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

    I Why does this inverse square calculation fail to predict actual data?

    The test data and notes are attached - showing that the inverse square calculations fail to reasonably predict the actual dimming of light over a test distance of 168 mm. Did I err in my test design or my calculations?
  2. J

    I Element-wise square root of a vector notation?

    What is the notation to show element-wise square root of a vector or matrix?
  3. D

    Misc. Is My Steel Square Tubing Strong Enough?

    Summary: Trying to see if the steel tubing I bought is strong enough to carry load. Hello all I bought some square steel tubing today in hopes of putting up sail shades in my back yard, I am concerned now that I did not get big enough tubing. I have a triangular sail shade 20’ x 20’ x 20’ and...
  4. H

    MHB Number of ways to divide a square grid in half

    Consider a dotted square grid with $4$ rows and $4$ columns, as shown: By drawing a series of connected straight lines from dot to dot, it is possible to divide the square (which effectively has side length $3$) into two parts of equal area. One way of doing this is as shown: Other examples of...
  5. Physics lover

    Moment of inertia of a square along an axis inclined at an angle

    My attempt-:I extended the axis and made a triangle by joining other adjacent vertex to the line such that its angles are 15°,75° and 90°.I found the distance between the centre of square and upper vertex of triangle by using law of sines.And then i found out inertia along upper vertex of...
  6. Kaguro

    Infinite square well centered at the origin

    The problem is: Solve the time independent Schrodinger Equation for infinite square well centered at origin. Show that the energy is same as in the original case(well between x=0 and x=L). Also show that the solution to the this case can be obtained by setting x to x-L/2 in ##\psi## in the...
  7. K

    I Questions about the inverse square law

    In "An Introduction to Modern Cosmology" by Andrew Liddle, page 130, paragraph A2.3 Luminosity distance, explains why the inverse square law does not hold at very far distances. One reason given is the expanding universe. (Another was the geometry of the Universe.) Could there be also...
  8. W

    MHB Circles in a square and diameter of the circle

    A circle is inscribed in a square with sides = 40. A smaller (of course!) circle tangent to the above circle and 2 sides of the square is inscribed in one of the corners of the square. What is the diameter of this circle?
  9. D

    How to prove that ##f(x,y)## is not integrable over a square?

    I'm confused with how Riemann sums work on double integrals. I know that ##L=\sum_{i,j}fm_{ij}A_{ij}## and ##U=\sum_{i,j}fM_{ij}A_{ij}## where ##m_{ij}## is the greatest lower bound and ##M_{ij}## is the least uper bound and ##A_{ij}## is the area of each partition. ##A_{ij}=\frac{1}{n^2}## for...
  10. M

    How a square or sawtooth wave can have a certain frequency?

    Hello! I know that a square or saw tooth wave consists of infinite amount of sinousoids each having different frequency and amplitude. But when I look at their plot they seem to have a well defined frequency or period. Which term in the Fourier series determines their frequency? Does a saw...
  11. W

    MHB Find Side Lengths of Pythagorean Triangle ABC with Square DEFG Inscribed

    Pythagorean triangle ABC with area 8214 has square DEFG with sides = 60 inscribed in it. Side DE of the square lies on the hypotenuse. Find the triangle's side lengths. B E D F C G A
  12. A

    Convert solar radiation from Joule per cm square to Watt per meter^2?

    I have solar radiation data in the units of Joule per cm^2 (joule per square centimeter) measured hourly. I want to use this data in evapotranspiratin calculation which requires radiation units as Watt per meter squared. How can I do this conversion?
  13. K

    Square wire in a cylindrical magnetic field

    For if the axis of symmetry is oriented along the y-axis I have gotten as far as converting the main integral entirely to cartesian coordinates. $$\hat{\phi}=-sin(\phi)\hat{x}+cos(\phi)\hat{y} \therefore \hat{\phi} =-sin(tan^{-1}(x/y))\hat{x}+cos(tan^{-1}(x/y))\hat{y}$$...
  14. A

