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. 1

    Square root of a Mersenne Number is irrational

    Homework Statement A user on math.se wanted to prove that any Mersenne number m = 2^n - 1 has an irrational square root for n > 1. So, it can be proved rather easily that any non-perfect square has an irrational root, and that all of the numbers to be considered are not perfect squares...
  2. LunaFly

    Time Dependent Wave Function for Particle in Infinite Square Well

    Homework Statement A particle is in a bound state of the infinite square well. It is in a state represented by the following wavefunction, written here at t=0: ψ(x)= -√(2/3)√(2/L) * sin (3πx/L) + i*√(1/3)√(2/L) * sin (2πx/L) (a)Write the full time-dependent wavefunction for this state...
  3. S

    Wave function in infinite square well, with potential step

    Homework Statement A Particle energy A trapped in infinite square well. U(x)=0 for 0<x<L and U(x)=U0 for L<x<2L. find the wave function of the particle when A) E>U0 B) E<U0 C) E=U0. Homework Equations 1-D time independent Schrodinger equation. The Attempt at a Solution I have...
  4. G

    Inverse Square Law: Total Power at Earth per Unit Area

    Homework Statement The intensity (I) of sunlight (the received power per unit area) drops with distance (d) from the sun according to the inverse square law - i.e I2/I1 is proportional to (d1/d2)^2 What is the total power received at Earth (above the atmosphere) per unit of surface area...
  5. A

    If A and B are invertible square matrices, there exists

    Homework Statement If A and B are invertible matrices over an algebraically closed field k , show there exists \lambda \in k such that det(\lambda A + B) = 0 .The Attempt at a Solution Can anyone agree with the following short proof? I tried looking online for a confirmation, but I wasn't...
  6. L

    EMF in a square loop due to magnetic field from an infinite wire

    Homework Statement Determine the emf induced in the square loop in the figure if the loop stays at rest and the current in the straight wire is given by I(t)=(15.0A)sin(2500t) where t is in seconds. The distance a is 12.0 cm, and b is 15.0 cm. Homework Equations emf = Δmagneticflux/Δt...
  7. J

    Dimensioning of hollow square and circular rod

    Hi Can someone tell me how to determine dimensions for a square hollow rod and circular hollow rod when the material and maximum load is known?
  8. T

    Inverse Square Law: Magnifying Glass & Sunlight

    I found this forum on Google. This may not be the right section so excuse me if so. I have a rather simple question though. When you take a magnifying glass on a sunny day and position it just right over a piece of paper, the paper will start to burn. Is the inverse square law (distance) the...
  9. kmm

    Should the Normalization Constant be Positive or Complex?

    In finding solutions to the time independent Schrodinger equation we have to normalize \psi to find the constant A. So we get \int_{0}^{a} |A|^{2} sin^{2}(kx) dx = |A|^2 \frac{a}{2}=1 For A we then get |A|^2 = \frac{2}{a} . Griffiths says that this only determines the magnitude of A but...
  10. S

    What is the electric field at q due to 4 charges in a square configuration?

    http://puu.sh/7MuKv.jpg I'm not sure what equation to apply in this situation. I'm lead to believe Ke((|q1||q2|) / a) Is what I should be applying.The Attempt at a Solution No idea thus far.
  11. E

    Why does conditional probability used in mean square error equal zero?

    Hi guys, I am having trouble showing that \mathbb{E}\left[(Y-\mathbb{E}[Y|X])^{2}\right]=0. I understand the proof of why E[Y|X] minimizes the mean square error, but I cannot understand why it is then equal to zero. I tried multiplying out the square to get...
  12. N

    Electric field strength of 4 charges positioned in a square shape

    Homework Statement Four charged particles are at the corners of a square of side a as shown in the figure below. (Let A = 3, B = 5 and C = 6.) (a) Determine the electric field at the location of charge q. (Use the following as necessary: q, a, and ke.) (b) Determine the total...
  13. S

    How Do You Calculate the Net Torque on a Square Plate?

