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. M

    MHB How to Solve an Equation with Square Roots?

    Please Help me solve it \[ \sqrt{x}+\sqrt{x+8}=8 \] thanks
  2. Terrycho

    I The wave function in the finite square well

    Hello! I have been recently studying Quantum mechanics alone and I've just got this question. If the potential function V(x) is an even function, then the time-independent wave function can always be taken to be either even or odd. However, I found one case that this theorem is not applied...
  3. Rongeet Banerjee

    Root Mean Square Velocity of Gases

    This question came in NEET Exam 2018.Now my first query is that in the question,the mass of one Oxygen molecule is given wrong.Its exactly half it's true value.I don't think anybody has noticed this before because I couldn't find any change in the printed question on so many different books...
  4. M

    I Reduced chi square for few data points

    Hello! I need to make a straight line fit to 8 points, with errors on them. The data is like this ##x = [1,2,3,4,5,6,7,8]##, ##y=[377.488 691.191 , 1030.319, 1428.801, 1753.884, 2113.065 , 2398.642, 2797.664]##, ##y_{err}=[97.145, 131.452, 160.492, 188.997, 209.397, 229.840, 244.879...
  5. B

    Have I Done This Question Right?

    Here is the full question. I have already tried to answer the questions and have put a red dot next to the answers I think are right? Here is my working out to get the answers I had above Have I done this question right? Sadly I don't have the answers to check for myself here so I'm...
  6. R

    Electric field at (0,0) for this charged square conductor

    Can we assume that square charge resembles a sphere shell, and think like electric field at sphere shell's center is 0.
  7. M

    Can I Use a Transformation Matrix to Solve the Radon Transform of a Square?

    Can I attempt this problem using the transformation matrix? I'm not sure how to go about solving this?
  8. F

    Work done on a moving square wire loop in a B-field

    There’s a current i in the loop in the figure. The Ampere’s force iLB on a wire of length L exerts on charges in the wire but it does no work on the charges. The charges would go in circular motion if there were no wire. Then the wire exerts exactly iLB on those charges to keep the charges...
  9. R

    Does a square shaped line may have a circle shaped Gauss' surface

    Summary:: For finding the electric field at P in the photo below, may I select a gaussian surface circular? [Mentor Note -- thread moved to the schoolwork forums, so no Homework Template is shown]
  10. Hamal_Arietis

    How Do You Calculate the Electric Potential of a Square Plate?

    I found out the equation of electric potential, that is V=\int_{-a}^a \int_{-a}^{a} \frac{σdxdy}{4 \pi \epsilon_0\sqrt{x^2+y^2+d^2}}=\int_{0}^a \int_{0}^{a} \frac{σdxdy}{\pi \epsilon_0\sqrt{x^2+y^2+d^2}} but I couldn't calculate the integral. It seems convenient if we use the polar coordinate...
  11. B

    MHB Creating Linearly Dependent Square Matrix from Cam Mechanism Equation

    I have an equation that comes from an especific topic of cam mechanisms and it goes like this: $$ 2M[tan(B)-B] - \beta Ntan(B) - 2\pi\sqrt{1 - N^2} = 0 \ \ \ \ \ \ \ \ \ (1) $$ For this it doesn't matter what each variable means. I'm trying to create a 3x3 matrix with a determinant equal to...
  12. tworitdash

    A Integral of a sinc squared function over a square root function

    I want to find the analytical solution to the integral given below. \int_{-\infty}^{\infty} \frac{ sinc^2(\frac{k_yb}{2})}{\sqrt{k^2 - k_x^2 - k_y^2}}dk_y In other words, \int_{-\infty}^{\infty} \frac{ \sin^2(\frac{k_yb}{2})}{(\frac{k_yb}{2})^2\sqrt{k^2 - k_x^2 - k_y^2}}dk_y Can this be...
  13. phun_physics

    I Derivation of Average Square Energy Fluctuation in a Canonical System

    The canonical ( Boltzmann) distribution law for a canonical system is described the probability of state ##v## by ##P_v = Q^{-1} e^{-\beta E_v} ## where ##Q^{-1}## is the normalization constant of ##\sum_v P_v = 1## and therefore ##Q = \sum_{v}e^{-\beta E_v}##. Chandler then derives ##...
  14. N

    Calculating Electric Field for 4 Point Charges in a Square Configuration

    I have the following question and I can't figure out how to, is there anybody who can help?
  15. jk22

    B Is the sign of the square root dependent on the argument inside it?

