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. thebosonbreaker

    I Reason for the irrationality of (most) square roots?

    The square root of any integer that is not a square number is always an irrational number. I find this fact rather spectacular, but my question is why is this true? I have seen the formal proof for the irrationality of root 2 so I could vaguely see how one could prove that all (apart from sq...
  2. N

    I Square root of a complex number

    if a is a complex number then sqrt(a^2)=? Is it is similar to Real Number? Help me please
  3. L

    B Representation of complex of square root of negative i with unitary power.

    Can ##sqrt(-i)## be expressed as a complex number z = x + iy with unitary power?
  4. I

    Arc Length of Parabola & Square Root Function

    Homework Statement Consider the curves: y = x^2 from 1/2 to 2 and y = \sqrt{x} from 1/4 to 4. a. Explain why the lengths should be equal. b. Set up integrals (with respect to x) that give the arc lengths of the curve segments. Use a substitution to show that one integral can be...
  5. D

    Finding the Length of a Small Square

    Homework Statement 2. Homework Equations [/B] The Attempt at a Solution I can find the length of the large square. The small square is where the trouble starts. If I look at the part of the circle where the small square is and put a center of a coordinate system at the bottom part of the...
  6. T

    B Simple double integration of square wave question

    Hi, Simple question, sort of: I see that according to the internet the mathematical description of a triangular wave is rather complex, so I'll try to stay as far away from that as I can, because I'm a bit rusty. I understand that if you integrate a square wave you get a triangular wave on the...
  7. D

    B The Square of the Sum Formula and real world scenarios

    I'm starting with my self studying of math with Algebra I. The text I'm using is Gelfand and Shen's Algebra. I'm at the point where it talks about the Formula for the Square of the Sum, The Square of the Distance Formula, and The Difference of Squares Formula. In going over this, I understand...
  8. A

    I Why Is the First Derivative Zero in Least Squares Optimization?

    Hello Sir, I would studying the theory of least square and I find that the derivative of the error summation between the predicated line points and the true data is equal zero. Why the first derivative is equal zero?
  9. F

    Conservation Laws in Elastic Collision of Particle with Rotating Square

    Homework Statement A particle of mass m and and velocity v collides with a square of mass M (at rest)whose movement is confined to rotation about its centet. I must now solve for the angular velocity and the velocity of the particle after the collision (elastic collision) Homework Equations...
  10. jlmccart03

    Velocity of a particle kicked into four point charge square

    Homework Statement Consider the arrangment of charges (fixed in place) shown in the figure. The square has side length d. (Figure 1) Now suppose the particle with charge q is released. It is "kicked" so that it's initial speed is v. After an unspecified trajectory, it is observed that the...
  11. K

    B Square root differential problem

    Hi, I working on their text this equation did not make sense to me. From equation 1 it differentiate second term , I wonder how he got second term of equation 2. What I think is, what I wrote at the bottom
  12. Mr Davis 97

    I Proof that the square root of 2 is irrational

    Quick question: In the proof that the square root of 2 is irrational, when we are arguing by contradiction, why are we allowed to assume that ##\displaystyle \frac{p}{q}## is in lowest terms? What if we assumed that they weren't in lowest terms, or what if we assumed that ##\operatorname{gcd}...
  13. karush

    MHB 206.08.04.59 int completing the square

    $\tiny{206.08.04.59}$ $\textrm{Solve by completing the square}$ \begin{align*}\displaystyle I_{41}&=\int \frac{1}{\sqrt[]{x^2+2x+37}} \, dx\\ \end{align*} $\textit{from the radical we have}$ \begin{align*}\displaystyle x^2+2x+37&=x^2+2x+1 +37-1\\ &=(x+1)^2 + 36 \end{align*}...
  14. Adgorn

