What is Square: Definition and 1000 Discussions

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. B

    Square root of a 0 matrix

    At first I thought that there is no square matrix whose square is the 0 matrix. But I found a counterexample to this. My counterexample is: \left( \begin{array}{cc} 0 & 0 \\ 0 & 1 \end{array} \right) However it appears that my counterexample has a 0 row. I'm curious, must a square root of...
  2. M

    Explain how any square matrix A can be written as

    Homework Statement a) Explain how any square matrix A can be written as A = QS where Q is orthogonal and S is symmetric positive semidefinite. b) Is it possible to write A = S_1 Q_1 Where Q1 is orthogonal and S1 is symmetric positive definite? Homework Equations A = U \Sigma...
  3. T

    Optimizing Knights on 8x8 Chess Board with Integer Programming

    Homework Statement On a 8x8 chess board format an Integer program to optimize the amount of knights required such that every square is covered by at least one knight. Homework Equations I know of a similar problem where we use duality for the placing 5 queens such that the maximum...
  4. G

    A function for a line in a square (or a triangle or a etc)

    a function for a line in a square (or a triangle or a pentagon etc) I don't have one off the top of my head (my maths is very rusty) but I think that ,starting from a cartesian point it is possible to create a function that allows one to draw a polygon in 2 or 3(?) dimensions. This...
  5. B

    Scalar product square matrix hermitian adjoint proof

    Homework Statement If M is a square matrix, prove: (A, MB) = (adj(M)A, B) where (A, MB) denotes the scalar product of the matrices and adj() is the adjoint (hermitian adjoint, transpose of complex conjugate, M-dagger, whatever you want to call it!) Homework Equations adj(M)=M(transpose of...
  6. R

    Differential and square of differential

    Hi I often see the following in books but I do not understand how they are equal. So can someone please tell me for what conditions does the following equality hold? (\frac{dy}{dx}) 2 = (d2 y)/(dx2)
  7. nukeman

    Finding derivative of a square root - Quick question

    Homework Statement Ok, working on a inverse function question, and I got stuck with something. Can someone explain the steps that makes this possible here. Something I am missing :( f(x) = √(x^3 + x^2 + x + 1) How is the inverse of the above function this... 3x^2 + 2x + 1 / 2√(x^3 + x^2 +...
  8. N

    Multiplying a vector with Square Matrix vs. its transpose

    Hi, I am new to Math so I am trying to get some intuition. Let's say I have a matrix A of n x n and a vector B of n x 1 what is the difference between A x B and A' x B? Thanks
  9. R

    What is the correct method for solving the infinite square well energy problem?

    Hi I have attached my attempt of solving the infinite square well for Energy. The value I get is different from that of the book, also in the attachment, Kindly explain if my answer is correct given the fact that I proceeded step by step and used no tricks. Thank you.
  10. V

    Square of transpose of two matrices

    Homework Statement Let A and B be two square matrices of order n such that AB = A and BA = B. Then, what is the value of [(A + B)t]2? Homework Equations The Attempt at a Solution [(A + B)t]2 = AtAt + AtBt + BtAt + BtBt. I tried to use the fact that AB = A and BA = B to keep...
  11. B

    Reduced row echelon form of a square matrix

    I am wondering about the relation betwen RRE forms and identity matrices. Consider the reduced row echelon form of any square matrix. Must this reduced row echelon form of the matrix necessarily be an identity matrix? I would suppose yes, but can this fact be proven? Could anyone provide an...
  12. J

    Heisenberg interaction Hamiltonian for square lattice

    Hi, I just started self studying solid state and I'm having trouble figuring out what the hamiltonian for a square lattice would be when considering the Heisenberg interaction. I reformulated the dot product into 1/2( Si+Si+δ+ +Si+δ+S-- ) + SizSi+δz and use Siz = S-ai+ai Si+ =...
  13. ElijahRockers

    Infinite Square Well (Quantum Mechanics)

    Homework Statement An electron is trapped in an infinitely deep potential well 0.300nm in width. (a) If the electron is in its ground state, what is the probability of finding it within 0.100nm of the left-hand wall? (b) Repeat (a) for an electron in the 99th excited state (n=100). (c) Are...
  14. ElijahRockers

    Finding the eigen function for an infinite square well (quantum mechanics)

    Homework Statement Quantum mechanics is absolutely confusing me. A proton is confined in an infinite square well of length 10-5nm. Calculate the wavelength and energy associated with the photon that is emitted when the proton undergoes a transition from the first excited state (n=2) to the...
  15. T

    Inverse square law resolves Olbers' paradox

    Treatment originally used to discard inverse square law as solution to Olbers' paradox was not set up correctly. If we include sensor (camera) in the treatment and model light as photons the result describes what we actually see.
  16. D

    Prove that the square of any integer, when divided by 3. only by odd and even.

