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. B

    Square Of A Number Is Non-negative

    Hello, I am seeking some aid in proving that the square of a number is always non-negative. Here is some of my proof: A number, call it a, is either positive, negative, or zero. A number squared is produced when you take the number and multiply it by itself. So, we have three cases to...
  2. anemone

    MHB Compute a square root of a sum of two numbers

    Compute $\sqrt{2000(2007)(2008)(2015)+784}$ without the help of calculator.
  3. I

    Integrating a Square Root Function: Solution

    Homework Statement ∫(0,1) √x/√[3]1-x Homework Equations \Gammap\Gammaq/\Gammap+q The Attempt at a Solution p-1=1/2 →p=3/2 q-1=-1/3 →q=2/3 β(3/2,2/3)=\Gamma(3/2) \Gamma(2/3)/\Gamma(13/6) \Gamma3/2=1/2\Gamma(1/2)=√π/2 \Gamma2/3=-1/3 \Gamma13/6=7/6 1/6=7/36 β(3/2,2/3)=-6√π/7
  4. rrw4rusty

    All stars in Milky Way equal one square light year?

    Hello, Can anyone confirm or, refute and correct the following statements? The volume of our galaxy, is roughly 8 trillion cubic light years. The combined volume of all the stars in our galaxy only equals one cubic light year. Thanks for any help you can provide! Rusty
  5. kini.Amith

    What is the Value of √i + √-i?

    Homework Statement The value of √i + √-i , where i=√-1 is (a) 0 (b) 1/√2 (c) √2 (d) -√2 Only one option can be chosen Homework Equations The Attempt at a Solution Let (x + iy)2=i Solving for x and y, I got √i = +1/√2 (1+i) or -1/√2...
  6. A

    Finding the power series of a square root

    Homework Statement Find a power series for f(x) = \frac{1}{\sqrt{4+x^{2}}}, at x=0. 2. The attempt at a solution I have looked up the Taylor series of \frac{1}{\sqrt{4+x^{2}}}, but I don't find any similarity with a power serie like \sum_{n\geq 0} a_{n} x^{n} I don't know how to start...
  7. W

    MHB Solve Completing Square Problem: ((x2)/18)-(x/9)=1

    help I am stumped on this ((x2)/18)-(x/9)=1(Headbang)(Headbang)(Headbang)(Headbang)
  8. P

    MHB Using matrix to complete the square

    Given a quadratic form: x^2 - 4xy + 6xz + 2xt + 4y^2 + 2yz + 4yt + 5z^2 - 6zt - t^2, find the symmetric matrix that defines this, row reduce this matrix into row echelon form, and use this upper triangle matrix to complete the square and write the quadratic form as the sum/difference of...
  9. PhizKid

    Completing the square using a matrix in quadratic form

    Homework Statement Complete the square using the symmetric matrix that defines the given quadratic form: ##x^2 - 4xy + 6xz + 2xt + 4y^2 + 2yz + 4yt + 5z^2 - 6zt - t^2## and write this quadratic as the sum and difference of squares after completing the square using the matrix. The Attempt at...
  10. P

    Most probable position of electron in an infinitely deep square well

    Homework Statement An electron in an infinitely deep square well has a wave function that is given by http://postimg.org/image/s159u7ynt/ What are the most probable positions of the electron?The Attempt at a SolutionI got the values as L/6, L/2, 5L/6 by finding the x values that made the wave...
  11. E

    Gravitational force from a square plate

    I ordinarily would put this up in a homework/ coursework forum, but this isn't either one, its just something I was curious about given that I am in a Mechanics class. So, I have done calculations for finding the gravitational force from a sphere and from a ring, and a flat circular plate. All...
  12. A

    Defining the square root of an unbounded linear operator

    I have started coming across square roots (H+kI)^{\frac 12} of slight modifications of Schrodinger operators H on L^2(\mathbb R^d); that is, operators that look like this: H = -\Delta + V(x), where \Delta is the d-dimensional Laplacian and V corresponds to multiplication by some function. But...
  13. S

    MHB Question concerning simplification of numerical expression with square roots.

