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. D

    MHB Find unknowns in equation going from perfect square? to quadratic format?

    Hi all I'm trying to work out how to answer this type of problem. (6x+2z)^2-64=(ax+2z+8)(-8+bx+cz) where a, b and c > 0 I have attempted the problem by expanding the brackets: =36x^2+24xz+4z^2-64 This is the same as (6x+2z)^2-(8)^2 Then subtracting from either 'side' of the quadratic and...
  2. kaliprasad

    MHB Square Int x: $x(x+1)(x+7)(x+8)$ is Square Integer

    Find all integers x such that $x(x+1)(x+7)(x+8)$ is square of an integer
  3. Kirito123

    Finding volume of Square pyramid

    Homework Statement Homework Equations V= a21/3 h The Attempt at a Solution I may be wrong or right I don't know. I'm pretty sure I did it right.
  4. karush

    MHB S6.7.r.19 Rational Expression Integral (complete the square?)

    $\Large{S6.7.R.19}$ $$\displaystyle I=\int\frac{x+1}{9{x}^{2}+6x+5}\, dx =\frac{1}{18}\ln\left({9{x}^{2}+6x+5}\right) +\frac{1}{9}\arctan\left[{\frac{1}{2}\left(3x+1\right)}\right]+C $$ $\text{from the given I thought completing the square would be the way to solve this} \\$ $\text{but I...
  5. R

    I How to find if a quadratic expression is a perfect square

    How to find if a quadratic expression of the form 4x2 + 4.n.x - P ......(x,n and P are natural number) is a perfect square. For example, 4x2 + 64x - 31 Thanks.
  6. C

    MHB Chi-Square Test: Solving Doubt w/ Kepler

    Good afternoon, I'm glad I've joined this forum. Here's my doubt: I have a serie of values in a table like this: Case 1 34 55 Case 2 23 10 Case 3 55 40 etc... the 34 means the observed value, and the 55 the control group, and so on. It's easy to do the test of course if... The problem is: if...
  7. Rectifier

    Limit of $\sqrt{x+1} - \sqrt{x}$ as $x \to \infty$

    The problem $$ \lim_{x \rightarrow \infty} \left( \sqrt{x+1} - \sqrt{x} \right) $$ The attempt ## \left( \sqrt{x+1} - \sqrt{x} \right) = \frac{\left( \sqrt{x+1} - \sqrt{x} \right)\left( \sqrt{x+1} + \sqrt{x} \right) }{\left( \sqrt{x+1} + \sqrt{x} \right) } = \frac{x+1 - x }{\left(...
  8. JulienB

    Reduced chi square test in physics

    Homework Statement Hi everybody! Our experiments teacher asked us to perform a reduced chi square test in order to estimate how good a model fits to our measured data. The experiment was the melde's experiment (vibration of a string) and we measured the frequency ##f_n## for ##n=1## to ##9##...
  9. Planobilly

    Can square waves cause a DC voltage

    I read this statement from Lenard Audio. "When a large signal spike is created by un-plugging or plugging in signal leads, or when a pre-amp valve is driven hard into distortion (guitar amps), a large non-symmetrical square wave may cause a temporary DC Voltage to appear across a coupling...
  10. TheAnt

    Does the inverse square rule work with a magnetic field?

    I am interested in mini magnetospheres. How do i calculate the intensity of the field at a certain distance if i already know theits intensity at the source?
  11. A

    B How Can 4(x + 1/2)^2 + 1 Be (2x + 1)^2 + 1?

    How ##4(x + \frac{1}{2})^2 + 1## can be ##(2x + 1)^2 + 1##?
  12. T

    MHB Simplifying a square root expression

    I have this expression: $$\sqrt{ 1 - \frac{16}{\sqrt{x^2 + 16}}}$$ And the textbook simplifies it to $$\frac{x}{\sqrt{x^2 + 16}}$$ But I'm not sure how it does this.
  13. M

    I Infinite square well solution - periodic boundary conditions

    If we have an infinite square well, I can follow the usual solution in Griffiths but I now want to impose periodic boundary conditions. I have \psi(x) = A\sin(kx) + B\cos(kx) with boundary conditions \psi(x) = \psi(x+L) In the fixed boundary case, we had \psi(0) = 0 which meant B=0 and...
  14. parshyaa

    I Find the square root of (-2-3)^2?