    Proving the square root of a positive operator is unique

    Homework Statement The problem relates to a proof of a previous statement, so I shall present it first: "Suppose P is a self-adjoint operator on an inner product space V and ##\langle P(u),u \rangle## ≥ 0 for every u ∈ V, prove P=T2 for some self-adjoint operator T. Because P is self-adjoint...
  15. M

    How Can I Generate a 1Hz Pulse for a Digital Clock Using 74LS90 and 74LS47?

    i'm new on creating my own circuit. And I'm trying to create a digital clock, using 74ls90+74ls47 I have problem on creating 1hz square pulse part. This is my teacher's Simulation I have searched on google that i can create 1hz pulse by using NAND gate, crystal, or Ne555, but i can't find any...
  16. A

    I Square of the difference of four-vectors

    What is the correct way to expand (p3-p4)2 where p3 and p4 are 4-vectors, with metric gmu nu=diag[1,-1,-1,-1], p = [wp, p], where p is 3-vector, and wp= (p2+m2)(1/2)
  17. Mathysics29

    Olympiad problem -- Sum involving many square roots....

    √(2-√(2^(2)-1))+√(4-√(4^(2)-1))+√(6-√(6^(2)-1))+...+√(80-√(80^(2)-1)) How the find it's value
  18. B

    B ##AB = I \implies BA = I##, for square matricies ##A,B##

    Let ##(AB)_j## be the jth column of ##AB##, then ##\displaystyle (AB)_j = \sum^n_{r= 1} B_{rj} \alpha_r## where ##\alpha_r## is the rth column of ##A##. Also ##(BA)_j = B \alpha_j \implies A(BA)_j = \alpha_j## susbtituting this in the sum ##\displaystyle (AB)_j = \sum^n_{r = 1} B_{rj}A(BA)_r##...
  19. H

    I Square of Dirac delta function

    Is the square of a Dirac delta function, ##(\delta(x))^2##, still a Dirac delta function, ##\delta(x)##? A Dirac delta function peaks at one value of ##x##, say 0. If it is squared, it still peaks at the same value, so it seems like the squared Dirac delta function is still a Dirac delta...
  20. H

    B Understanding r^2 and the Role of Square Root in Data Analysis

    Hi guys. I was wondering something. In my math class, we were analyzing how strong the data was, and there was an r and r^2 value. I know the significance of r, but what's the point of knowing the square of the r value? Also, what's the use of square root? Like where does it help? I saw it one...
  21. binbagsss

    Integration question involving square root

    Homework Statement How to integrate ## \frac{dx}{dt}=\sqrt{\frac{k}{x}-1}## AND ## \frac{dx}{dt}=\sqrt{\frac{k}{x}+1}## k a constant here. I'm unsure what substitution to do. Many thanks in advance. Homework EquationsThe Attempt at a Solution I can't really get started as I'm unsure...
  22. M

    MHB Square Root vs Cube Root

    I know that x^2 = 4 yields two answers: x = -2 or x = 2. I also know that x^3 = 8 yields x = 2. Question: Why does the square root yield both a positive and negative answer whereas the cube root yields a positive answer?
  23. pHartless

    How Much Weight Can a 45-Degree Square Steel Tube Structure Support?

    I have a problem to do with my project in college. I'm creating a hanging fire pit, basically made of 3 lengths of square steel bar connected to a plate at the top and on hinges. The 3 legs of the frame move in slots and when in the open position would be at 45 degrees. The actual fire pit is...
  24. S

    Electric/Magnetic field Inverse square

    Homework Statement Using magnetic field over electric field Homework Equations no equation needed The Attempt at a Solution THis may not make sense but did an experiment dealing with the inverse square law and we measured the magnetic field in this case. Want to know is there some type of...
  25. M

    B Why Must the Expression Inside a Square Root Be Non-Negative?

    When we find solution set of an equation inside a square root why we should assume that inside of square root should be equal to or greater than zero? For example ##\sqrt{5x-4}##. How can I use here equal to or greater than zero symbol? Thank you.
  26. B

    Coulomb's law without a pure inverse square relationship?