    how does \frac{5700}{\sqrt{15,300}} turn into \frac{570}{\sqrt{153}} ??
  14. L

    Logarithmic singularities are locally square integrable

    Homework Statement I will like to show that the function f:\mathbb{R}^2\rightarrow \mathbb{R} defined by f(x)=\ln\bigg(1+\dfrac{\mu}{|x-x_0|^2}\bigg),\quad\mu>0 is in L^2(\mathbb{R}^2). Homework Equations A function is in L^2(\mathbb{R}^2) if its norm its finite, i.e...
  15. B

    Finding the magnetic force in square loop wire.

    Homework Statement Suppose that the magnetic eld in some region has the form B = kzx(hat). (where k is a constant). Find the force on a square loop (side a), lying in the yz plane and centered at the origin, if it carries a current I, flowing counterclockwise, when you look down the x axis...
  16. L

    Force needed to bend 2 inch square tube

    My question is: Researching two sizes of square steel tubing to use for a project. material 2 inch square tubing with 0.25 thick wall and 3 inch square tubing with 0.25 thick wall. The square steel tubing will be welded on to a frame at an angle so the corners point up and down , or another...
  17. P

    Gravity: Not Proportional to Inverse Square?

    Hi, a long time ago, back in high school, I remember my teacher was explaining the force of gravity to us. He gave us the equation for the force of gravity, which was proportional to the inverse square of the distance. However, he later said that something about Einstein and other researchers...
  18. Jalo

    Archived Find the vortices of a square after a transformation given by a tensor

    Homework Statement Given a square and the respective distension tensor, ε, find the position on his vortices after the transformation. ε = 0.1...0.25 ...0.25...0.1 Homework Equations The Attempt at a Solution I got kind of lost in this question. I started thinking that maybe...
  19. O

    Bound state of a square well, no allowed bound state mean?

    Homework Statement Show in the graph ,there will be no allowed bound states with odd-parity if the well depth is less than ${V_min}$ Find ${V_min}$ in terms of k and a.where a is the half of the well width. What does no allowed bound state mean? Homework Equations $cotz=-pa/z$ where p^2...
  20. A

    MHB Division with square roots at the base

    Hi, I am new here and I don't know if anyone is going to answer to this post, but if you do so thank you very much. I have been frowning on these kind of problems! I have been trying to solve some exercices from my homeworks. However, I don't know if I am doing them correctly. Here is one...
  21. P

    Approximation to an average of integer square roots

    I have stumbled upon an approximation to the average of integer square roots. \sum^{n}_{k=1}{\sqrt{k}/n} \approx \sqrt{median(1,2,...,n)} Sorry I am not very good at LaTeX, but I hope this comes across okay. Could anyone explain why this might be happening? In fact, I just discovered that...
  22. S

    Calculating Work for a Bead on a Square Loop in an Electric Field

    Homework Statement A small bead is on square loop in the xz plane with dimensions (±R, 0, ±R). An electric field is turned that is ##\vec{E}(\vec{r})=-Cx\hat{z}## Calculate W Homework Equations ##W= \int q\vec{E}\bullet dl## The Attempt at a Solution Starting with z direction...
  23. O

    Bound state of finite square well, why do we make this statement?

    Reading from http://quantummechanics.ucsd.edu/ph130a/130_notes/node150.html Again we have assumed a beam of definite momentum incident from the left and no wave incident from the right. Why is the above statement made? What does the reflected wave mean? There is now all why reflected...
  24. J

    Classical Square Well: Hamiltonian Form & Elastic Collision

    My understanding is that a classical idealized particle, moving in one dimension, with momentum p and kinetic energy T comes into contact with an infinite step-function potential V, there will be an (instantaneous) elastic collision - the particle's momentum becomes -p, so its energy remains...
  25. F

    Matrix transformations and effects on the unit square

    I was looking over my notes today, and I realized that there was a point that isn't pretty clear. If we have the image under T (being T a matrix transformation induced by a matrix A) of the unit square, then its area should be abs(det(A)). Why is this though? I was looking at the proof and I...
  26. G

    How come, for any n > 2, the nth triangular number + the nth square

    number cannot be prime? I have checked this for n from 3 to 53,509, the latter being the limit for unsigned int. I believe this is true, and I thereby claim that this is a true statement. However, I don't see any obvious explanation for it.
  27. H

    What is the limit of a function under a square root?

