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. J

    Frequency for Vibration Modes of a Square Membrane

    So the equation to obtain the frequency of the modes of a square membrane is something like ω m,n = ∏ [(m/a)^2 + (n/b)^2]^(1/2) This equation can be used to get the frequency for Modes such as (2,1) and (1,2). How do I get the frequency for such modes as (2,1)+(1,2) and (2,1)-(1,2) ...
  2. Kaustubh sri

    Find the length of largest square

    Find the length of largest square accommodated in a right angled triangle whose perpendicular length is 16 m and base's length is 8 m. My attempt I have tried a lot to find the length but every time it comes in fraction , i think that the figure i have made is wrong . The answer I am getting is...
  3. P

    Mastering Simplification of Square Roots with Multiple Terms

    How do I solve, 1: (√3*√3*√3)/(√3+√3+√3)? How do I simplify it? I'm confused on how to shorten √x+√x+√x, I just don't get it. Also if: √700 = 26.46, then how is √70000 = 264.6? Shouldn't it be 2646?
  4. S

    Strength (mostly axial)of square steel tubing

    I am designing a Power Rack like this. Would I benefit anyhow using 3"x3" tubing instead of 2"x2" tubing? The most weight that thing is going to be subjected to is around 800 lbs (400 kg approx). Also will bolting the pieces be dangerous or should I just weld them? Finally I also want to omit...
  5. S

    What Is the Method to Complete the Square in Algebra?

    Homework Statement I identify the curve by finding a Cartesian equation for the curve. Homework Equations r = 3sin(θ) The Attempt at a Solution r^2 = 3r(y/r) x^2+y^2 = 3y x^2-3y+y^2 = 0 Now I'm stuck, I don't remember how to complete the square as I haven't done it in ages.
  6. jnbp13

    Easiest Method to Evaluate Imperfect Square Root up to 5 Decimals?

    Easiest Method to Evaluate Imperfect Square Root up to 5 Decimals? Any ideas?
  7. P

    Magnitude of electric field with square loop

    Homework Statement The square loop shown below is made up of four identical wires of length scripted l = 18 cm each charged with a linear density λ = 18 nC/m. Find the magnitude of the electric field at a distance z = scripted l/2 above the center of the loop. Homework Equations...
  8. A

    Oscillations and inverse square law

    Homework Statement A particle of mass m moves in 1 dimension along positive x direction.It is acted on by a constant force directed towards origin with magnitude B,and an inverse square law repulsive force with magnitude A/x^2.Find equilibrium position. Homework Equations B+A/x^2=m*a...
  9. M

    Find Steel Tubing Size for 4000lb Log Ramp - 8' Long

    I am making a ramps to load logs onto a portable sawmill. I would like to know the size steel tubing I need for logs weighing 4000 lbs. the ramps would be 8' long and at the following angles; never less than 25 degrees never more than 38 degrees. 1.5 x .125 tubing is available locally, but that...
  10. johann1301

    Proving √2 Irrational - Explanation & Solution

    Homework Statement In this task we will show that √2 is irrational. Assume that √2 = a/b where both a and b are natural numbers. Let a = p1p2p3...pn, and b = q1q2q3...qm be the prime factors a) explain why 2q1q1q2q2q3q3...qmqm = p1p1p2p2p3p3...pnpn √2=a/b b√2=a...
  11. Albert1

    MHB Prove y is not a perfect square

    $x\in N$ $y=x^4+2x^3+2x^2+2x+1$ prove:$y$ is not a perfect square
  12. T

    Define boundary conditions of a polygon in a unit square cell

    Hi, I am wondering as to how to define the boundary condition for a shape in a unit cell. Just imagine that the shape is the hole for the unit cell. Hence, for a constant thickness on the untextured boundary, thickness is, let's say C, then for the circle, it's C+depth. For example for...
  13. anemone