    Homework Statement A square metal plate 0.180 m on each side is pivoted about an axis through point O at its center and perpendicular to the plate (Figure 1) . Calculate the net torque about this axis due to the three forces shown in the figure if the magnitudes of the forces are F1 = 25.0N ...
  14. MarkFL

    MHB Radius of Sphere Inscribed in Square Pyramid: Michelle's Q&A

    Here is the question: I have posted a link there to this thread so the OP can view my work.
  15. Albert1

    MHB Manipulation of square root function

    $\dfrac {\sqrt {3-3x}+\sqrt {x+6}}{\sqrt {1-4x}+\sqrt {2x+8}}=\dfrac {\sqrt {3-3x}-\sqrt {x+6}}{\sqrt {1-4x}-\sqrt {2x+8}}$ please find :$x$
  16. MarkFL

    MHB Kim's Questions on Babylonian Method for Estimating Square Roots

    Here are the questions: I have posted a link there to this thread so the OP can view my work.
  17. L

    What is the Mean Square of a Signal and Why is its Time Average Zero?

    I was reading about noise and noise voltage/root hertz here - http://www.stanford.edu/class/me220/data/lectures/lect02/Noise_writeup.pdf What exactly is mean square. why do we need Mean square. How do we know time average of noise voltage is zero?
  18. N

    MHB Square Matrix Proof: Diagonal Entries & Properties

    Hi, I have two questions. firstly; 1) If M is the coefficient matrix of a linear system, Mx = 0, what are the solutions? Describe the set of solutions geometrically. Now this is just a trivial solution since x = 0, but to describe the solution geometrically, how would you do that? Do you just...
  19. P

    Raising to half power = PRINCIPAL square root?

    This may seem like a very elementary question...but here goes anyway. When a positive number is raised to the power 1/2, I have always assumed that this is defined as the PRINCIPAL (positive) square root, e.g. 7^{1/2} = \sqrt{7},. That is, it does not include both the positive and negative...
  20. C

    Normalizing a State Function for an Infinite Square Well

    Homework Statement Normalize: \Psi_1 (x,t) = N_1 \cos(\frac{\pi x}{L}) e^{-\frac{iE_1t}{\hbar}} Where N_1 and E_1 are the normalization constant and energy for the ground state of a particle in an infinite square well. Homework Equations Normalization Condition: \int_\infty^\infty P(x,t)...
  21. evinda

    MHB Prove that number is not a perfect square

    Hey! :) Prove that no number of the form $3k-1$ is a perfect square. Do I have to use the theorem: "If n is a positive integer such that n mod(4) is 2 or 3, then n is not a perfect square",or is there also an other way?
  22. C

    Number Theory - Proving x is not a perfect square?

    Hey Guys, This is my first post to Physics Forums. If I posted this question in the wrong area or am violating some other etiquette, please let me know! I'm working on a proof and am currently stuck. I'm trying to prove that x (a weird number, an infinite product to be specific), is NOT...
  23. N

    Integral involving square root and exp

    Homework Statement \int\frac{dx}{\sqrt{e^{x} + 1}} Homework Equations Using u-substitution The Attempt at a Solution Let u = \sqrt{e^{x} + 1} \Rightarrow u^{2} - 1 = e^{x} Then, du = \frac{e^{x} dx}{2\sqrt{e^{x} + 1}} \Rightarrow dx = \frac{2u du}{u^{2}-1} So...
  24. U

    Delta wall and infinite square well potentials ,and 2 other questions

    Consider the following potential function: V=αδ(x) for x=0 and V=∞ for x>a and x<-a , solve the shroedinger equation for the odd and even solutions. solving the shroedinger equation I get ψ(x)=Asin(kx) +Bcos(kx) for -a<x<0 and ψ(x)=Asin(kx) +Bcos(kx) for 0<x<a is it...
  25. M

    MHB Show that the number a is not a square of an integer

    Hey! :o I have to show that the number $a=201340168052123987111222893$ is not a square of an integer, without doing calculations.Could I solve this in $\mathbb{Z}_8$? I mean that the number $a$ can be written as followed: $$a=3+9 \cdot 10 +8 \cdot 10^2 + 2 \cdot 10^3+...$$ Since at...
  26. evinda

    MHB Show that x^2+y^2 is not a square

    Hello! :) Let $(x,3)=(y,3)=1$.Show that $x^2+y^2$ is not a square.How can I do this? I thought that I could use these relations: $$ax+3b=1$$ $$yc+3d=1$$ But,using them I found: $x^2+y^2=\frac{cx(1-3b)+ay(1-3d)}{ac}$.. I think that we can't conclude it from this..or am I wrong?? :confused:
  27. M

    What is the Constructibility of the Square Root of 2?

