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. A

    Quantum: why can't you square every operator?

    In Griffiths book, he says (a+ + a-)2 = a+2 + a-2 + a+a- + a-a+. Why can you NOT do the same thing for a+2 = (-ip+mωx)2 ?! When I do this to find the 2nd excited state of SHO, it gives me wrong answer. I actually have to apply a+ two times to ψ0 in order to get ψ2. It is ridiculous that...
  2. B

    Bending moment of square tubing

    I have some square tubing 3x3x1/4" A36 that will be fixed on one end and free on the other the material 9' long how was I find the bending moment?
  3. Z

    How are square sound waves possible? How does a speaker sustain peak?

    Hello everyone :smile:, after spending many hours watching youtube videos, reading wikipedia articles and other related material, I came to the conclusion that my best hope at understanding this is to have an explanation personally explained to me, and I trust this is the right place to ask for...
  4. Drakkith

    Inverse Square Law: Explaining Reduced Data Rate w/ Distance

    Quoting from Wiki, bolded section mine: What exactly is going on here with the data rate? Is it just the strength of the signal that is falling off as distance increases? If so, how does that reduce the data rates that can be used? If not, what limits the data rates?
  5. D

    MHB Volume of a triangle type shape with a square bottom

    How do I find the volume of this shape? The bottom is a square in the xy plane where \(0\leq x,y\leq 1\). The object isn't a prism or pyramid so I am not sure what to do.
  6. STEMucator

    Proving outer content zero for a subset of the unit square

    Homework Statement Let ##S = \{ (x,y) \space | \space x=\frac{1}{n}, n = 1, 2, 3,... \}## be a subset of the unit square. Prove ##S## has outer content zero. Homework Equations ##C(S) = inf\{ \sum A_i \} = inf\{Area(P)\}## The Attempt at a Solution There are no answers I can check my work...
  7. S

    Rationalizing the denominator involving more than one square root

    Here's my problems: How might you "rationalize the denominator" if the expression is \frac{1}{2+7√2+5√3} or \frac{1}{\sqrt[3]{2}+1}? I know that in typical problems where we rationalize the denominator, we simply have to multiply the denominator and numerator by the conjugate of the denominator...
  8. S

    Square matrix to the power of a imaginary unit

    Hi; How to raising a square matrix to the power of a complex number? for example: [1 2;3 4]^(1+i) or mathematics software such as Scilab how solve such problems? -->[1 2;3 4]^(1+%i) ans = - 0.1482039 - 0.2030943 - 0.3046414 - 0.4528453 Thanks in advance...
  9. Math Is Hard

    Analyzing Enrollment Campaigns with Chi-Square: Is It the Right Approach?

    Homework Statement I'm trying to test a hypothesis that sending people both an email announcement and direct mail announcement produces significantly more enrollments in a free webinar than email or direct mail alone. I'd like to do an analysis on these groups created from 400 people...
  10. A

    Square Pulse Train Fourier Series help?

    Square Pulse Train Fourier Series help?? Homework Statement problem+directions below: Homework Equations ω=2\pif β=\frac{2\pi}{\lambda} The Attempt at a Solution Since the problem asks to make all time-dependent sinusoidal functions deal with x-direction, i don't think i need to...
  11. B

    Flux through a square and rectangle

    Homework Statement Flux: a. Calculate the flux of the vector v1 = (1, 3 5) through a 2×2 square in the x-z plane (i.e., y = 0). b. Calculate the flux of the vector v2=(z, y, -x) through this rectangle:0≤ x ≤3, 0≤ y ≤ 2, z = 0.. The Attempt at a Solution I guess flux is suppose to be...
  12. M

    Light's intensity increases by the square?