    Spin-##\frac{1}{2}## particles in infinite square well

    Homework Statement Construct the four lowest-energy configurations for particles of spin-##\frac{1}{2}## in the infinite square well, and specify their energies and their degeneracies. Suggestion: use the notation ##\psi_{n_1,n_2}(x_1, x_2) |s,m>##. The notation is defined in the textbook...
  15. anemone

    MHB Inequality involves radical, square and factorial expression 3√{x}+2y+1z^2⩽ 13

    If $x^2+y^2+z^2+xyz=4$ and that $x,\,y,\,x\ge 0$, prove $3!\sqrt{x}+2!y+1!z^2\le 13$.
  16. T

    Atmospheric pressure per square cm

    Hi, I have a problem to understand one small thing. They say that air pressure per square cm at sea level is approximately 1 kg. So at 2 sq cm it will be 2 kg, at 3 sq cm it will be 3 kg etc. But... Here where I have a problem. The thing is that inside 2 square cm you can put 4 one square cm...
  17. chwala

    Find the area of the shaded region as a ratio to the area of the square

    Homework Statement find the area of the shaded region as a ratio to the area of the square (kindly see attached diagram)Homework EquationsThe Attempt at a Solution ##A= \frac 1 2####b×h## ##A= \frac 1 2####×2x × 3x##
  18. O

    B Irradiance: difference between distance and the square of the distance?

    What's the difference between distance and the square of the distance? Many Thanks
  19. C

    Alternative to a square linear bearing?

    Anyone know of an alternative to the 7mm Drylin square linear bearing? They seem on the expensive side, 30GBP for just the plastic insert/bearing surface. https://www.igus.co.uk/product/983 Ideally I'm looking for something smaller, say for a 3mm shaft/rail?
  20. Boltzman Oscillation

    Square of the sum of two orthonormal functions?

    Homework Statement Given: Ψ and Φ are orthonormal find (Ψ + Φ)^2 Homework Equations None The Attempt at a Solution Since they are orthonormal functions then can i do this? (Ψ + Φ) = (Ψ + Φ)(Ψ* + Φ*)?
  21. majormuss

    Finding the electrostatic potential of a square sheet.

    Homework Statement Consider a uniform surface charge density σ on a square of unit area. (a) Compute the electrostatic potential Φ along the line normal to the center of the square. My current attempt at a solution (image attached) is either incomplete or is simply wrong but I am unable to...
  22. V

    MHB Square root n limit ( sum question )

    Hi! $$(x_{n})_{n\geq 2}\ \ x_{n}=\sqrt[n]{1+\sum_{k=2}^{n}(k-1)(k-1)!}$$ $$\lim_{n\rightarrow \infty }\frac{x_{n}}{n}=?$$ I know how to solve the limit but I don't know how to solve the sum $\sum_{k=2}^{n}(k-1)(k-1)!$ which should be $(n! - 1)$ The limit would become $\lim_{n\rightarrow \infty...
  23. Jozefina Gramatikova

    Classical Mechanics Problem: Particle in a Square Potential Well

    Homework Statement CLASSICAL MECHANICS [/B]Homework Equations E=U+K[/B]The Attempt at a Solution Guys, can you please help me with part b) ? I am not sure how to find the velocity. Thanks
  24. Jozefina Gramatikova

    Classical mechanics: Square well with Bounded particle

    My question is can we have negative energy in classical mechanics? Also I would need help for finding the velocity in part b)
  25. marino

    B Proof That ##\sqrt{x}## Isn't Rational (Unless ##x## is a Perfect Square)

    According to you this theorem is correct? Exercise 1.2 * Proof that ##\sqrt{x}## isn't a rational number if ##x## isn't a perfect square (i.e. if ##x=n^2## for some ##n∈ℕ##). In effect, if ##x=\frac{25}{9}##, so ##x## isn't a perfect square, then ##\sqrt{x}=\sqrt{\frac{25}{9}}=\frac{5}{3}##...
  26. JD_PM

    How to compute a mean square average

    Homework Statement We know that $$< (x_1 - x_2)^2 > = \frac{K_bT}{K}$$ $$< (x_2 - x_3)^2 > = \frac{K_bT}{\gamma}$$ What's ##< (x_3 - x_1)^2 >## equal to? Homework EquationsThe Attempt at a Solution I have tried: ##< (x_2 - x_3)^2 > - < (x_1 - x_2)^2 >## but did not get ##< (x_3 - x_1)^2...
  27. K

    I Which function space do square waves span?