    MHB Prove 2x⁴+2y⁴+2z⁴ is the square of an integer

    The sum of three integers $x,\,y,\,z$ is zero. Show that $2x^4+2y^4+2z^4$ is the square of an integer.
  14. N

    Indoor Flower Garden & Plant Growth: Inverse Square Law

    Hi all looking for a bit of advice me the misses and the kids are starting a indoor flower garden and some herbs for the kids now my problems have come down to the lighting I have found out the colour spectrums needed as well as the luminous intensity required for heathly plant growth but the...
  15. M

    Divergence of an inverse square field

    Reference to Griffith electrodynamics question:- 1.16 Compute the divergence of an inverse square vector field. Now gradient is (∂/∂r)(r cap) Hence upon taking divergence of inverse square field (r cap)/r^2...We don't get 0. In fact we get (-2)/r^3. But if we write the vector field and...
  16. Q

    How to Solve the Schrodinger Equation with Delta Function Potential?

    Homework Statement Consider an electron subject to the following 1-D potential: U(x) = -U_0 \left( \delta(x+a) + \delta(x-a) \right) where U_0 and a are positive reals. (a) Find the ground state of the system, its normalized spatial wavefunction and the parameter κ related to the ground...
  17. anemone

    MHB Prove a fraction is a perfect square

    If $x,\,y$ are positive integers such that $\dfrac{x^2+y^2}{1+xy}$ is an integer, then $\dfrac{x^2+y^2}{1+xy}$ is a perfect square.
  18. S

    Generate a Formula for Square Spiral Algorithm | 10x10 Problem Statement

    The problem statement Form a formula to generate every value in the 10x10 square spiral shown above. Use the variables: x = the column of the cell, y = the row of the cell, s = the size of the spiral (in this case 10). The formula must work for any size of spiral, where s is the width...
  19. I

    B field at Center of Conducting Square

    Hi there I am just really confused as to how they arrived at the answer to this problem. I attached a picture of the entire question and the solution. Homework Statement Please see attached file. Homework Equations Biot Savart Law for Magnetism of a Wire where the length of wire is much...
  20. B

    How to determine the max load capcity of a steel square tube

    A square tube beam, 4in x 4in x .1875in thick. Length= 36in Cross sectional Area= 2.859in^2 A36 steel How do you determine its max load capacity?
  21. A

    My proof that the square root of 2 multiplied by r is irrational

    Here it is, for you to critique. This is a proof by contradiction. This is a good example of how I usually go about doing proofs, so if you give me tips on how to improve this particular proof, I'll be able to improve all my other proofs. I just learned how to do proof by contradiction...
  22. R

    MHB Proving an inequality with square roots

    This is problem 13 from section I 4.7 of Apostol's Calculus Volume 1: Prove that 2(\sqrt{n+1}-\sqrt{n})<\frac{1}{\sqrt{n}}<2(\sqrt{n}-\sqrt{n-1}) if n\geq 1. Then use this to prove that 2\sqrt{m}-2<\displaystyle\sum_{n=1}^m\frac{1}{\sqrt{n}}<2\sqrt{m}-1 if m\geq 2. I have proved the first...
  23. P

    Bound States of Infinite Square Well

    Hi all, So I was recently set straight on the fact that bound state does *not* necessarily mean E<0 but rather is the statement that E<V(+/- infinity). So how do we apply this definition to the infinite square well where the potential at +/- infinity vanishes, and yet the bound states have...
  24. U

    Infinite Square well with a Finite square well inside

    Ok here's a potential I invented and am trying to solve: V = -Vo in -b<x<b and 0 in -a<x<-b , b<x<a where b<a and ∞ everywhere elseI solved it twice and I got the same nonsensical transcendental equation for the allowed energies: \frac{-k}{\sqrt{z_0 - k^2}} \frac{e^{2kb} +...
  25. B

    Finite Square Well: Deriving Eq. (1)

    Hello everyone, I am reading about the Finite Square Well in Griffiths Quantum Mechanics Text. Right now, I am reading about the case in which the particle can be in bound states, implying that it has an energy E < 0. After some derivations, the author comes across the equation \tan z =...
  26. C

    Prove that n(n+1) is never a square.

