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



◻


{\displaystyle \square }
ABCD.

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  1. S

    Magnetic field at the center of a square conducting loop

    Homework Statement Problem and solution attached Homework Equations B = [4uI/(4pi)]sin(theta1-theta2] The Attempt at a Solution I understand fully how to do it except determining the value of theta1 and theta2. The solution says theta1 is 45(deg) and theta2 is -45(deg). How did they get those...
  2. M

    MHB Square Root Solutions for Complex Numbers

    Helppp for part (ii). I got 3$e^{\frac{1}{6}\theta i}$
  3. B

    Is the square root of 4 a constant?

    I don't know what to say. sqrt(4) = +/- 2, but constants are fixed. When written sqrt(4), it seems sqrt(4) is a constant, but not in the latter case. Help!
  4. S

    Square of x , added to one is not equal to n

    $$x^{2}+1 \neq n! $$since $$x^{2}+1=(x+i)(x-i) $$so ,$$ x^{2}+1$$ has only prime of the form of (4k+1) , where n! has prime of the form( 4k-1) and (4k+1) . :oldbiggrin:
  5. bhobba

    Least Square Estimator for Matrices: Bill's Problem

    I recently came across the following interesting problem. Suppose A = BC where A,B, and C are matrices. We know a ton of A's and their corresponding C's. We want the least square estimator of B. When A and C are vectors the solution is well known. But what is the solution when they are...
  6. karush

    MHB Integral completing the square

    $\int\frac{1}{\sqrt{16+4x-2{x}^{2}}}dx$ factored out 2 then completed the square $\int\frac{1}{\sqrt{2\left[9-{(x-1)}^{2}\right]}}dx$ next?
  7. OlderOwl

    When n*(n+1)/2 - k is never a square

    I found that the series represented by An = n∗(n+1)/2 - k never includes a perfect square if and only if the prime factorization of 8∗k+1 includes a prime factor, p, to the ith power where p = +/−3 mod 8 and i is odd and that this can be proved mod p(i + 1) For instance, 8* 4 + 1 = 3^1 * 11^1...
  8. W

    Time Dependent Wavefunction in Infinite Square Well

    Homework Statement A particle of mass m is confined to a space 0<x<a in one dimension by infinitely high walls at x=0 and x=a. At t=0, the particle is initially in the left half of the well with a wavefunction given by, $$\Psi(x,0)=\sqrt{\dfrac{2}{a}}$$ for 0<x<a/2 and, $$\Psi(x,0)=0$$ for a/2...
  9. L

    Square matrix and its transpose satisfying an equation

    Homework Statement Show that if a square matrix A satisfies A3 + 4A2 -2A + 7I = 0 Mod note: It took me a little while to realize that the last term on the left is 7I, seven times the identity matrix. The italicized I character without serifs appeared to me to be the slash character /. then so...
  10. G

    Why there is dc component in square signal

    hi! when I send a square wave to a digital oscilloscope it detects the signal + dc signal. I wanted to know why. I was thinking about internal resistance of coaxial cable i was using. signal got out of an oscilloscope/wave generator and in channel A of the same oscilloscope/wg. It was +-1...
  11. Shackleford

    Integrate f(z) = Re(z) along contour of the square

    Homework Statement Integrate f(z) = Re(z) = \frac{z+\bar{z}}{2} along the contour of the square {z = x + iy | |x| ≤ 1, |y| ≤ 1} with counterclockwise rotation. Homework Equations Cj: φj(t) = z0 + (z1 - z0)t C1: 1 -i + 2it C2: 1 +i - 2t C3: -1 +i - 2it C4: -1 -i + 2t The Attempt at a...
  12. Math Amateur

    MHB Shade/Black a Square: Get Help from Peter

    I recently posted a suggested proof to a theorem and wish to mark the finish of the proof with a filled-in or shaded/black square as some texts do ... I typed in \square as a guess and got an unshaded square ... how to do get a shaded or black square? Hope someone can help ... Peter
  13. T

