Pi Definition and 514 Threads

Homework Statement The number a is called a triple zero (or a zero of multiplicity 3) of the polynomial P if: P(x) = (x - a)3q(x) and q(a) = 0. Prove that if a is a triple zero of P, then a is a zero of P, PI, PII, and PIII(a) = 0. Homework Equations The Attempt at a Solution...

Say we have sp2 hybridization of nitrogen, can the unhybridized p orbital form sigma bonds too or can it only form pi bonds? So in the case of nitrogen, it would be able to form molecules with 2 sigma bonds and one pi bond, correct? Thanks

A passage from "Excursions in Number Theory": "A transcendental number is not a solution of any algebraic equation. Pi is a familiar example of such a number and there are infinitely many others. A circle, centered at the origin, with radius pi (or any other transcendental number) has on it...

http://pirsa.org/10110052/ Quantum polyhedra in loop quantum gravity Eugenio Bianchi "Interwiners describe quanta of space in loop quantum gravity. In this talk I show that the Hilbert space of SU(2) intertwiners has as semiclassical limit the phase space of a classical system originally...

Hello Everyone, I am trying to put together a PI controller for a boost converter. Vin = 150V Vout = 300V (Require this much boost) Switching Frequency = 25KHz I am attaching a schematic in PSPICE. Please , someone, tell me if the connections are right. Also V-PULSE / SAWTOOTH = (0...

Homework Statement \Pi_{n=1}^{5} n Homework Equations My teacher assumed I learned this in calc 2 but I was never taught this. Can someone tell me what this thing is called?

Why do pi electrons in a benzene move?

Hi, this thought came to my mind..not sure how correct this is. In extreme gravity, the space curves. Will the value of Pi change in this case, for a circle near such gravity ? pi = circumference/diameter.

ln(-1)/i=pi this equation does not use limits or integrals, as you can see, but it does involve imaginary numbers. Does this make it an open expression, or does the fact that it uses i not matter?

My calc is a bit rusty & i can not solve this problem for the life of me. its the integral of x^2sin pi x. I know you must integrate by parts..& i am have tried using both x^2 and sin pi x as my u. Any help? time is of the essence.

The proof is intuitively wrong, but I just can't figure out where. (Circumference = 2pi*r) 1. Consider a rod of length L = 2. Draw a semicircle around it, which has radius R=1 and arclength C= pi 2. Now draw two small semi circles, one going from the midpoint of the rod to the top and to...

Homework Statement I am looking for a proof of Buckingham PI theorem in dimensional analysis, but can't really find one anywhere. I saw a proof involving posing the problem as a question in linear algebra, but it was quite unclear.

note that by limit I mean the calculus operation, as in limf(x) as x->a. I was playing around with numbers earlier today and came up with a limit that gives an exact value for pi. I want to know if others have devised limits that equal to pi, because I am not sure if I am the first because my...

Pi is an irrational number with an unpredictable distribution of the numbers 0 to 9. Yet patterns do emerge. Can we say with certainty that there is some point in pi where there are a billion consecutive zeros? Is there any way to calculate the number of digits of pi that must be expanded to...

I was reading a book on number theory, and there was an interesting dicussion about pi and e. It state that it took about one third less time to compute e to 100,000 places when compare to pi. Additionally, it stated that no "simple" partial fraction (that is, one in which all numerators are...

So if Pi is an irrational number, and therefore has an infinite line of numbers after the decimal point; my intuition tells me it would take an infinite amount of time to determine its exact value. a) Do calculators and computers somehow know Pi's exact value or is it just an estimate? b)...

So, I was browsing the complaints in the Forum Feedback today, just for fun, and I thought of something. Pi is commonly misspelled as "pie". And I got thinking, which is more important? Pi or pie? Which would you rather have? And this poll was born, in a feverish stupor I might add. So...