    A reading from e=mc2 by David Bodanis, The big question though is why? Why is squaring the velocity of what you measure such an accurate way to describe what happens in nature? One reason is that the very geometry of our world often produces squared numbers. When you move twice as close...
  13. D

    QM - Transmission coefficient for square well

    Homework Statement A steady stream of 5 eV electrons impinges on a square well of depth 10 eV. The width of the well is 7.65 * 10^-11 m. What fraction of electrons are transmitted?Homework Equations The following equation for the transmission coefficient, T, is given: T = [1 + \frac{V_0 ^2...
  14. J

    Strange square matrix question

    Homework Statement Show that for a square matrix the (i,j) entry is equlivant to the (j,i) entry in a symmetric matrix. Homework Equations The Attempt at a Solution I just felt this question was weird. They don't give the answers so I'm looking for confirmation. I guess...
  15. K

    8 Electrons in a 3-D Infinite Square Well w/ Spin

    Homework Statement A cubical box whose sides are length L contains eight electrons. As a multiple of $$\frac{h^2}{2mL^2}$$ what is the energy of the ground state of the eight electrons? Assume the electrons do not interact with each other but do not neglect spin. Homework Equations...
  16. M

    Number of triangles in a square grid of unknown size

    Hello. I came up with this problem while I was waking up this morning, and some of the finer aspects have me pretty confused. First off, I made the simplification of a square grid because I'm not yet ready to deal with non-square grids, but maybe we can get to that later. Here's where I got...
  17. N

    Charge distribution along a square loop in equilibrium

    Homework Statement A conductor (wire) is folded into a square loop with each side having a length of a. Total charge of Q is transferred onto the conductor. Describe the line charge density of the square loop in equilibrium. (If I am interpreting this correctly what is required is...
  18. S

    Area of region inside a square

    Hi, This question is killing me (please note that it's not homework, this is from self study): The shaded region inside a square of side "a" consists of all points that are closer to the centre of the square than any of its edges (emphasis on any of its edges--the resulting region is like a...
  19. P

    Calculating Rotational Inertia and Speed of a Square Plate

    Homework Statement A uniform square plate ABCD has mass 0.8 kg and side length .8 m. The square is pivoted at vertex D and initially held at rest so that sides AB and CD are horizontal (see the diagram). After it is released, the plate swings downward, rotating about the pivot point...
  20. micromass

    Challenge IV: Complex Square Roots, solved by jgens

    This is a well-known result in complex analysis. But let's see what people come up with anyway: Challenge: Prove that there is no continuous function ##f:\mathbb{C}\rightarrow \mathbb{C}## such that ##(f(x))^2 = x## for each ##x\in \mathbb{C}##.
  21. MarkFL

    MHB Calculate Volume of Truncated Square Pyramid | Yahoo Answers

    Here is the question: I have posted a link there to this topic so the OP can see my work.
  22. 7

    Particle in an infinite square well - interval -d/2<x<d/2

    Homework Statement Particle is in an infinite square well of width ##L## on an interval ##-L/2<x<L/2##. The wavefunction which describes the state of this particle is of form: $$\psi = A_0\psi_0(x) + A_1\psi_1(x)$$ where ##A_1=1/2## and where ##\psi_0## and ##\psi_1## are ground and first...
  23. R

    An Integral With A Square Root In The Denominator

    How would you integrate it? \int \frac{d \varphi}{\sqrt{1 + \frac{a^2 b^2 \sin^2 \alpha}{(a \sin \varphi + b \sin (\alpha - \varphi))^2}}} I know that solving it numerically would probably be easier, but I would prefer a closed form solution in this case.
  24. N

    Square pivoted at corner-conservation of energy

    Homework Statement A uniform square plate ABCD has mass 2.5 kg and side length 0.8 m. The square is pivoted at vertex D and initially held at rest so that sides AB and CD are horizontal (see the diagram). After it is released, the plate swings downward, rotating about the pivot point...
  25. D

    Calculating Moment of Inertia for Square Particle System

    Homework Statement There are four masses (particles) with a mass of 30gr each and they are at the vertices of a square that has each side with a length of 90cm. What is the moment of inertia of this system through a perpendicular axis that is at the center of the square?The Attempt at a...
  26. T

    Square loop, find the charge in the resistor

    Homework Statement A square loop of wire is made up of 50 turns of wire, 45 cm on each side. The loop is immersed in a 1.4T magnetic field perpendicular to the plane of the loop. The loop of wire has little resistance but it is connected to two resistors in parallel as shown. (a) When the loop...
  27. tomwilliam2