    Homework Statement I know you could prove this by stating every integer is either 3m, 3m+1 or 3m+2. However I am trying to prove this just using either even numbers or odd numbers. so for example, when I try: (2x+1)^2 = 4x^2 + 4x + 1 - expand = 3x^2 + x^2 + 3x + x + 1 - group like...
  17. S

    Proving square root of 2 is irrational with well ordering principle?

    Homework Statement I know how to prove that square root of 2 is irrational using the well ordering principle but what I'm wondering is, how can we use the well ordering principle to prove this when the square root of two isn't even a subset of the natural numbers? Doesn't the well ordering...
  18. D

    MHB Equations of Sides of Square Inscribed in Circle

    Find the equations of the sides of square inscribed in the circle $3(x^2+y^2)=4$, one of whose sides is parallel to the line $x-y=7$.
  19. T

    Light in vacuum and inverse square law

    Does inverse square law apply to light in vacuum?
  20. A

    How do you use a chi square table?

    For example, if the moment generating function is (1-2t)^(-6), then the degree of freedom r=3, right? The question is asking me to find P(X< 5.23)...I want to use the chi-square table, but I'm not sure how... This is what the question states: If (1-2t)^{-6}, t<1/2, is the mgf of the...
  21. T

    What is the square root of x^2?

    It can't be x, because you get a positive number when x is negative.
  22. S

    Electrostatic Separation of Variables in a Square Pipe

    Homework Statement I'm solving a problem where a conducting pipe with a square cross section is being analyzed to find the potential everywhere in space. The pipe lays along the z-axis, so we're really concerned with the x-y plane. My issue isn't so much the general solution via separation...
  23. M

    Best way to produce a 10-40kHz square wave

    Hi! I should probably start off by saying that I did attempt to search for this, but I wasn't able to find a thread that had a similar question. I'm driving an RLC network (in effect) with a square wave to saturate a ferrite core. The image is pretty close to what I'm trying to achieve. I...
  24. U

    Condition for this polynomial to be a perfect square

    Homework Statement The condition that x^4+ax^3+bx^2+cx+d is a perfect square, is Homework Equations The Attempt at a Solution If the above polynomial will be a perfect square then it can be represented as (x-\alpha)^2(x-\beta)^2 where α and β are the roots of it.This means that two...
  25. A

    Biology Punnet Square Question

    Homework Statement The Xolo is the national dog of Mexico. The striking characteristic of this dog is that it has no hair. Xolos carry a mutation in Chromosome 17 that, when homozygous, is lethal. If two hairless Xolos were mated, what fraction of their surviving offspring would be...
  26. M

    Infinite Square Well Electron Jumps from n=4 to ground state

    Homework Statement An electron is trapped in an infinite square-well potential of width 0.5 nm. If the electron is initially in the n=4 state, what are the various photon energies that can be emitted as the electron jumps to the ground state?Homework Equations ΔE=13.6(1/nf2-1/ni2)...
  27. M

    A flat, square surface with side length

    Homework Statement A flat, square surface with side length 3.00cm is in the xy-plane at z=0 . Calculate the magnitude of the flux through this surface produced by a magnetic field B=(0.150T)i+(0.350T)j-(0.500T)k What I'am doing is I know that the magnetic flux= BAcos(theta) So I...
  28. C

    Solving for Eigenvalues in a Finite Square Well with Both Walls Finite

    Homework Statement Already defined that for a 1D well with one finite wall the eigenvalue solutions are given by k cot(kl) = -α Show the eigenvalue solutions to well with both walls finite is given by tan(kl) = 2αk / (k^2 - α^2) Well is width L (goes from 0 to L) with height V_0...
  29. L

    Surface area of a square and a tube

    Ok, so if I have a square that is exactly 10 inches by 10 inches, then the surface area is 100 square inches exactly. But if I roll up that square into a tube and calculate its surface area, it's 2∏r times the length. And since the calculation involves ∏, that means I won't get an exact answer...
  30. L

    Incorporating Inverse Square Law In Gravity

    First of all, I'm 13 so I might not comprehend the complex vocabulary or symbols others might use. Second, I just joined! Okay, let's get to it. I think I know what the inverse square law is: if a number goes up by x, then the other number is the square of x but in the negative side...
  31. D

    MHB Mean square convergence of Fourier series

    What is the statement of the mean square convergence of Fourier series?
  32. M

    What is the Maximum Distance in a 300x300 Square?