    Root of (-2-3) ^2 = -5 ( because root of squared number is the number itself) but alsoo square of (-2-3) is 25 and its root is (+5) /(-5). Therefore what is the correct answer and reason . I think it is -5(google answer is Also -5) but I don't have any reason. Please help me
  15. C

    Complete Square + Leibniz question (2 questions)

    Homework Statement 1. How did they complete the square for these equations in the picture below? What was their thought process? 2. distance/velocity = time , velocity/acceleration = time , In leibniz notation how does this cancel out? When you divide, how does it cancel out to give you a...
  16. S

    I Time evolution after "turning off" square well

    How how can we calculate the future evolution of a particle after the infinite square well potential is (somehow) turned off, releasing it into a free state? Assuming that it was in the ground state before.
  17. T

    How Does the Inverse Square Law Apply to Calculating Distances Between Charges?

    I am faced with the following question: Two point charges X and Y, exert a force F on each other when they are at a distance d apart (x and y are opposite charges). When the distance between them is 20mm, the force exerted on each other is 0.5F. What is the distance d? I know that, e.g...
  18. fatay

    B My combination theorem : square

    Hi i am fatih from turkey.i am high school student.question is "how many squares are in an rectangle subdivided into unit squares?"(a<=b) My theorem about this question.Please write your comments.Thanks For your time, thanks all mathematicians !:)
  19. B

    Show that this equation is inverse square

    Homework Statement F = k(Q2*Q1)/(r^2) Homework EquationsThe Attempt at a Solution I asked my teacher and he said that this is an inverse square law. Didn't say anything else. He also mentioned k is constant. I assume i can plug in random values and see if there is a pattern... k=1 for all Set...
  20. W

    Electric field due to a charged square

    Homework Statement there is a square on the XoY plane, centered at the origin (just outlines of the square) it has a charge Q (Q>0) and side 2L, i must evaluate the electric field along the z axis. see attached image Homework Equations E=k*q/r^2 The Attempt at a Solution So first i divided...
  21. S

    How Does the Least Squares Estimator Minimize Error in Linear Regression?

    Homework Statement Suppose that ##Y \sim N_n\left(X\beta,\sigma^2I\right)##, where the density function of ##Y## is $$\frac{1}{\left(2\pi\sigma^2\right)^{\frac{n}{2}}}e^{-\frac{1}{2\sigma^2}(Y-X\beta)^T(Y-X\beta)},$$ and ##X## is an ##n\times p## matrix of rank ##p##. Let ##\hat{\beta}## be the...
  22. M

    Using a set square to reduce parallax error

    Homework Statement In one of my revision guides, there is an experiment for calculating the acceleration of free fall using the electromagnet and trap door arrangement. The biggest error is in the measurement of the height over which the ball falls. The guide says: "You could reduce the error...
  23. F

    Perturbation matrix: free electron model on a square lattice

    Homework Statement Nearly free electron model in a 2D lattice. Consider a divalent 2D metal with a square lattice and one atom per primitive lattice cell. The periodic potential has two Fourier components V10 and V11, corresponding to G = (1,0) and (1,1). Both are negative and mod(V10) >...
  24. D

    I Square of determinant is symmetric

    This property is given in my book. The square of any determinant is a symmetric determinant. Well it works when I take a determinant say 3x3 and multiply it by itself using row to row multiplication. But it fails if I multiply using row to column. Thanks
  25. T

    A Solving polynomial coefficients to minimize square error

    Hi there, I'm working on a problem right now that relates to least squares error estimate for polynomial fitting. I'm aware of techniques (iterative formulas) for finding the coefficients of a polynomial that minimizes the square error from a data set. So for example, for a data set that I...
  26. N

    MHB Efficient Method for Extracting Square Root of Complex Expressions

    Hello! Is there a way to extract the square root of this expression without expanding? Please teach me how to go about it. $4\left((a^2-b^2)cd+ab(c^2-b^2)\right)^2+\left((a^2-b^2)(c^2-b^2)-4abcd\right)^2$ I tried expanding it and it was very laborious and I end up not getting the correct answer.
  27. J

    Magnitude and DIRECTION of electric field of a square.