    Could it be said that since ##a=A(f(x))\sqrt{f(x)}##, with ##A(x)\in\{1,-1\}## then ##a^2=f(x)##,, that ##a## is the square root of ##f(x)## ? In other words could the sign of the root depend on the argument inside it ? Else it would have to be chosen by human free will and to be blocked for...
  16. A

    Comp Sci Recursive Double code to Calculate the sum of the square roots <= a number

    #include<stdio.h> #include<math.h> double foo(int n){ if(n==1){ return(1); } if(n!=0){ return( sqrt((n)+foo(n-1) ) ); } } int main(){ int num; printf("Enter the number: "); scanf("%d",&num); foo(num); printf(" %lf ",foo(num)); return(0); }I...
  17. obstinatus

    I (Baby QM) Analytic Solution to the Infinite Square Well Problem

    Hi, I think I'm having a bit of a brain fart...I'm messing with this numerical code trying to understand the 1-D time-independent Schrodinger's equation infinite square well problem (V(x) infinite at the boundaries, 0 everywhere else). If normalized Phi squared is the probability of finding...
  18. LCSphysicist

    Exploring the TL Interval Square Measurement

    I was reading about the general theory of relativity, and came to a chapter that the author start to talk about an invariant measurement by [TL] named interval square. It's the first time that i read about it, and i don't get it yet. An event, what he is calling, is anything? If I am thinking...
  19. M

    MHB Method of least square: initial position & velocity

    Hey! :o A point is moving linearly with constant velocity $v$ and the movement is $x=a+vt$. The below information is given: Find the initial position $a$ and the velocity using the method of least square. Could you give me a hint how we use this method here? Couldn't we use the data of...
  20. CrosisBH

    Computing the wave function of a square potential

    The book's procedure for the "shooting method" The point of this program is to compute a wave function and to try and home in on the ground eigenvalue energy, which i should expect pi^2 / 8 = 1.2337... This is my program (written in python) import matplotlib.pyplot as plt import numpy as...
  21. D

    Thick square loop made of Al with the top half exposed to a B field

  22. Tony Hau

    Potential energy as a function of the square of this angle

    The problem of my question is the b part below: I know that the potential energy is just the gravitational potential energy, which is mgh(𝜃) = mg[(R+b/2)cos𝜃 +R𝜃sin𝜃], derived from the geometry. The equilibrium point is at 𝜃=0 and the system is a stable equilibrium for R>b/2. However, I have no...
  23. Zack K

    Infinite Square Well with polynomial wave function

    Some questions: Why is this even a valid wave function? I thought that a wave function had to approach zero as x goes to +/- infinity in all of space. Unless all of space just means the bounds of the square well. Since we have no complex components. I am guessing that the ##\psi *=\psi##. If...
  24. C

    A Square of an integral containing a Green's Function

    Let's say you have a tensor u with the following components: $$u_{ij}=\nabla_i\nabla_j\int_{r'}G(r,r')g(r')dr'$$ Where G is a Green function, and g is just a normal well behaved function. My question is what is the square of this component? is it...
  25. I

    Infinite Square Well Expansion: Mass m in Ground State

    A particle of mass m is in the ground state on the infinite square well. Suddenly the well expends to twice it's original size (x going from 0 to a, to 0 to 2a) leaving the wave function monetarily undisturbed. On answering, for ##\Psi_{n}## I got ##\Psi_{n}## = ##\sqrt{\frac{1}{a}}...
  26. Eggue

    Moment of inertia of a rod bent into a square

    I tried to find the moment of inertia of 2 rods connected at the corners by adding up their moments of inertia: \frac{1}{3}(\frac{M}{4})a^2 + \frac{1}{3}(\frac{M}{4})a^2 = \frac{1}{6}Ma^2 I then tried to solve for the moment of inertia at the center of mass of the 2 rods using the parallel...
  27. D

    What is the Max Load Capacity for 4x4x.188 HSS Square Tubing?

