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. 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...
  2. 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...
  3. C

    Infinite Square Well, finding Psi(x,t)

    Homework Statement A particle in the infinite square well has the initial wave function ## \Psi (x, 0) = Ax(a-x), (0 \le x \le a) ##, for some constant A. Outside the well, of course, ## \Psi = 0 ##. Find ## \Psi (x,t) 2. Homework Equations : Equation [1.0]:## \displaystyle c_n =...
  4. J

    MHB Optimizing Least Square Method for Ill-Conditioned Linear Problems

    Hi does anyone know the "formula/process" for the least square method if the are giving several (x,y) points and asking me to find y=Ax^2 + B?
  5. W

    Electron in one dimensional infinite square well

    An electron in the ground state of a one-dimensional infinite square well of width 1.10 nm is illuminated with light of wavelength 600 nm. Into which quantum state is the electron excited? ok so I first calculated the engery of the electron in the first ground state of the square well...
  6. R

    Graph of Tension force vs. the square of the speed

    Working on a physics lab report regarding uniform circular motion, one of the questions asks to graph the Tension Force vs. the square of the speed. Another part of the same question asks what the slope of the graph represents, which is where I'm stuck.
  7. phosgene

    Wavefunction of infinite square well potential between -L<x<L

    Homework Statement Solve for the wavefunctions and energy levels of an infinite square well potential extending between -L<x<L. Hint: It may be worth noting that for a potential symmetric in x, then the observed probability density must also be symmetric in x, i. |ψ(x)|2 = |ψ(-x)|2. Homework...
  8. Barioth

    MHB How to Solve These Challenging Integrals with Square Roots?

    Hi everyone I have these 2 integrate that I can't solve, I have tried them with mathematica and wolfram, but they can't find an answer, maybe someone have an idea on how I could tackle these 2 bad boy! The first one is \int{ \sqrt{ \frac{1+( \frac{1}{10}+ \frac{s}{25})^2}{ \frac {s}{10}+...
  9. D

    Forgotten how to solve for square roots

    Homework Statement compute f'(x) using the limit definition. f(x) = \sqrt{x} Homework Equations f'(x) = \stackrel{lim}{h→0} \frac{f(x+h)-f(x)}{h} The Attempt at a Solution Plugging in the function values gives you f'(x) = \stackrel{lim}{h→0} \frac{\sqrt{(x+h)}-\sqrt{x}}{h}...
  10. I

    Root mean square velocity question

    If at 120 K the Vrms is v , then at 480 K it will be a. 1 b. 2 c. 3 d. 4 Which formula is to be used here? Plz solve this.
  11. O

    My Taylor Square Root C Program doesn't like me

    Homework Statement 4. Implement a simple method to find the square root of a double precision floating point number x. A simple method is to consider the error produced by a “guess” y of the solution. Square the value y and compare with the value x. If y is correct, the error e=|y2-x| where ||...
  12. B

    Scattering from finite square barrier

    Homework Statement Use the boundary conditions to show that \frac{A+B}{A-B}=\frac{k_1}{k_2}\frac{C+D}{C-D}=\frac{k^2_1}{k^2_2} Homework Equations A+B=C+D and k_{1}A- k_{1}B = k_{2}C- k_{2}D C e^{i k_{2}L}+D e^{- ik_{2}L} = F e^{i k_{1}L} and k_{2}C e^{ ik_{2}L}- k_{2}D e^{-i...
  13. S

    Linear algerba: trace of square matrix is a linear functional

    Lets define trace for each square matrix A its trace as sum of its diagonal elements, so tr_{n}(A)=\sum_{j=1}^{n}a_{j,j}. Now proove that trace is a linear functional for all square matrix. I would be happy to know what has to be true for anything to be a linear functional? If I...
  14. G

    Is Taking the Principal Square Root Always Necessary?