    Electrostatic field at the square center

    I have just begun studying electrostatic and I'm trying to do this exercize: We have a square with charges +q , -2q, +2q, -q1)Compute the electrostatic field \vec{E}at the center of the square. I did this way : I find \vec{E_A}=\frac{q}{2 \pi \epsilon_0} \vec{u} {E_B}=\frac{-q}{ \pi...
  14. N

    Chi Square Distribution Problem

    Homework Statement Suppose that X has normal distribution. Find the distribution of n(Sample Mean - μ)2/σ2. The Attempt at a Solution I honestly have no idea where to begin with this problem. Any ideas?
  15. Milsomonk

    Expectation value of the square of Momentum

    Homework Statement The expectation value of <P^2>= -ħ∫ψ* ∂^2ψ/∂x^2 dx For the Guassian wave-packet ψ(x)=(1/(π^1/4)(√d))e^-((x^2)/(2d^2)) Limits on all integrals are ∞ to -∞. Homework Equations <P^2>= -ħ∫ψ* ∂^2ψ/∂x^2 dx ψ(x)=(1/(π^1/4)(√d))e^(iKx)-((x^2)/(2d^2)) The Attempt at a Solution Ok...
  16. gfd43tg

    Finite square well ##\psi(x)## solution for ##-a < x < a##

    Hello, in Griffith's section on the Finite Square Well, ##\psi(x)## (what is the name of this anyway?, I know ##\Psi(x,t)## is called the wave function but how do I call just ##\psi(x)##?) Anyways, The solution is For x < a and x > a, the terms that are infinite as x approaches infinity are...
  17. V

    Electric field above a square loop

    Homework Statement Problem 2.4 from Griffiths Intro to Electro[/B] Find the electric field a height z above the centre of a square loop with sides a and linear charge density λ. height is given to be z and sides given to be a, ∴ distance from origin to side is given by a/2 Homework Equations...
  18. anemone

    MHB Proof that x=0 for Integers with Perfect Square Property

    The integers $x$ and $y$ have the property that for every non-negative integer $n$, the number $2^nx+y$ is a perfect square. Show that $x=0$.
  19. H

    Square wave and sine wave -- How standing waves are formed?

    Why do the sound waves reflect and form standing wave when they travel along a string with sinusoidal waveform? But they do not reflect back when they are in square waveform ?
  20. gfd43tg

    Infinite Square Well Homework: Solutions

    Homework Statement Homework EquationsThe Attempt at a Solution (a) $$ \int_{0}^{a} \mid \Psi (x,0) \mid^{2} \hspace {0.02 in} dx = 1 $$ $$ \int_{0}^{a} \mid A[ \psi_{1}(x) + \psi_{2}(x) ] \mid^{2} \hspace {0.02 in} dx = 1 $$ Since the ##\psi_{1}## and ##\psi_{2}## are orthonormal (I don't...
  21. B

    Finite square well potential numerical solution

    hi guys i need some help with the iteration made in a numerical solution for the eigenstates in a finite square well potential using the effective length approximation First, i find the eigenstate for a infinite square well, then i define the related alpha and i use it to define an effective...
  22. S

    MHB Square Roots Calculation Tricks

    hi all... i have problem about square roots for fast calculation, like below sample : is there fast calculation method not commonly/usually ways. it's possible? please, see my picture? thanks in advance.. susanto
  23. I

    Integrating an inverse square to find U

    Hello everyone, This is probably going to come off as a very silly question. However, I have not had calculus in several years. I was angry that my physics textbook did not have a derivation of Electric Potential Energy. So, I finally came across it, and I see that the integration of the...
  24. DocZaius

    Moment of Inertia of a Square: Problem with Certain Method

    For fun, I thought I would try to derive the moment of inertia of a square using different approaches (in each case, changing the differential area being integrated). Everything went well until I tried the approach of first considering the disk in the center of the square, then adding the bits...
  25. R

    How to simplyfy a square root term? Phonon dispersion relati

    I'm having trouble simplyfying this, I guess there's a trick but for the life of me can't remember what it is. Here is what I have so far: ##\omega ^{2} = f\left ( \frac{1}{m}+\frac{1}{M} \right )-f(( \frac{1}{m}+\frac{1}{M} \right ))^{2} - \frac{4q^{2} a^{2}}{mM})^{\frac{1}{2}}## so I divide...
  26. B

    Who has experience with AD8333 to demodulate a square wave?