    Homework Statement Calculate the magnitude of the electric field at the center of a square 42.5cm on a side if one corner is occupied by a −38.2μC charge and the other three are occupied by −26.9μC charges. (This part done) Choose the correct direction of the electric field at the center of...
  28. kq6up

    A Phase factors and Modulus Square?

    If I have something like: $$\lvert \langle M \lvert \hat{L}_x+i\hat{L}_y \rvert M-1 \rangle \rvert ^2=c$$. where ##c## is any old real number. If I undid the modulus square to find: $$ \langle M \lvert \hat{L}_x+i\hat{L}_y \rvert M-1 \rangle=\pm \sqrt{c} $$ Would I not have to consider...
  29. C

    Adiabatic expansion of infinite square well

    Homework Statement Suppose that an infinite square well has width L , 0<x<L. Nowthe right wall expands slowly to 2L. Calculate the geometric phase and the dynamic phase for the wave function at the end of this adiabatic expansion of the well. Note: the expansion of the well does not occur at...
  30. M

    Expectation value and momentum for an infinite square well

    Homework Statement √[/B] A particle in an infinite square well has the initial wave function: Ψ(x, 0) = A x ( a - x ) a) Normalize Ψ(x, 0) b) Compute <x>, <p>, and <H> at t = 0. (Note: you cannot get <p> by differentiating <x> because you only know <x> at one instance of time)Homework...
  31. G

    Inverse Square Law, Temperature Change, and Heat Source Temp

    I've been trying to wrap my head around the relationship between temperature increase of an object at a distance and temperature of a heat source. From what I've found, the temperature increase of an object from thermal radiation is affected by the inverse square law...
  32. S

    Interval of Convergence of Power Series with Square Root

    I'm trying to find the answer to a question similar to this posted it earlier but in the wrong section I think and not explained well. $$ \sum_{{\rm n}=0}^\infty \left (-\sqrt x \right )^n \ \ \rm ?$$ Find the interval of convergence? I tried using the root test and got from 0 to 1 but when I...
  33. S

    I Square Root in an alternating power series

    I had a question similar to Σ0∞ (-1)^n (x)^(n/2) and attempted to solve it using the root test getting abs(√x)<1, but I've also seen some places answer it as √abs(x)<1 so am I skipping a step.
  34. S

    Radiation from a Square Loop of Current

    It is well known that a circular loop of steady current does not radiate, even though each individual charge is undergoing centripetal acceleration. How about a loop of steady current that is shaped in a square? Does this structure radiate?
  35. D

    Harmonic function in square -PDE

    Hello, I have the solution of a problem but there's something I don't understand Homework Statement Find the harmonic function in the square {0<x<1, 0<y<1} with the boundary conditions u(x,0)=x u(x,1)=0 ux(0,y)=0 ux(1,y)=y²tHomework EquationsThe Attempt at a Solution Part1:[/B] We first solve...
  36. InverseSquareLaw

    B Who Created the Inverse Square Law Theory

    I Am Wanting to Find out who Created the inverse square law.
  37. S

    Infinite Square Well, Potential Barrier and Tunneling

    Homework Statement Consider a one-dimensional, non-relativistic particle of mass ##m## which can move in the three regions defined by points ##A##, ##B##, ##C##, and ##D##. The potential from ##A## to ##B## is zero; the potential from ##B## to ##C## is ##\frac{10}{m}\bigg(\frac{h}{\Delta...
  38. Destroxia