    Sorry for any mispellings, English is not my first language. So, I'm studying irrational numbers and I got curious about something and my teacher couldn't give me the answer. I understand Pi must exist because it's the simple result of a division (perimeter by diameter). But how can the...
  28. U

    Transcendental equation from a finite square well potential

    if I have a transcendental equation such as this one: tan(l a) = -l / sqrt (64/a^2 - l^2 ) Where l=sqrt(2m(E+V) /hbar^2 ) and 'a' is the width of a finite square well, how can I solve this equation in terms of both l and a. I have successfully graphed the two sides of the equation...
  29. B

    Approximate transmission coefficient of a square barrier

    Homework Statement Two conductors are separated by an insulator. Model the insulator as a square barrier of height 0.01 keV and a width of 5nm. Determine the transmission coefficients for electrons of 7,000 meV. The only thing is I have to use the approximation formula for finding the...
  30. anemone

    MHB Square of Integer: Showing Integer's Square

    Show that $\displaystyle \sum_{k=0}^{2013} \dfrac{4026!}{(k!(2013-k)!)^2}$ is the square of an integer.
  31. S

    MHB How do I complete the square for $6z + 5$ without a third number?

    How do you complete the square of $6z + 5$ if there isn't a third number. Can someone show me real quick? I've just forgot. First I was thought it would be like 6z + (5/2)^2 + 5 so 6z + 25/4 + 5. Yea I know this is easy, I'm doing it wrong though... In all I just need help completing the...
  32. P

    Net force on a charge in a square

    Homework Statement There are 4 charges in the corner of a square with the lengths of the sides measuring 18.2cm q1= 2.34μC (top left) q2=-1.58μC (top right) q3= 2.03μC (bottom left) q4= -3.00μC (bottom right) →Calculate net force on q4 →Calculate net force at the center of the square...
  33. S

    Vibrational Motion - Calculating Mean Square Displacement

    Homework Statement Calculate the mean square displacement x2 of the particle from its equilibrium position.Homework Equations ∫ from -\infty to +\infty of Nv2 * Hv(y) * e-y^2 dy Since y=x/\alpha, \alphady=dx yHv = vHv-1 + (1/2)Hv+1The Attempt at a Solution...
  34. S

    Algebra and square root simplification

    Homework Statement Points A and B are 10 km apart and it is determined from the sound of an explosion heard at those points at different times that the location of the explosion is 6 km closer to A than B. Show that the location of the explosion is restricted to a particular curve and find...
  35. A

    MHB How to Integrate (x^2 + 2x + 1)sqrt(4x^2 + 8x + 5)?

    how do i integrate (x^2 + 2x + 1)sqrt(4x^2 + 8x + 5)??
  36. M

    How do Galilean transforms affect wave equations?

    Hi, if oyu look at question 16b in the link below in order to get the second derivative wrt to t they take the square of the first derivative. I don't get it, how does multiplying the first derivative by itself get you the second derivative...
  37. W

    MHB Solving how many square inches within a flag

    Hello all. I'm new here. Trying to help my daughter with her homework but I can't solve this problem wondering if there is any out there that is willing to help. Thanks a Head of time.
  38. F

    Complex Square Root Analyticity

    Homework Statement Let f(z) denote the multivalued function (z^{2} − 1)^{1/2} . Define a branch of f(z) which is analytic in the interior of the unit disk |z| < 1 2. The attempt at a solution Having a bit of trouble getting started. I have rewritten f(z) as ((z-1)(z+1))^{1/2} as...
  39. N

    Why Does Completing the Square Yield Complex Numbers in This Equation?