    Homework Statement Prove that n(n+1) is never a square for n>0 The Attempt at a Solution n and n+1 are relatively prime because if they shared common factors then it should divide their difference but (n+1)-n=1 so 1 is their only common factor. So the only possible way for n(n+1) to be a square...
  27. T

    A square looks at light squared

    Third thread same topic. Non physicist asks question-why speed of light squared? Answers Its the derivitive that makes the equation work. The speed of light is some kind of ultimate measuring device. You are too stupid to understand. I think the questioners are incorrectly phrasing what...
  28. P

    Does the mod square of the wave function always have to be real?

    Homework Statement Doing a bit of QM from Griffiths intro to QM and got stuck early on on the following worked example: http://imgur.com/6aPVGIr I was under the impression that the mod square of the wave function ψ(x,t) should always be a positive, real number, but I cannot understand...
  29. individ

    MHB Solve triple square Diophantine equation

    Once you know how to solve it, then explain how to solve Diophantine equation: X^2+Y^2=aZ^2 a - integer. Write the equation when it has a solution.
  30. karush

    MHB Volumn of parabola and line with perpendicular cross sections being a square.

    The base of a solid is the region bounded by the parabola y^2=4x, and the line x=2 . Each plane section perpendicular to the x-axis is square. (I assume this means the cross-section of the solid will be square) then we are not revolving but slicing. The volume of the solid is? (the ans is...
  31. Saitama

    MHB Solve for the coordinates of square

    Three unit circles $C_1$, $C_2$ and $C_3$ in a plane have the property that each circle passes through the centres of the other two. A square $ABCD$ surrounds the three circles in such a way that each of its four sides is tangent to at least one of $C_1$,$C_2$ and $C_3$. $A=(0,0)$, $B=(a,0)$...
  32. D

    Unusual movement of square fridge magnets

    At home I have a series of small square fridge magnets (about 25mm by 25mm and about 1mm thick). If I select two of these fridge magnets and place them together then, as you would expect, they attract one another. However the interesting observation is that sometimes the fridge magnets are only...
  33. T

    Vector & Square Root Question for GCSE Maths

    I have attached a copy of a vector question which i cannot do, i do not even understand what the question is asking can someone help? On a different note i seem to have a lot of trouble with simplifying square roots for example what is the square root of 2704/ is there any way to find the...
  34. BiGyElLoWhAt

    Reasoning behind determinants of high n square matrices

    1st: Not a specific problem, I just didn't know where else to put it. We just covered this today in class. Basically what we're doing is reducing higher level matrices to 2x2 matrices and using them to calculate the determinant. I asked my teacher where that came from, and he was really...
  35. Q

    Area of a Square: Derivation & Integration

    So I was reviewing my random process notes. In it there is an integral that they have that I can't seem to get the right derivation of when they try to simply the math for ergodic mean. Basically, you have the following: A square from (-T,T) on both the x-axis and y-axis. What they want to...
  36. M

    Simplifying Square Roots of a Parametrized Path

    Homework Statement Find the arclength of the parametrized path x(t) = (t^2)/2 , y(t) = (t^3)/3 for 1<t<3. Homework Equations Arc Length Formula The Attempt at a Solution x'=t and y'=t^2. Putting them into the arc length formula, I get sqrt(t^2 + t^4) inside. I'm confused...
  37. Sudharaka

    MHB Is a Latin Square always invertible?

    Hi everyone, :) An interesting question I thought about recently. Is it true that a Latin Square of integers (or real numbers) treated as a matrix is always invertible? If not can anybody give a counterexample. I think latin squares are invertible but I am unable to prove it. Hope you can help...
  38. H

    Inverse square law explains Olbers' paradox?