    Six points have to be the maximum distance from each other within or on the sides of the square, what is the distance?
  33. C

    Square of a finite deltafunction

    Hi. I'm reading "Quantum Field Theory - Mandl and Shaw" about how to derive the cross-section and in the derivation the authors make the following argument "For large values of T and V, we can then take \delta_{TV}(\sum p_f' - \sum p_i) = (2\pi)^4 \delta^{(4)}(\sum p'_f - \sum p_i) and...
  34. S

    Square wave symmetric around zero volts

    Hi everyone For a pre-lab, I am asked to draw a square wave symmetric around zero volts. I am not sure what this graph looks like, can someone give me an example? Thank You
  35. W

    Quick simplification/factoring of a square root

    If you could see the image attached, I think it looks better than me typing it here. Didn't know how to embed the image. I would just like to know how it becomes 2v to √2v. EDIT: Ignore. Figured it out. Don't know why I was even baffled. :/
  36. O

    Derivative of a function involving square root of sum of squares

    Provided is a function f(x)=\sum_{j=1}^n ||x-x_j||, for x being a two dimensional vector, where ||.|| denotes the Euclidean distance in 2D space. How could one obtain a derivative of such a function?
  37. C

    Square root of volume in fourier expansion of the vector potential

    Hi. I just wondered why we use a 1/\sqrt{V} in the Fourier expansion of the vector potential. A regular 3 dimensional Fourier expansion is just f(\vec r) = \sum_{\vec k} c_\vec{k} e^{i \vec k \cdot \vec r} but as the solution to the equation (\frac{\partial ^2}{\partial t^2} -...
  38. 1

    Limit of square root function.

    I have to find the limit as x→∞ of √(x2+x)-xI can't rearrange this into a form where I can put infinity into the expression and get a meaningful answer. I've tried taking out square roots to get √x( √(x+1)-√x ) but if I put infinity into this I just get ∞(∞-∞) which is meaningless. Now I know...
  39. E

    Relationship between line search and least mean square algorithm

    Hi there, I am going thru basics of optimization and I see line search being used in many sophisticated optimization algorithms. From what I understand, it works by taking the derivative at a point and moves in a direction that minimizes the function. I have earlier experience using...
  40. T

    Combining Transformations; Completing the Square

    Hello PF! Homework Statement The graph of the function y = 2x2 + x +1 is stretched vertically about the x-axis by a factor of 2, stretched horizontally about the y-axis by a factor of 1/3 and translated 2 units right and 4 units down. Write the equation of the transformed function Homework...
  41. R

    Solve ∫(e^x)/(√4-e^(2x)) w/ arcsin of x

    Homework Statement ∫(e^x)/(√4-e^(2x)) Homework Equations arcsin of x The Attempt at a Solution I know how the problem should be solved and have an idea of what the final answer will be. My only question is, how would I take out the four from the square root, in order to make it...
  42. I

    Find dy/dx of y= the square root of ln x

    Homework Statement Find dy/dx when y=\sqrt{ln x} Homework Equations d/dx of ln x is equal to 1/x times d/dx of x. The Attempt at a Solution I tried to raise the ln x to the 1/2 power instead of keeping it under a square root sign, but I had no luck. I'm struggling with Calculus. I...
  43. F

    Signal excited by square wave

    Homework Statement 11. What kind of frequency components can be observed in the output if a linear system is excited by a symmetric square wave? 12. What kind of frequency components can be observed in the output if a non-linear system is excited by a symmetric square wave? Homework...
  44. D

    Proof of the Laplace transformation of the Bessel function with square argument

    Homework Statement Could anyone help me please? I would like to know the proof of the following Laplace transform pair: Homework Equations \mathcal{L}_{t \rightarrow s} \left\{ J_0 \left( a\sqrt{t^2-b^2} \right) \right\}=\frac{e^{-b\sqrt{s^2+a^2}}}{\sqrt{s^2+a^2}} The Attempt at a Solution...
  45. G

    Question about square brackets and parentheses in MATLAB.

    I'm trying to figure out what these do in certain implementations. I can't seem to find the answer in the documentation. http://www.mathworks.com/matlabcentral/fileexchange/30580-binary-amplitude-shift-keying[1] for ii = 1:1:length(bit_stream) ASK_signal = [ASK_signal...
  46. R

    Stabiliser Groups of a vertex/edge of a square

    Homework Statement Given the dihedral group of symmetries of a square; what is the stabiliser group of a vertex (or edge)? Homework Equations The stabiliser group is G_x={g\inG|gx=x} I guess for a vertex/edge that means the transformations in D4 (generated by reflection in x-axis and...
  47. Q

    Solve Gradient Squared: ((grad(f(x,y,z))))^2

    How do you solve ((grad(f(x,y,z))))^2?
  48. M

    Charges at the corners of a square.

    Homework Statement Four positive charges are located on the corners of a square of side-length a. The charges are A=4, B=2, C=8 4q----a----q |------------| a-----------a |------------| 2q----a----8q Determine the magnitude and direction of the electric field experienced by charge q in terms of...
  49. C

    Distributing into a square root

    Its been a while since I have taken any kind of math class, I am a bit rusty in general algebra. Can someone explain how I would multiply an equation like this (2x-1)sqrtof x-3x is it just like normal distribution? Would I just put the answer underneath the square root? sqrt2x^2-6x^2-x+3x?
  50. J

    Completing the square for integration of e^( )

    Homework Statement I'm working on problem 2.22 from Griffith's Intro. to Quantum Mechanics (a free particle problem). I am stuck on the final integral from part b. Part a of the problem is normalizing: A*e-a*x2 which I did. Part b wants the general, time-dependent wave function. Homework...
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