Square Definition and 1000 Threads

In geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, or 100-gradian angles or right angles). It can also be defined as a rectangle in which two adjacent sides have equal length. A square with vertices ABCD would be denoted



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{\displaystyle \square }
ABCD.

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  1. S

    Is My Integral Setup Correct for the Electric Field of a Square Sheet?

    Homework Statement Field the electric field of a square sheet. I understand this is a simple problem, I just want to confirm I have the integral set up correctly. Homework Equations \vec{E} = \sigma z \int_{-a/2}^{a/2} \int_{-a/2}^{a/2} \frac{dx' \, dy'}{(x'^2 + y'^2 + z)^{3/2}}...
  2. L

    Integration by parts involving square root

    Homework Statement |x3sqrt(4-x2)dx Homework Equations uv - | vdu The Attempt at a Solution u = x2 v = -1/3(4-x2)3/2 du = -2xdx dv = x(4-x2)1/2 uv - | vdu x2(1/3)(4-x2)3/2 - | 1/3(4-x2)3/2(2xdx) x2(1/3)(4-x2)3/2 +(1/3)|(4-x2)3/2(2xdx) u = 4 - x2 du = -2xdx...
  3. D

    MHB Find $A_0$ in Root Mean Square & Parseval's Theorem

    I am reading about the root mean square and Parseval's Theorem but I don't understand how we find $A_0$. So it says the average $\langle x\rangle$ is zero and the $x_{\text{RMS}} = \sqrt{\langle x^2\rangle}$ where $$ \langle x^2\rangle = \frac{1}{\tau}\int_{-\tau/2}^{\tau/2}x^2dt $$ The Fourier...
  4. J

    How does distance affect light intensity according to the inverse square law?

    Homework Statement I have a general question about light and Lumens and the inverse square law? So Intensity = Initial Lumens/Lenth^2 So @ a Length of 1, there is no loss of light intensity. What unit is this 1. 1 meter? 1 foot? Homework Equations The Attempt at a...
  5. S

    Mutual Inductance Between Square and Circle Circuit

    Homework Statement There are two circuits in the XY plane: one is a square (side 0.2 m in length) centered on the origin. The second is circle or radius r also centered on the origin. The circle is smaller than fits inside) the square. By assuming the radius of the circle is small compared...
  6. B

    Energy levels of a 3 dimensional infinite square well

    Homework Statement Calculate the wavelength of the electromagnetic radiation emitted when an electron makes a transition from the third energy level, E3, to the lowest energy level, E1. Homework Equations E_n = \frac{\left (n_{x}^{2}+n_{y}^{2}+n_{z}^{2} \right) \pi^{2}...
  7. V

    Buckling limit of a square plate over a circular hole

    Hi, I am carrying out a series of experiments which consist of a square plate object placed over a circular hole. The experiment is done in such a way that I can apply a point force at the center of the plate and see how much force is required to pull the plate through the hole. I should add...
  8. C

    Does EM Radiation Dissipate at a 1/r^5 Ratio for Circularly Polarized Waves?

    inverse square vs cube = ? If the electric field falls off at the inverse square ratio, and magnetic at inverse cube, does EM radiation dissipate at 1/r^5 ratio for circularly polarized waves?
  9. W

    Aluminum square tubing strength

    I am wondering if anyone would be so kind as to help me with a project. I am wondering what size aluminum square tubing it would take to build a "T" with the horizontal top being 4 feet in length and being able to hold 250 lbs. at each end and 1 ft. in from each end, totalling 1,000 lbs. I...
  10. T

    Infinite Square Well for Bosons in an optical lattice

    I'm working on a research project and was wondering what you could use to experimentally create a periodic infinite square well (dirac comb?) in a direction orthogonal to a different potential, say a periodic potential. To help you understand what I'm trying to do picture a grid of atoms and...
  11. 1

    (for fun) Any non-perfect square has an irrational 2nd root

    Homework Statement I'm trying to see if I can prove that any non-square number's square root is irrational. I'm using only what I already know how to do ( I like trying to prove things myself before looking up the best proof), so it's going to be round-about. Attempt#1 Eventually required me...
  12. M

    Why Do Matrix Expressions Often Involve A A^T in Factorization?