    Square of z-component of angular momentum eigenvalues

    Homework Statement I'm trying to demonstrate that if: $$\hat{L}_z | l, m \rangle = m \hbar | l, m \rangle$$ Then $$\hat{L}_z^2 | l, m \rangle = m^2 \hbar^2 | l, m \rangle$$Homework Equations $$\hat{L}^2 = \hat{L}_x^2 + \hat{L}_y^2 + \hat{L}_z^2$$ $$\hat{L}_z = -i\hbar \left [ x...
  28. Y

    MHB Exploring the Equality of Square Roots: A Basic Question

    Hi, I have a very basic question that suddenly hit me regarding square roots. Why this is equal \[\sqrt[3]{(1+x^{3})^{2}}=(1+x^{3})^{^{\frac{2}{3}}}\] but this isn't \[\sqrt{(x-2)^{3}}\neq (x-2)^{\frac{3}{2}}\] (well according to Maple it isn't) I understand why the first one is correct...
  29. T

    Force on charges placed at vertices of a square.

    Hello. This isn't a homework, but rather my own self-study of a textbook (Franklin's Classical Electromagnetism), so if this is an inappropriate place for these types of questions let me know. Homework Statement Four equal charges q are placed at the vertices of a square of side L. What is...
  30. E

    Moment of inertia of a square lamina through a diagonal

    Homework Statement Square lamina (of side a) of uniform density. Find I about a diagonal. Homework Equations I = ∫ dm*l^2 The Attempt at a Solution So I drew a square and its diagonal and I imagine a differential mass drawn somewhere on the lamina. The distance squared to that...
  31. J

    Trig Help: Measuring Length & Coordinates on a Unit Square Grid

    0. The app does not have the template built in so ill do my best, sorry i don't have a computer right now. 1. This is a personal project, and there is a lot to it but I'm cutting out down to where i need help. Imagine a 2x2 grid of squares (2d for now). The center vector is at (0,0), and the...
  32. C

    Intuition why area of a period of sinx =4 = area of square unit circle

    Homework Statement This isn't really homework, but I've been reviewing calc & trig and realized that the area of one period of sin(x) = 4. Since sin(θ) can be understood as the y-value of points along a unit circle, I noticed that the area of a unit square that bounds the unit circle is...
  33. Jalo

    Finite square well potential energy

    Homework Statement Hello. Imagine a particle bound in a square well potential of potential energy V0 if |x| > a 0 if |x| < a The wave function of the particle is: (ignoring the time dependency) -A*exp(kx) if x<-a B*sin(3*pi*x/4a) if |x|<a A*exp(-kx) if x>a where k =...
  34. M

    Help in calculating the square of a number in sexagesimal notation?

    How would you go about calculating a number's square entirely in sexagesimal notation (i.e. base 60). For example, how would you calculate the square of 37 + 4/60 + 55/60^2? If you can please show me how to calculate a number's square entirely in sexagesimal notation without using decimals it...
  35. A

    Solving for "a" in Square Root Equation

    Homework Statement Get the value of a if \sqrt{6-\sqrt{a}}+\sqrt{6+\sqrt{a}}=\sqrt{14} The Attempt at a Solution nothing succesfull Feel free to move this thread,..I actually place it here to tap more brains
  36. A

    Magnetic Field at the center of a square

    Homework Statement Homework Equations not sure The Attempt at a Solution I am not sure how to start this problem.
  37. B

    Root Mean Square Or Standard Deviation

    Hello, I've been trying to find online where I could calculate my grade based off a college curve. So the average grade on the test was a 63. The RMS is 16. I got a 86. So what will my grade curve to? This is out of 50 people. Also, the professor curves to a 70 (I think).
  38. T

    Calculate the net force on square loop (Magnetism)