    Hi there, I am very new to the forum, but the reason I ended up here in the first place, is that I was trying to find some working strengths, specifically on 4"x4"x.188" HSS Square Tubing(A500). I would like to know what the max point load that an 8'L resting on 7'W supports(leaving 6" at each...
  28. P

    Magnetic field Calculation of a Square Wire Loop (with a changed segment)

    I tried to solve the above i have one confusion here. I have marked the areas as shown B2 = B4 = 0; B1 , B5 Out of Page ; B3, B6 Into the Page. B1 and B5 Calculation Now main doubt is regarding the B field of the finite wire let us say 1. I took the derivation of the infinite wire as below from...
  29. K

    I Are there upper and lower limits to the inverse square law?

    Quoting from Modern Cosmology by Andrew Liddle on pages 130 and 131: "Let me stress right away that the luminosity distance is not the actual distance to the object, because in the real Universe the inverse square law does not hold. It is broken because the geometry of the Universe need not be...
  30. M

    Find the probability of a particle in the left half of an Infinite Square well

    Attempt: I'm sure I know how to do this the long way using the definition of stationary states(##\psi_n(x)=\sqrt{\frac {2} {a}} ~~ sin(\frac {n\pi x} {a})## and ##\int_0^{{a/2}} {\frac {2} {a}}(1/5)\left[~ \left(2sin(\frac {\pi x} {a})+i~ sin(\frac {3\pi x} {a})\right)\left( 2sin(\frac {\pi x}...
  31. P

    MHB Square Sheet of Cardboard Problem

    The question and the answer choices are in the screenshots. I need it asap if possible please. Thanks!
  32. G

    MHB What is the Surface Area of a Square with Given Points and Side Lengths?

    Let E, F be such points inside the ABCD square that | ∢AEF | = | ∢EFC | = 90∘ and | AE | = 2, | CF | = 6 and | EF | = 6. Calculate the surface of ABCD.
  33. A

    I How Far Can the Square Kilometre Array 'Listen' for Extraterrestrial Signals?

    As some of you probably know, the Square Kilometre Array will become the biggest radio telescope on Earth, with a collecting area of 1 square kilometre. The construction will start in 2021 and the first light is expected to take place in 2027. It will cover the frequencies from 50 MHz to 15...
  34. F

    How to derive a log-antilog opamp square law transfer function?

    Firstly, this is not a homework question. I found a worksheet online with an example of a square law circuit built using log-antilog operational amplifiers. I tried to derive the transfer function but I can't seem to eliminate the reverse saturation current term ##I_S##. I would really...
  35. M

    MHB Induction: Each square can be covered by L-stones

    Hey! :o A square with the side length $2^n$ length units (LU) is divided in sub-squares with the side length $1$. One of the sub-squares in the corners has been removed. All other sub-squares should now be covered completely and without overlapping with L-stones. An L-stone consists of three...
  36. Math Amateur

    MHB Complex Function Theory: Explaining Example 1.5, Section 1.2, Chapter III

    I am reading Bruce P. Palka's book: An Introduction to Complex Function Theory ... I am focused on Chapter III: Analytic Functions, Section 1.2 Differentiation Rules ... I have yet another question regarding Example 1.5, Section 1.2, Chapter III ... Example 1.5, Section 1.2, Chapter III...
  37. Math Amateur

    MHB Complex Square Root Function: Qs from Bruce P. Palka's Ex. 1.5, Ch. III

    I am reading Bruce P. Palka's book: An Introduction to Complex Function Theory ... I am focused on Chapter III: Analytic Functions, Section 1.2 Differentiation Rules ... I need further help with other aspects of Example 1.5, Section 1.2, Chapter III ... Example 1.5, Section 1.2, Chapter III...
  38. Math Amateur

    MHB Differentiating Complex Square Root Function: Bruce P. Palka, Ex. 1.5, Ch. III

    I am reading Bruce P. Palka's book: An Introduction to Complex Function Theory ... I am focused on Chapter III: Analytic Functions, Section 1.2 Differentiation Rules ... I need help with an aspect of Example 1.5, Section 1.2, Chapter III ... Example 1.5, Section 1.2, Chapter III, reads as...
  39. Cocoleia

    Infinite square well, dimensionless Hamiltonian..