    I feel kind of ridiculous making this post, but here we go: What would be the correct answer to this question; Choose all the number sets (natural, integer, rational, or irrational were the only options given) that -√81 belongs to, and show how you found your answer. What I said was this...
  15. S

    Square Root of Positive Operator

    Homework Statement Suppose U = T^2 + \alpha T + \beta I is a positive operator on a real inner product space V with \alpha^2 < 4 \beta . Find the square root operator S of U.Homework Equations The Attempt at a Solution Isn't this just the operator S \in L(V) such that S e_k = \sqrt{...
  16. A

    Quantum Mechanics - Finite Square Well - Graphical Solution

    Homework Statement http://img842.imageshack.us/img842/4917/physp6.jpg I am trying to solve the above problem. However, I am supposed to solve it with the following values: U=54.7eV L=0.2nm Particle is an electron, so: m=9.109E-13kg=0.511eV/c^2 Essentially I am supposed to...
  17. S

    Fair to say there are twice as many square matrices as rectangular?

    Fair to say there are "twice" as many square matrices as rectangular? Is it fair to say that there are at least twice as many square matrices as there are rectangular? I was thinking something like this... Let R be a rectangular matrix with m rows and n columns, and suppose either m < n...
  18. S

    How Do You Calculate the Average Value of a Square Waveform?

    Homework Statement Alpha=0.91 ,beta=2.92, T0=0.91 Homework Equations The value of a0 for the square waveform The Attempt at a Solution 1/T0 * area = 1/0.91*(2.92-0.91)*0.91
  19. C

    Inverse Square Law - Calculating the solid angle

    Hi Everyone, For an individual inquiry and formal lab report task at school I have chosen to conduct an experiment to find out whether hot shoe mounted flash units follow the inverse square law and how the flash zoom is affected by the inverse square law. My first question is that In order...
  20. J

    Power percentage, square wave, Fourier series

    Homework Statement What is the percentage of power (out of the total power) contained up to the third harmonic (power in DC component, a1 , a-1 , a2 , a-2 , a3 , a-3 ) of the square waveform shown above? (the duty cycle = D = τ/T0= 0.5) Homework EquationsThe Attempt at a Solution Hey all...
  21. B

    MHB Trig problem: max square cut from circle

    [SOLVED]Trig problem: max square cut from circle Since this one is homework related, ill ask this as a procession so that I can make sure that I am grasping the logic. the question is that with a round log with a diameter of 16cm, what is the strongest log that can be cut where the strength =...
  22. M

    How Do You Find The Exact Value Of Square Root of 3, 5, 7, 11?

    Is there any method to find the exact value of the square root of 3,5,7,11,13,14,15,17,18, etc.? Thank you
  23. C

    Integral of 1 - 2*sinx in square root?

    Hello PF members, I want to solve this integral but I cannot find a method. \int\sqrt{1 - 2sin(x)}dx for 0 < x < ∏/6 Or more generally \int\sqrt{a - bsin(x)}dx for a > b How can I solve this? Thanks in advance
  24. Z

    Integration U substitution then square it I think.

    1. ∫ 1/(2√(x+3)+x) 2. Not sure if I'm beginging this correctly or not but I get stuck. 3. Let u= √x+3 then u2 = x+3 2udu=dx dx=2√[(x+3) Therefore: ∫1/u2-3 Not sure where to go from here?
  25. M

    Using least square to find the perfect fit of a figure

    Homework Statement Hello all, So I am working on my engineering project, and my professor told us to play with the graphs,and try to find something interesting about them. So what I want to do is form a better fit for the figure below. " figure 2b" , and find out why the choose not to...
  26. H

    Moving Square Loop through a Magnetic Field

    Homework Statement A square loop of side 1.5m and Resistance 2Ω is pulled with a constant velocity v=0.3m/s through a smaller region with a constant magnetic field B (out of the page) of 4T. The figure shows the position at t=0. Calculate the magnetic flux of the coil at t=4s.. Here is a...
  27. T

    Square Loop Moving Through Varying Magnetic Field

    Homework Statement A square loop of side length L is moving in the x direction with velocity v. v=vx. B points along the z axis and is defined by B=αxez where α is a constant. Find EMF along the loop Hint: Find forces on charges in rod by virtue of motion of the rod.Homework Equations...
  28. J

    Prove that a perfect square is a multiple of some number?