    Homework Statement lim x-> 2+ f(x)=sqrt(4-x^2)whats the value of the following function?? Homework Equations The Attempt at a Solution i tried and got the answer as does not exist but some people got it as 0 which is the correct answer
  28. T

    Energy of an Infinite Square Well

    Hey guys, this is my first post so go easy on me. I was looking over the simple case of a 1D particle restrained inside an infinite square well potential ("particle in a box") and was having some difficulty understanding the relationship between the energy states and the expectation value for...
  29. D

    Square of x component of Orbital Angular momentum?

    Homework Statement Solve for ##L^2_x## ##L_x = \frac{\hbar}{i} (-sin(\phi)\frac{d}{d\theta} - cos(\phi)cot(\theta)\frac{d}{d\phi}##** the d's should be partial derivatives, but I'm not sure how to do that symbol. Sorry! Homework Equations Solve for ##L^2_x## ##L_x = \frac{\hbar}{i}...
  30. Superposed_Cat

    Generating square vector field

    Hi all, my friend is writing a sci-fi/fantasy book and for it he asked me for a function that generates a vector field like picture A. So far the closest I've got is i*-(1/x)+1/-yj, which generates B. How would I generate B without using conditions? any help appreciated, thanks.
  31. R

    Gibbs phenomenon and ringing in square waves: causality?

    A seemingly good way to understand the overshoot and decay (ringing) of a square wave on a scope is that it is the result of bandwidth limiting. In that case, the Fourier series of a square wave \Pi(t) = \frac{1}{2 \pi} \sum_{n=-\infty}^\infty \frac{\sin(n \omega/2)}{n \omega/2} \exp(i n \omega...
  32. R

    What Does a 22.5° Duty Cycle Mean in a Tachometer Square Wave Signal?

    I'm looking to get some help understanding the tachometer out specifications for an MSD 6AL ignition control unit. It specifies that "The Tach Output wire produces a 12 voltage square wave signal with a 22.5° duty cycle." I'm fine with the fact that its a 12 volt square wave, but I'm a...
  33. S

    Can a Robot Traverse a Twisting Square Tube?

    Hello, I was wondering if I could get some advice on how to build a robot that can traverse the inside of a twisting square tube, whilst staying at its centre. Heres an image of the kind of tube it will be: Its probably doable with a rollercoaster style design but it seems like an...
  34. Q

    An infinite square well problem

    Homework Statement Particle in well: V(x)=0 for |x|<\frac{L}{2} V(x)=∞ for |x|>\frac{L}{2} initial wave function \Psi(x,0)=\frac{1}{√L}[cos\frac{\pi*x}{L}+ i*sin\frac{2*\pi*x}{L}] a) calc P(p,t) (momentum prob density) Homework Equations Anything from Griffiths QM The Attempt at a...
  35. D

    Fourier Series - Asymmetric Square Wave

    Good morning everyone, I am taking a signals and systems course where we are now studying the Fourier series. I understand that this is for signals that are periodic. But I get hung up when determining the Fourier coefficients. In the video by Alan Oppenheim, he derives the equation for...
  36. P

    Finding momentum distribution for particle in square well

    Homework Statement A particle of mass ##m## is trapped between two walls in an infinite square well with potential energy V(x) = \left\{ \begin{array}{cc} +\infty & (x < -a), \\ 0 & (-a \leq x \leq a), \\ +\infty & (x > a).\end{array} \right. Suppose the wavefuntion of the particle at time...
  37. J

    What Is the Transition Amplitude for an Infinite Square Well?