    Work done by Three Dimensional Inverse Square Field

    Homework Statement Find the work done by the three-dimensional inverse-square field ## F(r) = \frac {1} {||r||^3} r ## on a particle that moves along the line segment from P(6, 2, 3) to Q(4,2,4) Homework Equations ## \int_C F \bullet dr = \int_a^b f(h(t), g(t)) \sqrt {(\frac {dx} {dt})^2 +...
  39. J

    I Probability current in positive finite square potential

    Hello! I want to prove that the probability current is a continuous entity at the boundaries of the square for the situation of 0< E< Vo in the problem where V is zero except a finite region in space where it is +Vo and we consider an incoming particle from the left(for example). I thought that...
  40. DavidReishi

    I Square of absolute value of amplitude for a single photon

    I understand that this determines a probability, but of what exactly for a single photon? The probability that the photon will be detected on a surface where the photon is pumped, e.g. where on the surface the laser is aimed?
  41. L

    I Inverse Square Law and various space dimensions

    I am interested in the derivation of the inverse square law in various dimensions via Green's functions. I think the trick is to imagine a sphere and then to integrate over it. Does anyone know a book or notes where this is explained? I found this below from here, but could not really...
  42. DavidReishi

    I Inverse square law and ensembles of photons

    I'm trying to visualize the effect of the inverse square law, not on a direct source of light, but on scattered light carrying visual data, such as that responsible for our everyday sight of things as well as our images of Earth from satellites. It seems to me that it should be true that, while...
  43. H

    Calculate the EMF induced in the square?

    Homework Statement A square of wire with side length 1.4 m rotates about an axis through one corner that is perpendicular to the plane of the square with an angular speed of 3 rev/s. There is a uniform magnetic field of 1.2 T perpendicular to the square. Calculate the EMF induced in the...
  44. O

    I Evidence for Inverse Square Law at Extremely Large Distance?

    This is just an oddball question that's been rattling around in my head. What evidence do we have that the Coulomb force of, say, a spherical charge distribution Q, is actually nonzero at very large distances? I can easily imagine that the inverse square law is very accurate out to some...
  45. P

    Root Mean Square: What It Is & Why It Matters in Electrical Engineering

    What is the root mean squad (RMS) of a signal (or wave) and why is it important for electrical engineering? How do you Find it? What is it used for? Thank You All
  46. D

    Goodness of fit, Residual STD, chi square

    Homework Statement Hello, I am using CasaXPS to model synthetic peak models for X-ray photoelectron spectroscopy data. I am fitting. The software has a lot of manuals online but they do not explain how they yield a Residual Standard Deviation, after each fit iteration. Most software use...
  47. Elvis 123456789

    Magnetic Field at the center of a square loop

    Homework Statement A square wire loop 12.0 cm on each side carries a clockwise current of 15.0 A Find the magnitude of the magnetic field at its center due to the four 1.30 −mm wire segments at the midpoint of each side. Homework Equations B = (μ0*I)/(4π)*(2a)/(x√(x^2+a^2)) The Attempt at a...
  48. P

    Electron in a Finite Square Well

    Homework Statement An electron in a finite square well has 6 distinct energy levels. If the finite square well is 10nm long determine: a) Approximate the possible values for the depth of the finite square well ##V_0##. b) Using a well depth value in the middle of the results obtained from part...
  49. Elvis 123456789

    Magnetic Field at center of a Square loop

    Homework Statement A square wire loop 12.0 cm on each side carries a clockwise current of 15.0 A Find the magnitude of the magnetic field at its center due to the four 1.30 −mm wire segments at the midpoint of each side. Homework Equations B = (μ0*I)/(4π)*(2a)/(x√(x^2+a^2)) The Attempt at a...
  50. kaliprasad

    MHB Perfect Cube & Square: 5-Digit Number

    Find 5-digit number whose half is a perfect cube and one-third is a perfect square
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