi^2 * sin...

Sin [Pi. (x-1)] / x-1; for x =1,2,3,...N Sin [ Pi. (x-1) ] / (x-1) = ? for x=1,2,3,4,...N I think for Sin (x) / x =1 but, what about that.

The Perimeter Institute has a talk on the Feynman chessboard / checkerboard model scheduled for a few days from now. This will be recorded and you can play it back, sometime after November 18th. Links: Speaker(s): Garnet Ord - Ryerson University Ord's website...

I just got invited to Sigma Pi Sigma and I'm wondering if it's worth paying the fees to join. It does not seem to be very selective (it says GPA > 3.0), so I'm not really sure if it means much being in it. The way I see it, I am paying $45 for something to fill one of the "Honors and...

Hi everyone, I am completely new to MATLAB. But I have to write a source-code in MATLAB to explain how a proportional-integral (PI) controller works. I have got my source-code, but it doesn't really work, therefore, can everyone help me out? Urgent~! %%%---------------------------------%%%...

What is the physcial signifcance of pi's appearance in a mathematical solution, if any?? Pi, the circumference of a circle divided by diameter, shows up in all sorts of mathematical solutions..classical, quantum, sometimes in unexpected mathematical results. As an example, Unruhs law is...

Hi, When exactly does the phase change of \pi occur when a EM wave reflects from a surface? I notice that it happens in Lloyd's mirror for example, and also when considering non reflective coatings on lenses. Is it just when the EM wave is going into a medium with higher refractive index or...

I know pi/2 = 90 degrees and that it's related but how do I express this?

I assert that an omnipotent creator (calling it God just for the sake of convenience) could not change the value of Pi, and therefore omnipotence itself is impossible, that there are some universal laws that are immutable and exist purely by virtue of logic, neither requiring a creator nor...

by writing arctan as a power series, you can obtain an approximation to arctan (1/root 3) and hence approximate pi. I've done this by multiplying my answer for arctan (1/root3) by 6 to get 3.14... radians. I would like to know How can this approximation be improved? thanks!

Howdy ho. No reason for a welcome around here, it's not about me it's about the Mathematical Anti-Telharsic Harfatum Septomin, eh!? (I hope at least one of you are familiar with that guy) Nonetheless, I've become obsessed with the transcendental property, and thusly therein my familiarization...

Hi all, I am working on aerodyanmics homework, and I've been stuck on this problem for a while. "The shockwaves on a vehicle in supersonic flight cause a component of drag called supersonic wave drag Dw. Defined the wave-drag coefficient as Cdw = Dw/(qS), where S is a suitable reference...

Hello. This is driving me a little mad, and some assistance would be hugely appreciated. Homework Statement Show how the following transformation can be achieved (more than one step may be involved) Homework Equations The Attempt at a Solution The only approach i could come up with was the...

Have you guys noticed how the acceleration of gravity is almost equal to pi squared?

1) Let F be the smallest number field containing pi. Prove that F is countable. The first trouble I am facing is: What actually is the smallest number field containing pi? How can we know its cardnality? Could someone please help me? Thanks!

Hi I couldn't find any specific reading material for T and PI network based compensation in control systems. I was hoping someone could point me in the right direction. If you happen to know something about this, please do reply to this thread. Thanks in advance.

Just pondering... If pi continues without ending and can be considered to "contain an infinite number of digits" then isn't there a repeating sequence of infinite length contained in pi, thus making it a repeating decimal? Obviously not...but what is the reason? Thanks!

I guess one could use any irrational numbers here, but phi and pi are favorites. I am sure that most people are aware of the infinite monkey theorem. If not use http://en.wikipedia.org/wiki/Infinite_monkey_theorem as a reference. By using this theorem, could one say that the the first...

Homework Statement Locate & name the singularity of the function Sinz /z- ∏ Homework Equations The Attempt at a Solution The function has singularity at z= ∏ but am not able to figure out what type of singularity it is , at z=∏ it gives 0/0 form which is indeterminate form...

http://www.piday.org/

I have a amateur question regarding pi. I know what pi is, in a general sense, but I am looking at equations (e.g, the cosmological constant, Heisenberg's uncertainty principle, etc) where pi appears, but I do not see any relation to circles in those equations. I am sure there is, but I just...

Hi, I have a BA II plus Prof. and there's no "pi" key, I tried using the trig functions to get the value but it always give me a something in degrees. I want to avoid using 22/7 as it's not close enough. Is there any way to get the number instead of memorizing it? THanks!

Let a,b\inR^{m}, b\neq0 and set \phi(t)=a+tb. We must show that the angle between \phi(t_{1})-\phi(t_{0}) and \phi(t_{2})-\phi(t_{0}) is 0 or \pi for any t_{0},t_{1},t_{2},\inR with t_{1},t_{2}\neq. The 0,1, and 2 are supposed to be subscripts next to t, but my Latex is showing is as...

The question is exactly this: Prove that the maximum speed (Vmax) of a mass on a a spring is given by 2(pi)fA. where f = frequency and A =Amplitude We are given such formulas as: f=[1 / 2(pi)]square_root (k /m) or f=[1 / 2(pi)]square_root (a /-x) the formula for total energy in a...

prove that \frac{1}{1^2.3^3.5^2}-\frac{1}{3^2.5^3.7^2}+\frac{1}{5^2.7^3.9^2}-...=\frac{1}{9}-\frac{\pi}{2^6}-\frac{\pi^3}{2^9}

Homework Statement Via iteration. A continued fraction for pi is: Write an algorithm to compute this to n terms using Matlab. 1st term would be 3+1/9 The Attempt at a Solution p = '1'; for k = 1:n p=3+(-1+2^n)/(3+p); end p I'm very new to programming, and I can...

Is there a proof or disproof that any given finite string of digits will occur somewhere in Pi?