Homework Statement I am posting for my son, who needs the full readout for a formula, more than what a small graphing calculator can do. Is there such a program for that? Am I in the right place to get an answer for this? I would appreciate any help in this for my mathmatical skills are...

I am posting for my son, who needs the full readout for a formula, more than what a small graphing calculator can do. Is there such a program for that? Am I in the right place to get an answer for this? I need the numeric result of "2 times the inverted sign of 1 minus the inverted sign of...

Hi, I am independently learning analysis, I found videos online and Rudin's textbook, though I am unclear on one thing. I thought the point of dedekind cuts was to construct the reals without explicitly talking about the irrationals, which is why to get at the square root of 2 you let the cut be...

Homework Statement If pi ≤ Θ ≤ 2pi and cos Θ = cos 1, what is the value of Θ? Round to nearest hundredth. Homework Equations The Attempt at a Solution cos 1 = ~.54 then I didn't really understand how to interpret the "If pi ≤ Θ ≤ 2pi" Thanks for your help.

Dear readers, At my webpage: http://domingogomez.web.officelive.com/brocotfraction.aspx I have posed a challenge entitled "To PI or not to PI", it deals with a generalized continued fraction (bifurcated fraction) whose coeficients are all the Stern-Brocot fractions, that is, all...

How can I go about using a power series representation of arctan(x) to approximate Pi to five digits?

Homework Statement Determine the Fourier series of f(x) = pi + x Homework Equations The Attempt at a Solution I see you have to calculate the two "series" separately and then add them. I know that the Fourier series of pi is just pi - but i was wondering why (i know that sounds...

I was looking up how pi was derived, and found this: http://mathforum.org/library/drmath/view/52589.html Question: How were the quantities n*sin(180/n) and n*tan(180/n) found/derived?

1. Compute all the values of e^ {\pi i} , indicating clearly whether there is just one or many of them. Trivially, exp(pi * i) = -1. However, we can also consider e to be the complex number z, and pi * i to be the complex number alpha. Then we get: e^{\pi i} = z^{\alpha} = e^{\alpha...

Is it true that every possible finite number sequence is present in the decimal expansion of pi?

Homework Statement Hi First of all this a textbook question from Stroud Advanced Engineering Mathematics, solution is given, but no steps are shown. A question I just can't seem to solve at the moment, as below. A function f(x) is defined by f(x) = \pi - x:0 < x < \pi f(x + 2\pi) = f(x)...

I was studying Huckel Rule. And I stuck on one of the point. (iv) The total number of pi electrons in the molecular species or ion should be 4n + 2 where n = 0, 1, 2, ...... etc. But I don't know how to calculate the number of pi electron. Do you have any idea about it.

Orthogonal Properties for Sine Don't Hold if Pi is involded?? Normally I know \int_{-L}^L \sin \frac{n x}{L} \sin \frac{\m x}{L} ~ dx = 0\mbox{ if }n\not =m , \ =L \mbox{ if }n=m but apparently this doesn't work for \int_{-L}^L \sin \frac{\pi n x}{L} \sin \frac{\pi m x}{L} ~ dx I am...

Homework Statement I need to find the residue of e^(az)/(1+e^z)^2 at I Pi. For some reason this is such much harder than I thought it was going to be. Mathematica is not even helping :(. Homework Equations Cauchy's kth Integral formula. The Attempt at a Solution I made an...

Homework Statement Using the Arctangent formula pi = 16 * arctan (1 / 5) - 4*arctan(1 / 239) to calculate the value of pi to 53 significant digits.Homework Equations The power series of arctangent(x) is = x − x^3/3 + x^5/5 − x^7/7 + x^9/9... The Attempt at a Solution...

I was thinking about this recently since it was pi a few days ago :) How is pi, the number, generated in a way that can go on forever? How are extra characters discovered? Thanks.