    I am wondering if anyone has used AD8333 to demodulate a square wave input (Not the LO, but the RF input).
  27. M

    MHB Help with Quadratic Equations by completing the square

    I understand how to solve these equations when the square is on this side of the equal sign: x2 + 8x + 7 = 27 But when the square is on the other side, I am thrown. Like this one... x2 = 14x - 33 The solutions manual shows the next step as the following, but what do you do to get to this...
  28. M

    The sound of a perfect square wave

    Hey guys, It is stated that a 100% perfect square shaped wave have infinite odd harmonics and it is impossible to produced theoretically. But, assuming if a perfect square wave is produced, what would it sound like? I remember someone said it in Youtube it would actually sound like a clarinet...
  29. I

    Square of a permutation matrix

    say i have the matrix (4,2,5,6,3,1) and on top I have (1,2,3,4,5,6) i.e. a 2x6 permutation matrix. Let's call it sigma. how would I calculate (sigma)^2? I can break it down into cycles: sigma = <1,4,6>compose<3,5> thanks.
  30. T

    Algorithm to find square root of a quadratic residue mod p

    I'm going through an explanation in a number theory book about Tonelli's algorithm to find the square roots of a quadratic residue modulo ##p## where ##p## is prime, i.e. I want to solve ##x^2 \equiv a \pmod{p}## with ##(\frac{a}{p}) = 1##. The book goes as follows: Let ##p - 1 = 2^s t##, where...
  31. I

    Understanding square root of a polynomial

    Hello This is not exactly a homework problem. I was browsing through an old book, "Elementary Algebra for Schools" by Hall and Knight, first published in England in 1885. The book can be found online at https://archive.org/details/elementaryalgeb00kniggoog . I was studying the process of...
  32. S

    Is Biot-Savart inverse cube or inverse square law?

    I know we can represent it two different ways. First: \mathbf{B} = \frac{\mu_0}{4\pi}\int_C \frac{I d\mathbf{l} \times \mathbf{\hat r}}{|\mathbf{r}|^2} If we open up unit vector, then it becomes: \mathbf{B} = \frac{\mu_0}{4\pi} \int_C \frac{I d\mathbf{l} \times \mathbf{r}}{|\mathbf{r}|^3} I...
  33. S

    Max Temp of Water Around Heated Square Rod

    Homework Statement A long squared rod with sides ##l##, thermal conductivity ##\lambda ##, specific heat ##c_p## and density ##\rho ## is cooled with water with constant temperature. Inside our squared rod we have a long square heater with sides ##l/2## and is completely centered inside the...
  34. A

    The Perfect Square: Leonardo DaVinci's Renaissance Discovery

    In the renaissance Leonardo DaVinci discovered that the perfect square is 1:1:618. I would like to know if there is a perfect square measure, then is there a perfect measure for a triangle or a circle? If so, could Pi be measured by a new and other calculation system which is similar to...
  35. cseil

    Faraday's and Lenz's Law - square coil

    Homework Statement A square coil rotates around an axis passing through the center. It is inside a magnetic field of B= 0.6T uniform and constant. The side of the coil is a = 2cm, the resistance R is 0.1 ohm. The coil is powered by a generator that gives an emf = 0.2 + 0.24sin(ωt). The current...
  36. Nathanael

    Probability of a point in a square being 0.5 from perimeter

    Homework Statement Consider a square of side length 1. Two points are chosen independently at random such that one is on the perimeter while the other is inside the square. Find the probability that the straight-line distance between the two points is at most 0.5. 2. The attempt at a solution...
  37. R

    Square Hill Barrier, weird question wording

    Homework Statement Consider a square hill barrier produced by a 10V potential. Incident upon this barrier is a steady stream of 5eV electrons. (a) If half the electrons are transmitted, how thick is the barrier? (Please derive the transmission probability rather than merely quoting it.)...
  38. karush

    MHB Indefinite integral complete square

    $$\int_{}^{} \frac{1}{\sqrt{16+4x-2x^2}}\,dx$$ $$\frac{\sqrt{2}} {2}\int_{}^{} \cos\left(\frac{x-1}{3}\right)\,dx$$ So far ? Not sure
  39. I

    MHB Growth proportional to square root of worth.