    Then it goes on explaining how Gauss law would fail because for a very large surface, E field would be vanish with flux through it and though we can calculate div for this field it won't depend on source density. But I don't get what makes this particular function so evil that it would break...
  27. R

    Quantum Mechanics - Question about the Finite Square Well

    Hi, I'm preparing for an exam, and I'm going over past papers. I've solved parts a & b of this question without any problems, however I'm finding it hard to understand part c. I thought of shifting the boundary conditions so I'd have 0 and L in the place of ± L/2, but that would not work...
  28. C

    Instantaneous doubling of the Infinite Square Well Width

    Homework Statement A particle of mass m is moving in an infinite square well of width a. It has the following normalised energy eigenfunctions: $$u_n (x) = \sqrt{\frac{2}{a}} sin(\frac{n \pi x}{a})$$ (1) a) Give an expression that relates two orthogonal eigenfunctions to each other and use it...
  29. G

    Probability Density in an infinite 1D square well

    Homework Statement The wave function of a particle of mass m confined in an infinite one-dimensional square well of width L = 0.23 nm, is: ψ(x) = (2/L)1/2 sin(3πx/L) for 0 < x < L ψ(x) = 0 everywhere else. The energy of the particle in this state is E = 63.974 eV. 1) What is the rest energy...
  30. A

    Two-value system with square roots

    Homework Statement I have a problem with lines in analytic geometry, and I solved it in a certain way (parallel lines interceptions) which gives the correct result, and I'm happy with that. There was another method I thought I could use to solve it though, which went through the formulas of...
  31. Albert1

    MHB Find A in abcd=A(four digital number) is a perfect square ,given ab=2cd+1

    $\overline{abcd}=A$(four digital nmber) is a perfect square ,given $\overline{ab}=2\overline{cd}+1$ find $A=?$
  32. F

    I Integral involving square and log

    I have this integral that when solved, involves squares and natural logs, where ##A\,##,##\,b\,##, and ##\,x_e\,## are constants while ##x## is a variable. ##A = \int_{x_e}^{x} \frac{x^2 - b^2}{x} dx = \int_{x_e}^{x} x \, dx -b^2 \int_{x_e}^{x} \frac{dx}{x} = \frac{x^2}{2} - \frac{x_e^2}{2} -...
  33. M

    MHB Square Root: Positive & Negative

    Why do we get two answers when taking the square root? For example, let a = any positive number sqrt{a} = - a and a. Why is this the case? What about 0? Can we say sqrt{0} = - 0 and 0?
  34. CynicusRex

    Minimum of x+1/x (Perimeter Square < Perim equal area rects)

    Homework Statement Gelfand - Algebra p.115 problem 264: Prove that a square has the minimum perimeter of all rectangles having the same area. Hint. Use the result of the preceding problem. Homework Equations Preceding problem: Prove that a square has the maximum area of all rectangles having...
  35. R

    Maximizing Strength: Square Tubing on Fulcrums

    Interesting project. I was going to post my question as a standalone but I'll post it here first, as you refer to square aluminum tubing. I've got a 2 foot long steel square tube, not a rod. If I were to place it on two fulcrums -- one on each end -- and hang a weight from the middle of the...
  36. qnach

    Reasons for choosing square antenna?

    Is there any particular reason to choose a square shape antenna like http://www.globalspec.com/reference/70592/203279/2-5-4-by-4-wavelength-rectangular-microstrip-antenna instead of a circular shape?
  37. R

    MHB If y = sin inverse (x square + 2x) find dy/dx

    if y = sin inverse (x square + 2x) find dy/dx
  38. Berker

    Motion of 4 charges positioned in a square shape

    Homework Statement Four particles with equal charges q and equal masses m are placed on a plane so that they form the corners of a square with side length a. The charges are then released from rest at this configuration (shown as (i) in the figure). After the release, the particles accelerate...
  39. F

    Gas Laws -- why calculate the mean square speed at 273K?