Happy Pi day everyone :) 3.141 5926 5358 9793 2384 6264 3383 2795 0288 4197 1693 9937 5105 8209 7494 4592 3078 1640 6286 2089 9862 8034 8253 4211 7067 9821 4808 6513 2823 0664 7093 8446 0955 0582 2317 2535 9408 1284 8111 7450 2841 0270 1938 5211 0555 9644 6229 4895 4930 3819 6442 8810 9756...

I went to Google this morning and found out that today is http://www.cnn.com/2010/TECH/03/12/pi.day.math/" . :biggrin:

I quite like the following definition of pi and I wonder which minimal algebraic rules are needed to make this definition work? \lim_{n\to\infty}\left(1+\frac{a}{n}\right)^n=1 \therefore |a|=2\pi k (For example, are there algebras more general than complex numbers, where this works?)

I understand the difference betw mathematical and physical pi. I also understand that in non-Euclidean space the value of pi would differ depending on a surface's deviation from flatness. But is there a different symbol for physical pi, to distinguish it from mathematical pi? Because I...

What's so special about PI? Why does it appear in so much in physics? Einstein's field equations, Coulomb's Law, Kepler's Third law constant, uncertainty principle... This wouldn't be a co-incidence. Surely there's an underlying reason for this that we don't know yet?

How is the number 3.14159...etc, derived? I know it has been calculated out to very great lengths and I'm wondering how it's done.

There is a geometric way one can show the relation between kinetic energy and momentum which is a mathematical curiosity in my opinion. Let the mass of an object be equal to 2 PI. Then: P = 2 pi v KE = 1/2 (2 pi ) v sq or KE = pi v...

Hello :smile: Sorry if this is in the wrong place, I don't know where else to put it. Is there a way to write radians as decimals in terms of Pi? I'm currently doing Polar Coordinates with Argand Diagrams, and this is something I'm curious about. I've just done a question and come...

Homework Statement Write in symbols the negation of the theorem stated in part a. part a:We immediately see that if g(x) is a nonnegative continuous function whose integral is finite, then there exists an a>0 such that a*g(x) is a continuous probability distribution (take a=1/\int g(x)dx...

If you were to imagine a line segment of length pi, I would guess it would have to be finite. But since pi is an irrational number, it has infinitely many decimals so can't you just keep sort of zooming in on the end of the segment so that it sort of keeps on getting longer indefinitely? Pi...

This is one question that's giving me a bit of trouble to handle. The Period of a pendulum is given by the following equation: where T= period of pendulum (seconds) L= Length of pendulum (meters) g= acceleration doe to gravity (meters per second2) Solve this equation in terms of L, T...

Homework Statement Find the period T for a wave of wavelength (lambda) . Express the period in terms of pi, lambda , and g. Homework Equations T = lambda/velocity, lambda = velocity/frequency T= 1/frequency k (wave number) = 2pi/lambda V = Squareroot of (g/k) The Attempt at a...

Heya, I'm new here and really need help! So I'm having trouble with the *Buckingham Pi Theorem*. I think I've got the jist of it bar one thing...So you have a bunch of variables e.g a force, velocity, denisty, length, viscosity, speed of sound: f(F, V, roh, L, mu, a) Do the (N variables - M...

Why do we take pi as the ratio of the circumference to the diameter, and not diameter to the circumference? Is it because circumference is always bigger than the diameter, so that it will be easy to work with the ratio? Or is it something fixed by those who discovered it and we can't change it?

Homework Statement Find the general and, if possible, particular solutions of the following ordinary differential equations: y''+9y=36sin3x (hint: modification rule for PI) Homework Equations Knowledge of ODE's y = y_{aux}+y_{particular} The Attempt at a Solution I get the compementary...

Homework Statement integrate: 4*cos(n pi t) d(t) Homework Equations The Attempt at a Solution is it: [4sin(n pi t)]/n.pi or [4t sin (n pi t)]/n.pi any help very much welcome.

as constrained by the Plank Length. Any ideas on how to solve this