    I have always seen this problem formulated in a well that goes from 0 to L I am confused how to use this boundary, as well as unsure of what a dimensionless hamiltonian is. This is as far as I have gotten
  40. Mathman2013

    Optimization problem (Max area of a combined semi circle and a square)

    A figure is made from a semi circle and square. With the following dimensions, width = w, and length = l. Find the maximum area when the combined perimiter is 8 meter. I first try to construct the a function for the perimeter. 2*l + w + 22/7*w/2 = 8 - > l = 4 - (9*w)/7 Next I insert this...
  41. karush

    MHB 7.4.32 Evaluate the integral by completing the square

    7.4.32 Evaluate the integral $\displaystyle \int_0^1\dfrac{x}{x^2+4x+13}\, dx$ ok side work to complete the square $x^2+4x=-13$ add 4 to both sides $x^2+4x+4=-13+4$ simplify $(x+2)^2+9=0$ ok now whatW|A returned ≈0.03111
  42. Math Amateur

    MHB Verify Gamelin's Remark: Complex Square and Square Root Functions

    I am reading Theodore W. Gamelin's book: "Complex Analysis" ... I am focused on Chapter 1: The Complex Plane and Elementary Functions ... I am currently reading Chapter 1, Section 4: The Square and Square Root Functions ... and need some help in verifying a remark by Gamelin ... ... The...
  43. J

    I Calculating the expected value of the square of an integral of Brownian Motion

    For a standard one-dimensional Brownian motion W(t), calculate: $$E\bigg[\Big(\frac{1}{T}\int\limits_0^TW_t\, dt\Big)^2\bigg]$$I can't figure out how the middle term simplifies. $$ \mathsf E\left(\int_0^T W_t\mathrm dt\right)^2 = \mathsf E\left[T^2W_T^2\right] - 2T\mathsf E\left[W_T\int_0^T...
  44. Haynes Kwon

    I Why does the square of the amplitude of a wave function represent P?

    Born's postulate suggests if a particle is described a wave function ψ(r,t) the probability of finding the particle at a certain point is ψ*ψ. How does this work and why?
  45. C

    Induced Current In a Tilted Square Inside and Outside a Solenoid

    Plot for the ring ^ Calculations for the Square ^ Plot for square without cosg on the outside calc ^ Plot for square with cosg on the outside calc ^ As can be seen the formulas for the square conductor do not connect at R, which I'm not sure if they should or if they should not as in this...
  46. karush

    MHB 5.3 Show that a square matrix with a zero row is not invertible.

    Show that a square matrix with a zero row is not invertible. first a matrix has to be a square to be invertable if $$\det \begin{pmatrix}1&0&0\\ 0&1&0\\ 3&0&1\end{pmatrix}=1$$ then $$\begin{pmatrix} 1&0&0\\ 0&1&0\\ 3&0&1\end{pmatrix}^{-1} =\begin{pmatrix}1&0&0\\ 0&1&0\\ -3&0&1...
  47. I

    Simple Finite Square Well Problem help *Ignore, made stupid mistake*

    I've tried to carry out the solution to this as a normal 2nd order Differential Equation ##\psi ##'' - ##-k^2 \psi ## = 0 Assume solution has form ##e^{\gamma x}## sub this in form ##\psi## and get ##\gamma ^2## ##e^{\gamma x} ## + ##k^2 e^{\gamma x}## = 0 Solution is ##\gamma## = 0 or ##k^2##...
  48. I

    Epsilon delta proof of the square root function

    Let ##\varepsilon > 0## be arbitrary. Now define ##\delta = \text{min}\{\frac{a}{2}, \varepsilon \sqrt{a}\}##. Now since ##a>0##, we can deduce that ##\delta > 0##. Now assume the following $$ 0< |x-a| < \delta $$ From this, it follows that ##0 < |x-a| < \frac{a}{2} ## and ##0 < |x-a| <...
  49. cianfa72

    I Gaussian elimination for a singular square matrix

    Hi, I've the following doubt: consider an homogeneous linear system ##Ax=0## with ##A## a singular square matrix. The resulting matrix attained through Gaussian elimination will be in upper triangular or raw echelon form ? Thanks.
  50. arcTomato

    How to show the root mean square deviation

    Hi I tried like this. ##σ^2=<(λ_1+λ_2+,,,+λ_i)^2>=<λ_1^2>+<λ_2^2>+,,,<λ_i^2>## And I know ##σ^2=Σ_in_iλ_i^2##from equation (4-12) (so this is cheat 😅). So I know also ##<λ_i^2>=n_iλ_i^2##, But why?? I know if I take ##λ=1 ,σ^2=n##,But I don't understand ##λ≠1## version. Sorry my bad...
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