    Hi All, I often see this term when factorizing out a matrix from brackets A(some other term)A^T where I assume A A^T represents the square within the bracket term, can someone explain the reasoning behind expressions of this kind or point me in the correct direction Many thanks
  13. G

    Square lemma for Paths, Homotopy

    Homework Statement In Lee's "Topological Manifolds", there is a result on page 193 called "The Square Lemma" which states that if I denotes the unit interval in \mathbb{R}, X is a topological space, F\colon I\times I\to X is continuous, and f,g,h,k are paths defined by...
  14. I

    Fourier Series Convergence for Square Wave Function

    Homework Statement what values does the Fourier series for f(t) converge to if t = 0 and t = 2? Homework Equations The Attempt at a Solution My answers the red rectangles for the even function t=0 >> 1 and t=2 -->1.5 and odd function t=0 >> 0 and t=2 -->1.5 because at t=0 is continuity...
  15. Sudharaka

    MHB Marie's Question from Facebook about Square Roots

    Marie on Facebook writes:
  16. B

    How Many Bound States Exist in a Half Finite Square Well?

    Homework Statement A particle of mass m is in the potential V(x) = \left\{ \begin{array}{rl} \infty & \text{if } x < 0\\ -32 \hbar / ma^2 & \text{if } 0 \leq x \leq a \\ 0 & \text{if } x > a. \end{array} \right. (a) How many bound states are there? (b) In the highest energy...
  17. H

    What Is the Correct Unit for Mean Square Velocity?

    hi... we know the unit of velocity is m/s2 and while calculating the mean square velocity we find the average(or mean) of the 'squares' of the given velocities. then the unit of MEAN SQUARE VELOCITY should be 'm2/s4' then how come its unit is also m/s2 and not m2/s4 ?
  18. X

    Log base 2 is the same thing as square root?

    Hi, Is is correct to say that the logarithm of base 2 of a number x, is the same thing as the square root of a number x?
  19. 8

    Group velocity in infinite square well

    ello everybody, how can I calculate the group velocity of a wave package in an infinite square well? I know only how it can be calculated with a free particle, the derivation of the dispersion relation at the expectation value of the moment. But in the well, there are only discrete...
  20. G

    Square root of a squared block matrix

    Hi everybody, I’m trying to compute the square root of the following squared block matrix: \begin{equation} M=\begin{bmatrix} A &B\\ C &D\\ \end{bmatrix} \end{equation} (that is M^(1/2))as function of A,B,C, D which are all square matrices. Can you help me? I sincerely...
  21. B

    Proof of square root 3 irrational using well ordering

    The part I don't understand is how they show there exists a smaller element. They assume s=t√3 is the smallest element of S={a=b√3: a,b€Z} . Then what they do is add s√3 to both sides and get s√3-s=s√3-t√3. I don't get how they thought of that or why it works.I know there exists an element...
  22. P

    Algebra step confusion and unnatural completing the square

    Let f(x) = ax - \dfrac{x^3}{1+x^2} where a is a constant Show that, if a ≥ 9/8 then f'(x) ≥ 0 first problem when taking the derivative in the solution they seem to have jumped a step which I don't see how: f'(x) = a - \dfrac{3x^2(1+x^2) - 2x(x^3)}{(1+x^2)^2} = \dfrac{a + (2a - 3)x^2 + (a...
  23. T

    How Do You Calculate the Derivative of sin(sqrt(3x+5))?

    Homework Statement Finding derivative of (sin(sqt3x+5)) Homework Equations None given. Chain Rule The Attempt at a Solution The answer is: (cos(sqrt3x+5)) * 1/2(sqrt3x+5) * 3 but I don't know how to get to the 3. I turned sin into cos and multiplied by the inside derivative giving the...
  24. T

    MHB How Is the Integral of the Square of Log-Sine Calculated?