    Homework Statement A square loop of wire of side length L lies in the xy-plane, with its center at the origin and its sides parallel to the x- and y- axes. It carries a current i, in a counterclockwise direction, as viewed looking down the z-axis from the positive direction. The loop is in...
  39. I like Serena

    MHB AM-GM inequality for sum of 3 square roots

    Let $a,b,c$ be positive real numbers with sum $3$. Prove that $√a+√b+√c≥ab+bc+ca$.
  40. R

    Reducing 20mm x 20mm x 1.6mm Square Tubing

    Hey Guys, I am currently working on a personal project for myself, please note I am not an engineer just a person with a big shed with tools. :devil: I am trying to create a swage machine, which will reduce 20mm x 20mm x 1.6mm RHS so it can fit into another unaltered piece and hold. Video...
  41. S

    Finding the Minimum Mean Square Estimator for Scalar Parameter w

    I am not able to understand how to go about this problem: Find the minimum mean square estimator for the scalar parameter w based on the scalar observation z = ln w + n where f(w) =1 if 0<=w<=1; 0 else: and f(n) =e^-n if n>= 0; 0 else I did f(z/w) = (f(n))...
  42. S

    MHB Linear Minimum Mean Square Estimator

    I am not able to understand how to go about this problem: Find the minimum mean square estimator for the scalar parameter w based on the scalar observation z = ln w + n where f(w) =1 if 0<=w<=1; 0 else: and f(n) =e^-n if n>= 0; 0 else I did f(z/w) = (f(n))/ g'(n)...
  43. C

    Probability of energy measurement in an infinite square well

    Homework Statement Consider a particle in 1D confined in an infinite square well of width a: $$ V(x) = \begin{cases} 0, & \text{if } 0 \le x \le a \\ \infty, & \text{otherwise} \end{cases} $$ The particle has mass m and at t=0 it is prepared in the state: $$ \Psi (x,t=0) = \begin{cases} A...
  44. A

    Rate of change of area of a square with respect to its perimeter

    oops I meant "Rate of change of area of a square with respect to its side length" Ok I have to use this annoying Stewart textbook for my Calc class in college. Most of the questions require what I like to call "Monkey Math," where you just memorize a set of steps and then follow them rigidly...
  45. A

    Mutual inductance between straight line cable & square shape Frame

    Homework Statement Calculate mutual-inductance between straight line cable and square shape frame, as shown on picture. Homework Equations I am not sure which equation will be used here because as far as my knowledge goes , mutual inductance should be concerned with turns in...
  46. V

    Formula & Conversion with a square root

    I'm comparing the shear formula for a beam in english and metric. But it seems the formula or result don't match. In English, the formula is Vc=2*b*d*sqrt(Fc) Given b=11.81102 inches d=18.11024 inches fc=4000 psi Vc=2*b*d*sqrt(Fc)=27056 lbs Now converting the units in metric...
  47. J

    I understanding the Fourier components of a square wave

    In my physics book there is an example of making a square wave by "simply" summing up a few cosine waves. The book says these first three waves are the first three Fourier components of a square wave, yet when I sum the three wave functions up, I get something way off; as does my calculator...
  48. MarkFL

    MHB Polo's question at Yahoo Answers regarding making a perfect square trinomial

    Here is the question: Here is a link to the question: Find the constant necessary to make a perfect square trinomal 5c^2-8c+__? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.
  49. Petrus

    MHB Integrate Sine and Square root Composite Function

    Hello MHB, I got stuck on integrate this function \int \frac{\sin^3(\sqrt{x})}{\sqrt{x}}dx my first thinking was rewrite it as \int \frac{\sin^2(\sqrt{x})\sin(\sqrt{x})}{\sqrt{x}}dx then use the identity \cos^2(x)+\sin^2(x)=1 \ \therefore \sin^2x=1- \cos^2(x) \int...
  50. B

    How to calculate a harmonic of a square wave

    Hi, I'm a bit of a newbie to additive synthesis.. I just want to clarify that I am doing the correct calculation before continuing. If I wanted to calculate the 5th harmonic of a square wave (the fundamental freq. being 200Hz and the amplitude of the fundamental being 1) would the...
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