    Hello, This is the thread I originally wanted to respond to, but it's closed: https://www.physicsforums.com/showthread.php?t=650126 I also found this on Wiki-talk page, which seems to be the same argument...
  39. adjacent

    Transformers and inverse square law

    Homework Statement This was in my test paper today: A transformer is cut into half so that one half contains the primary coil and the other half contains the secondary coil. They are moved 30cm apart. Explain why the transformer would not work The Attempt at a Solution My answer: The magnetic...
  40. E

    Inverse Square Law: Calculating Intensity at Different Distances

    Homework Statement Problem One: Two kilometres away from a point source of infrared waves, the intensity is 4 Mw−2. Calculate the intensity 1m away from the source. Problem two: Light from a candle has an intensity of 20.0 units when a meter is placed 3.0m away. What is the reading on the...
  41. C

    Why Does Solving Laplace's Equation in a Square Yield an Infinite Sum?

    Homework Statement i need to solve the laplace equation in square with length side 1 i tried to solve by superposition and i got infinite sum enen thouth i know that the answer should be finite Homework Equations 1.ψ(x=0,0≤y≤1)=0 2.ψ(y=0,0≤x≤1)=0 3.ψ(x=1,0≤y≤1)=10sin(∏*y)+3x...
  42. M

    Infinite square well, Probability of measurement of particle's energy

    Homework Statement Homework Equations The Attempt at a Solution I have managed to do the first 3 parts of the questions. The last two 4 markers are the ones I am having difficulties with. I have tried using the expansion postulate which states the wavefunction is equal to the...
  43. N

    How do I produce a hole with a square cross section?

    What are three different ways that i can produce a hole with a square cross section in a plate with a thickness of at least 1"?
  44. R

    MHB Limit with a lot of square roots

    I have the following problem: \lim_{x\rightarrow 4}\frac{\sqrt{2x+1}-3}{\sqrt{x-2}-\sqrt{2}} If I multiply by the conjugate of the denominator I get \lim_{x\rightarrow 4}\frac{\sqrt{(2x+1)(x-2)}+\sqrt{2(2x+1)}-3\sqrt{x-2}-3\sqrt{2}}{x-4} but am not sure where to go from here. Any...
  45. lonewolf219

    Finding the magnetic field at center of a square loop

    My textbook says that at the center of a square conducting wire of length ω, the magnetic field is: B=\sqrt{2}μ_{0}I/(\piR) I am not sure how to calculate this...? Because the Biot Savart law has a closed loop integral, we do not use piecewise addition of line integrals to find the...
  46. J

    Susskind said that the square of a differential equal zero

    Hello, I watched a lecture by Leonard Susskind, in which he said that a differential is so short that when you square it, you get zero. What exactly could he mean by this? Thank you for your time. Kind regards, Marius
  47. S

    Binomial series - Finding square root of number problem

    Homework Statement Expand ##(1+x)^(1/3)## in ascending powers of x as far as the term ##x^3##, simplifying the terms as much as possible. By substituting 0.08 for x in your result, obtain an approximate value of the cube root of 5, giving your answer to four places of decimals. Homework...
  48. C

    Infinite square well with barrier in the middle

    Homework Statement Show that the energy levels of a double square well V_{S}(x)= \begin{cases} \infty, & \left|x\right|>b\\ 0, & a<\left|x\right|<b\\ \infty, & \left|x\right|<a \end{cases} are doubly degenerate. (Done) Now suppose that the barrier between -a and a is very high, but finite...
  49. E

    What is the practical application of the trace of a square matrix?

    I'm interested in the use/application of the trace of a square matrix? I am trying to get an intuitive feel for what it 'means' . . . Along the lines of: for a 2x2 matrix, the determinant represents the area of the parallelogram. I know it is the sum of the entries of the diagonal of a...
  50. A

    MHB Simplifying with square roots?

    So, this is probably really simple...but I keep getting the wrong answer when trying to simplify this: 3\sqrt{\frac{(10x^3)^2}{(10x^6)^{-1}}}Could someone show the steps to simplifying it? Thanks so much. (:
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