    Prove that $$\int_0^{\pi/2} (\log \sin x )^2 dx = \frac{1}{24} \left(\pi ^3+12 \pi \log^2(2)\right)$$
  25. S

    What Does It Mean for k to Be a Square Modulo m?

    k is a square modulo m?? \:Homework Statement This is a portion of the problem. I have to prove that A holds if and only if k is a square modulo m. I have no idea what "k is a square modulo m" means. Homework Equations The Attempt at a Solution I've looked it up online and found some PDF's...
  26. I

    Rational Completeing the Square

    Homework Statement Homework Equations The Attempt at a Solution Alright so the solution is in the above pic, but I can't get anywhere close. You can see from the green circles that the "squares" aren't matching up. So I'm not sure if I can't multiply fractions anymore or what.
  27. Q

    Make a triangular matrix from a square matrix

    dear users I have a problem in finding eigenvalues of a 12*12 because the 12*12 matrix is so complicated so i decided to first make my 12*12 matrix in form of upper triangular form but I don't know how can I do it with MATLAB or mathematica? can you please tell me that what is the formula in...
  28. Albert1

    MHB Big Square composed of Small Squares ?

  29. R

    Getting the components of a sum of square waves

    If I have a periodic function that is say a sum of a number of sine functions I can use a Fourier Transform to get the component functions. Now, if I have a bunch of square waves of differing amplitudes and frequencies that I add up into a resultant waveform. Given that waveform what'd be...
  30. P

    Why n*p always equal to ni square? (semiconductor)

    Why n*p always equal to ni square?? (semiconductor) Hi, For you guys who studied semiconductor physics must be familiar with the equation: np=ni2 I can understand why this is true for the intrinsic case (the broken bonds would always provide electron and hole in pairs ) But why is this...
  31. A

    Find the electric field of a square at a given point?

    Homework Statement Two tiny objects with equal charges of 6.00uC are placed at the two lower corners of a square with sides of 0.580m. When facing the square, Point A is the top left corner. Point B is in the top middle. Point C is dead center inside the square. Find the electric...
  32. T

    Why does n^(c/n) approach 1 as n approaches infinity?

    My book is showing this as an intuitive step, but I'm not quite seeing the reasoning behind it. n**(c/n) → 1 as n → ∞, for, I think, any positive c. But why?
  33. P

    How Does Periodic Potential Affect the Energy Spectrum of a Bose Gas?

    Homework Statement Suppose an ideal bose gas sees a periodic potential with a period a in both x and y directions. Its eigenstates are altered from the free-particle form. The lowest band has energies \epsilon_\vec{k}=2t(2-cos(k_xa)-cos(k_ya)) where t is an energy scale that depends on the...
  34. C

    Proof about an integer being a perfect square.

    Homework Statement m and n are positive integers with m,n≥2 where m^2=kn^2 The Attempt at a Solution we know that all prime factors of m have an even amount , their are no prime factors that are repeated an odd number of times. The same goes for n. if k is not a perfect square...
  35. M

    Generating a square wave with a PIC12F

    Hi, using a PIC12F683 I'm attempting to toggle an IO pin every time the internal timer overflows (via the timer interrupt) but I can't seem to get it working. I'm viewing the voltage of the pin on a scope, expecting a square wave and getting a constant 5 volts. Also I've read the official...
  36. V

    General algorithm for a magic square

    Is there any algorithm to form a magic square of any size with a desired magic sum ? Also can we make a magic square not only with the numbers from 1 to n2 but using any random numbers ?
  37. B

    Proving the Inequality in Newton's Square Root Method

    Homework Statement Let e be the number close to sqrt(a) by Newtons Method (That is picking a number, diving a by it, and taking their average, divide a by average, get a number, find their average, so on). Using |e<sqrt(a)+e| prove that if |a/e-e|<1/10 then |sqrt(a)-e|<1/10 Note that e is...
  38. D

    Potential Function of Infinite Square Well - Help Needed!