    Hi, I am having trouble with completing the square in this question. I've looked at several online videos and I am still confused as to why I am not getting an answer that makes sense. I keep ending up with complex numbers and I am not sure what the next step to take is. Homework...
  40. N

    Calculating Mean Square Error with Pseudo Inverse Approach

    Find the mean square error using the pseudo inverse approach. I am given a 11X9 matrix A, a 11X1 vector F and R = 11X11 diagonal matrix so Rhat = A[(A'A)^-1 ]A' R . Then I get a 11X11 matrix. Shouldn't I get getting a 8X11 matrix How do I get the most optimum vector F?
  41. kaliprasad

    MHB 3 consecutive terms of AP that are perfect square

    find parametetric representation of 3 perfect squares which are successive terms in AP ($x^2$,$y^2$,$z^2$) such that $x^2,y^2,z^2$ are successive terms of AP. find x,y,z
  42. P

    How Do You Calculate Electric Field and Force in a Charged Square?

    Homework Statement A square has a charge at each corner. The square is 2cm x 2cm. In the upper left corner there is 1μc, in the upper right corner there is 2μc, the lower right corner there is 3μc, and the lower left corner there is 4μc. A. What is the magnitude and direction of the...
  43. S

    MHB How do I calculate the center of a square given its position and orientation?

    Hi, I want to find the world coordinates of the center of a square given: -The top left corner is the reference point -Its position relative to the world frame -Its orientation relative to the world frame The example that I have been using is that the square is at (0,2), has 0 orientation...
  44. S

    Root Mean Square Speed Units Question

    Homework Statement "At 273 K and 1.00x10^-2 atm, the density of a gas is 1.24x10^-5 g/cm^3. A.) Find the Vrms for the gas molecules B.) Find the molar mass and identify the gas (Choose from H2, He, H20, N2, O2, or CO2)" Homework Equations Vrms = √(3RT/Mm) pV = nRT The Attempt...
  45. J

    Normalization of the infinite square well.

    I have been going through my textbook deriving equations in preparation for my test on QM tomorrow. I noticed in the infinite square well that i was unable to complete the normalization. My textbook, Griffiths reads : (integral from 0 to a) ∫|A|^2 * (sin(kx))^2 =|A|^2 * (a/2) =1 Therefore...
  46. Saitama

    Bug on a hinged square metal frame

    Homework Statement A square metal frame in the vertical plane is hinged at O at its centre as shown in the figure. A bug moves along the rod PN which is at a distance ##l## from the hinge, such that the whole frame is always stationary, even though the frame is free to rotate in the vertical...
  47. F

    Two dimensional Square well and parity

    Homework Statement A particle is placed in the potential (a 2 dimensional square well) V(x) = (0 for -a/2 <= x =< a/2 and -a/2 <= y =<a/2, infinity for x>a/2, x<-a/2 and y>a/2, y<-a/2) The hamiltonian commutes with the parity operator P, Pψ(x,y) = ψ(-x,-y) = λψ(x,y), where the eigenvalue λ...
  48. C

    Proof that the Square Root of 2 is Irrational.

    I am trying to prove that √2 is irrational using proof by contradiction. Here is my work so far: √2 = p/q where p & q are in their lowest terms. Where q is non-zero. 2=p2/q2 2q2 = p2 Which tells me that p2 is an even number, using the definition of an even number. We can use this definition...
  49. E

    Implementation of the Numerov Method for the 1D square well

    I want to solve the Schrodinger via the Numerov Method but I had some troubles. I'm programing in C++, so here is my code: #include<cstdlib> #include<iostream> #include<cmath> using namespace std; double x_min=-4.0 , x_max=4.0; int N=2000; double...
  50. J

    Calculating the root mean square speed from pressure and density.

    Homework Statement A tyre contains gas at a pressure of 150 kPa. If the gas has a density of 2.0 kg m-3, find the root mean square speed of the molecules. Homework Equations These are the equations I believe to be relevant: c_{rms} = \frac{\sqrt{<c^2>}}{N} pV = \frac{1}{3}Nm<c^2> p =...
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