    Homework Statement Why is the formula ##p = \frac{1}{3}\rho<c^2>## used to calculate the mean square speed at 273K? Why 273K?
  40. L

    I Finite Square Well: Bond States and Asymmetric Potential Wells

    I am not sure how is it possible that asymetric potential well does not have bond states if ##E<U_1<U_2##. In symmetric case solution always exists. Why this is a case?
  41. I

    Maximum area of triangle inside a square

    Homework Statement ##ABCD## is a square piece of paper with sides of length 1 m. A quarter-circle is drawn from ##B## to ##D## with center ##A##. The piece of paper is folded along ##EF##, with ##E## on ##AB## and ##F## on ##AD##, so that ##A## falls on the quarter-circle. Determine the maximum...
  42. Bassa

    "Shooting Method" for simulating a Particle in an Infinite Square Well

    Hello! I am trying to write a program that solves the Schrodinger Equation for a particle in an infinite square well. I did a lot of research regarding the methods that could be used to accomplish this. I am writing this program in Matlab. The method I am using is called the Shooting Method. In...
  43. hilbert2

    A Scale invariant inverse square potential

    Yesterday, I was thinking about a problem I had encountered many years before, the central force problem with a ##V(r) \propto r^{-2}## potential... If we have a Hamiltonian operator ##H = -\frac{\hbar^2}{2m}\nabla^2 - \frac{A}{r^2}## and do a coordinate transformation ##\mathbf{r}...
  44. acdurbin953

    Time-Dependent Perturbation of a 1D Infinite Square Well

    Homework Statement At t < 0 we have an unperturbed infinite square well. At 0 < t < T, a small perturbation is added to the potential: V(x) + V'(x), where V'(x) is the perturbation. At t > T, the perturbation is removed. Suppose the system is initially in the tenth excited state if the...
  45. I

    Magnetic Flux Through a Square Loop

    Homework Statement A loop of wire in the form of a square 1.50 m on each side, its plane makes an angle of 40.0° with a uniform magnetic field of 0.95 T. What is the magnetic flux through the loop? Homework Equations Φ = BAcosθ A = s^2 The Attempt at a Solution I found the area of the square...
  46. A

    MHB Not a "help need" but a question about "a self made square root formula"

    Hello,first time posting a thread not just here but generally so i'll try my best. So while i was in class we were learning about square roots,at first it seemed fairly easy,but when i asked my math teacher how do we find them more easily, he smiled and talled me:"The problem is,you just...
  47. B

    Infinite square well doubled with time

    A particle is in its ground state of an infinite square well of width a <xl i>=√2/a*sin(πx/a) and since it's an eigenstate of the Hamiltonian it will evolve as <xlα(t)>=√2/a*sin(πx/a)e^(-iE1t/ħ) where E=π2ħ2/2ma2 If the well now suddenly expands to witdh 2a If the well suddenly expands to 2a...
  48. Cocoleia

    Electric field above a charged square loop

    Homework Statement Homework EquationsThe Attempt at a Solution I have the complete solutions for this problem, I just don't understand them: This is the first part. I don't understand what r' is, or how we found it. Otherwise I understand the concept of the problem just not the details...
  49. R

    MHB Solution To Equation Involving Square Root: Extraneous Solution?

    Hi everyone, What is the solution set of the equation: sqrt{x+2}= x-4 I got 2 and 7. Is it correct or is it just 7. If so why? Thanks:)
  50. I

    MHB What are the new formulas for x and y that will converge to $\sqrt{k}$?

    I'm not sure which category to post this question under :) I'm not sure if any of you are familiar with "Greek Ladders" I have these two formulas: ${x}_{n+1}={x}_{n}+{y}_{n}$ ${y}_{n+1}={x}_{n+1}+{x}_{n}$ x y $\frac{y}{x}$ 1 1 1 2 3 1.5 5 7 ~1.4 12 17 ~1.4 29 41...
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