    Please I'm new here, and would need your help with identifying what sort of potential function is described by the following expression: V(x) = 0 for |x| < 1, =1 at x = \pm 1, and =\infty for |x|>1. (Note that: \pm is plus (+) or minus (-) sign). Could it be referred to as the infinite...
  39. A

    Expected values in infinite square well

    Ok...this must sound stupid, because i didn't found answer on the web and on my books...but i am having trouble with the infinite square well. I want to calculate <x>. V(x)=0 for 0<=x<=a <x>=\frac{2}{a}\int^{a}_{0} x \sin^2(\frac{n\pi}{a}x)dx Doing integration by parts i got to...
  40. T

    Question about expanding a square root in powers of gradient

    Hi, I have a quick question about making quantum mechanics relativistic by simply replacing the hamiltonian by a relativistic hamiltonian. If we write the hamiltonian operator as: H = \sqrt{P2c2 + m2c4}, schrodinger's equation in position basis becomes: i\hbar\dot{\psi} =...
  41. Z

    Unraveling the Mystery of Quantum Mechanics: Square Wells & Momentum

    Homework Statement Here's an image http://i.imgur.com/oC8Y6.jpg Homework Equations The wave function for an infinite square well, the expectation values and operators for momentum and I guess the normalization condition? I don't really know because I don't understand the question. The...
  42. S

    Laplace equation in a square with mixed boundary conditions

    The length of the side of the square is a. The boundary conditions are the following: (1) the left edge is kept at temperature T=C2 (2) the bottom edge is kept at temperature T=C1 (3) the top and right edges are perfectly insulated, that is \dfrac{\partial T}{\partial x}=0,\dfrac{\partial...
  43. STEMucator

    Complete the square ( Potentially )?

    Homework Statement There was a question on my exam a few days ago. Using Lagrange to find the max/min on a region. We only had to answer a certain amount of questions and I never got to this one. I'm working on it now though out of curiosity. R = { (x,y) | x2 + xy + y2 ≤ 3 } f(x,y) =...
  44. F

    Infinite square well expectation value problem

    Homework Statement A particle in an infinite box is in the first excited state (n=2). Obtain the expectation value 1/2<xp+px> 2. The attempt at a solution Honestly, I don't even know where to begin. I assumed V<0, V>L is V=∞ and 0<V<L is V=0 I tried setting up the expectation...
  45. Kushwoho44

    Not sure what square brackets indicate when dealing with partial derivates

    Hi guys, attached is a picture of my problem and it is also underlined. I've been reading through this theory and I just don't understand what the square brackets indicate. I understand that ∇phi is the partial derivative with respect to the scalar function phi. But what is ∇phi...
  46. W

    Strength of Square Steel Tubing

    Hi I'm a high school student and need help with the calculations for a bike design. I am required for the design to use 1.5" mild steel square tubing at 1/16" thick for it. I need to know what the strength of the tubing is before i can make or tweak the design. Can anyone help with my predicament?
  47. M

    Line integral of a vector field over a square curve

    Homework Statement Please evaluate the line integral \oint dr\cdot\vec{v}, where \vec{v} = (y, 0, 0) along the curve C that is a square in the xy-plane of side length a center at \vec{r} = 0 a) by direct integration b) by Stokes' theoremHomework Equations Stokes' theorem: \oint V \cdot dr =...
  48. C

    Derivative of matrix square root

    If I have a matrix valued function A(x) of some scalar x, how do I compute the derivative of the square root of A with respect to x? It seems like it should be simple, but I can't find it anywhere on the internet. Thanks!
  49. M

    A is not square but rank(A) = rank(A') ?

    A is not square but rank(A) = rank(A') ? Hi Can anyone help with understand a basic idea, I have a matrix A in MATLAB which is 100x3000. I have checked and there exist many columns of A that are all zeros. But apparently rank(A) = rank(A') = 100 Wikipedia states that the rank of an m x n...
  50. C

    Radicals equations-negative square root and two radicals

    Is the answer to sqrt -81y^3 : y sqrt-81y? or is there no real solutions? Also for this radical equation: sqrt 2n-5 - sqrt 3n+4=2 I worked it out and can't seem to get an answer. Is there no real solutions?
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