    Hello! As the topic suggests I´m interested which functions space square waves span? Lets say we define them as https://wikimedia.org/api/rest_v1/media/math/render/svg/5b8953debf86627276f45bf8822140ff2bbaee56 . Do they span the same space as the sines and cosines in Fourier analysis? :/ Thanks!
  28. JD_PM

    Infinite Square Well -- Instantaneous expansion of the Well

    Homework Statement My doubts are on c) Homework Equations $$< H > = \int \Psi^* \hat H \Psi dx = \frac{2}{a} \int_{0}^{a} sin (x\frac{\pi}{a}) \hat H sin (x\frac{\pi}{a}) dx$$ The Attempt at a Solution I understand that mathematically the following equation yields (which is the right...
  29. F

    B Is the inverse square law exact near a spherical body?

    I'm forking this off another thread where I brought it up but it was getting OT. It is good enough for a first approximation but it is certainly not exact. Consider a test mass one radius from a spherical body. Work out the contributions form two points diametrically opposed on the surface...
  30. wrobel

    The Attractive Power of the Inverse Square Potential: Do Examples Exist?

    Do exist examples of attraction forces with such a type potential ##V(\boldsymbol r)\sim-\frac{1}{|\boldsymbol r|^2}, \quad |\boldsymbol r|\to 0## in physics ?
  31. M

    I Why can't I reach every cell in a 3x3 square?

    Hi, I was playing this game in which you start from any cells of a 3x3 or 5x5 square and draw a line that loops through every cell in the box. The line can go only through a vertical or horizontal side (not diagonally). When you start from certain cells (problem cells), you can't reach at...
  32. A

    Time evolution of wave function in an infinite square well potential

    For this problem at t=0 Ψ(x,0)=Ψ1-Ψ3 Where Ψ1 and Ψ3are the normalised eigenstates corresponding to energy level 1 and 3 of the infinite square well potential. Now for it's time evolution it will be Ψ1exp(-iE1t/ħ)- Ψ3exp(-iE3t/ħ) And taking the time given in the question the time part of the...
  33. A

    Time evolution of wave function in an infinite square well potential

    Homework Statement Homework Equations For this question my ans. is coming option (3) since the time part of the wave comes out to be same for both the energy states which is (-1)^(-1/8) and (-1)^(-9/8) respectively (using exp(-iEt/ħ)). But the correct option is given option (4). Am I right...
  34. E

    MHB Find the square roots of 4*sqrt(3)+4(i)

    So I have a study guide for my final which was written by a different professor from my actual professor. So I don't understand the question, I don't know if it's because my professor did not teach this or if the wording is different from what I'm used to: Find the square roots of 4*sqrt(3)+4(i)
  35. karush

    MHB -b.2.2.18 IVP DE complete the square?

    $\quad\displaystyle y^{\prime}= \frac{e^{-x}-e^x}{3+4y}, \quad y(0)=1$ rewrite $\frac{dy}{dx}=\frac{e^{-x}-e^x}{3+4y}$ separate $3+4y \, dy = e^{-x}-e^x \, dx$ integrate $2y^2+3y=-e^{-x}-e^x+c$ well if so far ok presume complete the square ?book answer $(a)\quad...
  36. M

    I How does the inverse square law apply to a focused detector?

    I am interested in evaluating light intensity variation in a digital image. A colleague wants to apply an inverse square law correction to account for distance variation. I am trying to justify that in this case, the inverse square law does not apply. Treating each pixel as a detector, it has...
  37. E

    Proving closure of square integrable functions.

    I'm trying to prove that the set of all square integrable functions f(x) for which ∫ab |f(x)|^2 dx is finite is a vector space. Everything but the proof of closure is trivial. To prove closure, obviously we should expand out |f(x)+g(x)|^2, which turns our integral into one of |f(x)|^2 (finite)...
  38. W

    MHB Can You Crack This Unique 1-15 Number Puzzle Grid?