    Hi! :o I'm stuck :confused: I was thinking I need to use the equation $f=kw^2$ but I'm really not sure.
  40. P

    Partial derivative of a square root

    Hi, I'm using partial derivatives to calculate propagation of error. However, a bit rusty on my calculus. I'm trying to figure out the partial derivative with respect to L of the equation: 2pi*sqrt(L/g) (Yep, period of a pendulum). "g" is assumed to have no error. I know I can use the...
  41. G

    A perfect square inside a circle and a perfect square

    A perfect square inside a circle (so the inner square's corners touch the circle) and a perfect square surrounds the circle (so the circle touches the sides of the outer square. Are the extra bits between the inner square and the circle equal to the extra bits between the circle and the outer...
  42. MidgetDwarf

    Show that for any square matrix, the matrix A +(A)^t is sym

    Show that for any square matrix, the matrix A + ( A )^t is symmetric. My attempt. I know that A square matrix has the property that asub (ij). Where i=1,..., m and j=1,..,n. M=n(same number of rows and columns). I know that a transpose of a matrix means to interchange the rows with columns...
  43. S

    Probability integral, Expectation Value and Square of Psi

    I have come across a bit of conflict in wording of some physics and chemistry textbooks about the probability of finding particles in certain places. To be more specific, I have come across 3 different statements: 1. $$\int_a^b {| \psi(x) |^2 dx}$$ The above integral is said to give the...
  44. G

    Fundamental frequencies of square wave and sine wave

    Homework Statement What are the fundamental frequencies for a 50 kHz square waveform of 50% duty cycle and a 25 kHz sinusoidal waveform, respectively? (The duty cycle of a square waveform is the ratio between the pulse duration and the pulse period.) Homework Equations My teacher then gave...
  45. Shackleford

    Find the square roots of a = root3 + root3*i

    I don't recall ever doing this but maybe I have. z2 = a = p [cos Ψ + i sin Ψ] = √3 + i*√3 p = √6 Ψ = π/4 Using the formula in the notes, z = 61/4 * exp[i*(π/4 + 2π*k)/2], k = 0, 1.
  46. R

    Electric Field at Center of Square: Mag & Dir

    Homework Statement In the figure, four charges, given in multiples of 5.00×10-6 C form the corners of a square and four more charges lie at the midpoints of the sides of the square. The distance between adjacent charges on the perimeter of the square is d = 1.30×10-2 m. What are the magnitude...
  47. D

    Error bars, Chi square distribution

    Hi, I'm doing a fit using Chi-square distribution. I have a data set and their errors, I found the best estimate minimizing Chi square, as usual, and I like to found the error bars of my best estimates but I don't know how to do that. Which is the standard form to do it?
  48. Mogarrr

    Prove Chi Square is Stochastically Increasing

    Homework Statement Prove that the X^2 distribution is stochastically increasing in its degrees of freedom; that is if p>q, then for any a, P(X^2_{p} > a) \geq P(X^2_{q} > a), with strict inequality for some a. Homework Equations 1.(n-1)S^2/\sigma^2 \sim X^2_{n-1} 2.The Chi squared(p) pdf is...
  49. R

    Figuring out changes in Intensity (Inverse Square Law)

    Homework Statement If I measure a sound intensity of 1.0 at distance R from its source, what intensity would I measure at distance 3R in a free, unbounded space? What is the difference in decibels? Homework Equations I know that the equation for this is 10 (log R2/R1) The Attempt at a...
  50. R

    Inverse Square Law HELP PLEASE

    Homework Statement If I measure a sound intensity of 1.0 at distance R from its source, what intensity would I measure at distance 3R in a free, unbounded space? What is the difference in decibels? & If I measure a sound pressure of 1.0 at distance R from its source, what pressure would I...
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