    Homework Statement A particle, mass m propagates freely in a box, length L. The energy states are: ϕ_n(x) = (2/L)^(1/2)sin(n∏x/L) and energies E_n = n^2∏^2/(2mL^2) at time t=0 the system is in state ϕ_1 and the perturbation V=kx is applied (k constant) and turned off at t=T...
  38. denjay

    Completing the Square Homework Statement

    Homework Statement Consider a charged particle of mass m in a harmonic potential and in the presence also of an external electric field E = E\hat{i}. The potential for this problem is simply V(x) = 1/2 mw^{2}x^{2} - qεx where q is the charge of the particle. 1) Show that a simple change of...
  39. L

    Wave function and infinite square well potential

    Homework Statement An electron in a one-dimensional infinite square well potential of length L is in a quantum superposition given by ψ = aψ1+bψ2, where ψ1 corresponds to the n = 1 state, ψ2 corresponds to the n = 2 state, and a and b are constants. (a) If a = 1/3, use the normalization...
  40. A

    Would a square wave look like a sine passed through a material?

    Sorry for the wording of the topic- I couldn't figure out how to make it fit. If I passed a hypothetical square wave through a material- be it wood, glass, cotton, etc.- would it change to look more like a sine wave?
  41. K

    If p is prime, then its square root is irrational

    Homework Statement Im trying to prove that if p is prime, then its square root is irrational. The Attempt at a Solution Is a proof by contradiction a good way to do this? All i can think of is suppose p is prime and √p is a/b, p= (a^2)/ (b^2) Is there any property i can...
  42. U

    How many Rb atoms to fit on a 9Cm^2 square?

    1. The problem is in the attachments 2. Basic chemistry knowledge 3. The radius of one Rb atom is 4.95/2 time 10^-8 cm, we calculate the area then divide 9 into the area of one atom, we get the number of atoms, why is 4.7 x 10^15 atoms wrong?
  43. T

    MHB Solve equation with square roots

    Can someone show me step by step guide,how to find all possible solutions for example?
  44. A

    Suppose you have an electron in the infinite square well

    Suppose you have an electron in the infinite square well. The system is completely isolated from the rest of the world and has been its entire lifetime. Do we then know that the wave function describing the electron is an eigenstate of the Hamiltonian? The question arose because I was given a...
  45. N

    Integral: square root of sum of trig polynomials

    Hi, I am trying to make progress on the following integral I = \int_0^{2\pi} \sqrt{(1+\sum_{n=1}^N \alpha_n e^{-inx})(1+\sum_{n=1}^N \alpha_n^* e^{inx})} \ dx where * denotes complex conjugate and the Fourier coefficients \alpha_n are constant complex coefficients, and unspecified...
  46. G

    Infinite Square Well - Particle in linear combination of states

    A particle of mass m is trapped in a one-dimensional infinite square well running from x= -L/2 to L/2. The particle is in a linear combination of its ground state and first excited state such that its expectation value of momentum takes on its largest possible value at t=0.I know the process of...
  47. A

    Understanding Free Electron Kinetic Energy on a Square Lattice

    Homework Statement Show for a simple square lattice that the kinetic energy of a free electron is higher at the corner of the first zone than at the midpoint a side face by a factor of 2. Homework Equations Simple geometry. The Attempt at a Solution I think I know how to solve, but...
  48. V

    Solving the Mystery of Negative Square Roots

    Hello everyone, What is the square root of a square of a negative number equal to? For example: \sqrt{-1}^{2} It seems there are two possible ways of doing this, the problem is that I am getting two different answers using these two approaches i.e; We can first take the square of -1 and then...
  49. D

    Simplified Radical Form with square and cubed roots

    I just got a new Ti-nspire Cx CAS calculator and I am having trouble with being able to express a Radical in simplified form when there are exponents and variables of x and y. My problem is that this calculator will not show the simplified form correctly. I have taken others advice in setting...
  50. A

    MHB Square Root Rules for Fractions: x∈[3,∞)

    \sqrt{\frac{x-3}{x}} = \frac{\sqrt{x-3}}{\sqrt{x}} that is not true for all x, it is true for x\in [3,\infty) I want to teach my students that the exponents distribute over fractions unless we have a case like that square root or any even root. what do you think ?
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