    A + B - C = D + / + E + F - G = H - / + I * J * K = L = = = M N 0 Al numbers from 1 to 15 used.
  39. D

    Approximations with the Finite Square Well

    Homework Statement Consider the standard square well potential $$V(x) = \begin{cases} -V_0 & |x| \leq a \\ 0 & |x| > a \end{cases} $$ With ##V_0 > 0##, and the wavefunctions for an even state $$\psi(x) = \begin{cases} \frac{1}{\sqrt{a}}cos(kx) & |x| \leq a \\...
  40. Krushnaraj Pandya

    Ratio of the length of resistive wires in a square

    Homework Statement In a given square ABCD each side is of 1 m and resistance of wire is 1 ohm/m. A resistance of 1 m is connected from A to E (which lies on side CD). A constant potential difference is applied across A and C, if potentials of B and E are same then find CE/ED. Homework...
  41. J

    Finding the Torque on a Fixed Square

    Homework Statement Hello, I'm having trouble with the following problem. I am given a square of length L and mass M that is fixed at its center. A rod of length l is is attached to the top left corner of the square, with a mass m attached on the other end. A motor applies a torque on the rod...
  42. cookiemnstr510510

    Square copper wire loop within a magnetic field

    Homework Statement In the figures below, a copper wire of circular cross section, A, has been bent into a square loop of side length, c, and arc welded at the seam for electrical continuity. Assume that the resulting square loop has a resistance, R, and a mass, M. The loop is originally held...
  43. S

    MHB What is the LMS Estimate of Theta for a Joint PDF on a Triangular Set?

    I have the following question and I am struggling to find the right answer. The random variables and are described by a joint PDF which is uniform on the triangular set defined by the constraints 0 <= x <= 1, 0<= theta <= x Find the LMS estimate of theta given that X = x , for in the range...
  44. A

    MHB Finding Squares in a Square Box: n > 1

    Determine all integers n> 1, for which in the square box of dimensions (n x n) you can enter different squares of integers, so that the sum of numbers in each row and in each column of the array is a square of an integer, and all the 2n sums are different.
  45. Krushnaraj Pandya

    Energy and root mean square velocity question

    Homework Statement I read the expression E=fRT/2 where E is internal energy of ideal gas and f is degrees of freedom, and ##V_{rms} = \sqrt{\frac{3RT}{M}}## Since internal energy for an ideal gas is purely kinetic (according to KTG) I can write 1/2 mv^2 = fRT/2. Now H2 is a diatomic molecule...
  46. Cheesycheese213

    How to find the square root of a square root?

    Homework Statement Simplify √(53 - 8√15) Homework Equations Numbers can be represented as √a - √b The Attempt at a Solution I had tried to make in an equation where the 2 expressions were equal, but after squaring both sides, I didn’t really know what to do. I had also tried to use something...
  47. W

    MHB How Can You Draw a Square with Only 3 Lines?

    Using 3 straight lines only, draw a square.
  48. R

    Proving that there is no rational number whose square is two

    Homework Statement The question is to prove that no rational number squared is = 2 Homework EquationsThe Attempt at a Solution I want to understand why for (a/b)^2 = 2, we assume one of the numbers is odd. Is this because, from approximation we know that root 2 is not a whole number, and If...
  49. E

    How to Determine Electric Flow Through a Square Surface Due to a Nearby Charge?

    Homework Statement determine the electric flow through a square surface of side 2l due to a load + Q located at a perpendicular distance l from the center of the plane I really don't know how to answer this question .i need help guys Thanks Homework EquationsThe Attempt at a Solution I ended...
  50. Safder Aree

    Contour Integration over Square, Complex Anaylsis

    Homework Statement Show that $$\int_C e^zdz = 0$$ Let C be the perimeter of the square with vertices at the points z = 0, z = 1, z = 1 +i and z = i. Homework Equations $$z = x + iy$$ The Attempt at a Solution I know that if a function is analytic/holomorphic on a domain and the contour lies...
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