    How do you prove that: Every perfect square is either a multiple of 3 or one more than a multiple of 3? There is something very basic that I don't seem to understand in the question. Here is proof that someone gave me: Every natural integer p must fall in one of the following case...
  29. S

    Arctangent2 without square rooting?

    basically i have a problem where i am rotating 1 vector to be parallel to another i get the axis of rotation by the cross product of the 2 vectors the angle by the arctangent of the magnitude of the axis and the dot product of the 2 vectors however arctangent2(magnitude(axis) ...
  30. H

    Evaluating difficult integral involving square roots

    Homework Statement Evaluate the following integral Homework Equations ∫ √(4-(√x)) dx The Attempt at a Solution I am having a mind block, I find this too challenging, help!
  31. K

    Calculating Deflection and Buckling in L-Shaped Square Tubing Legs

    I need to know how big of a radius I need to use on an L shaped leg made out of square tubing. Is there a general formula depending on the length and height required? How would I calculate the deflection at the end and the buckling on the vertical part? For the deflection part, would I...
  32. S

    Magnetic field at (z) axis of square loop

    Homework Statement We have a square loop with side length 2a, at xy plane. Now we know ( I have calculated ) that the magnetic field at the center of the square loop to be H = \frac{2I}{\sqrt{2} \pi a} Now we want to know what is the magnetic field at point P, which is on the axis which...
  33. A

    Square in denominator of derivative

    \frac{d}{d \sigma ^2} [log(\sigma ^ 2) - \frac{1}{\sigma ^ 2}] I think the first part is \frac{1}{\sigma ^ 2} but pretty clueless after that. I also want to take the second derivative. Any help or a reference would be great. Thanks!
  34. M

    Finding the least square solution with only positive coefficients

    Hi everyone. Is there any way to set demands on least square solutions? I have an equation on the form Ax=b, which is solved for x as: x=(A'*A)^-1*A'*b I do know for a fact that all values in x should be positive, but the least square solution for my particular system contains a...
  35. F

    Square wave exponential fourier series

    This is A and B my friend is telling me that Co is actually 0 and I am getting 1/2 and i don't see exactly what I am doing wrong if i indeed am doing something wrong hopefully someone here can check this out and let me know exactly where i went wrong.. Thanks
  36. iVenky

    What is the reason for the square attenuation?

    I have seen this concept in many places like electrical field, gravitational field, brightness from a distant star or in satellite communication. That is, they seem to be inversely proportional to the square of the distance from the source of that field. What's the reason behind it?
  37. icesalmon

    What is the Square Footage of the Barn Roof?

    Homework Statement A barn is 100 feet long and 40 feet wide. A cross section of the roof is the inverted catenary y = 31 - 10(ex/20+e-x/20). Find the number of square feet of roofing on the barnHomework Equations Arc Length Integral Hyperbolic trigonometric identities The Attempt at a...
  38. H

    Divergence of inverse square field and Dirac delta

    \nabla \cdot \frac{\mathbf{r}}{|r|^3}=4 \pi \delta ^3(\mathbf{r}) What's the proof for this, and what's wrong with the following analysis? The vector field \frac{\mathbf{r}}{|r|^3}=\frac{1}{r^2}\hat{r} can also be written \mathbf{F}=\frac{x}{\sqrt{x^2+y^2+z^2}^3}\hat{x}+...
  39. A

    MHB What is the simplest method for solving polynomial equations?

    In your opinion what is the best way to introduce completing the square, in fact I do not like the way sub and add the squared half of x coefficient, after making x^2 coefficient 1 saying it is complicated... Thanks
  40. A

    MHB Find the finite sum of the square and cube exponent of integers

    Hey, it is clear for me that \sum_{i=1}^{n} i = \frac{n(n+1)}{2} how to find a formula for \sum_{i=1}^{n} i^2 \sum_{i=1}^{n} i^3 Thanks
  41. B

    Nullspace of a square matrix A and A^2 are related?

    Homework Statement Say that A is a square matrix. Show that the following statements are true, or give a counter example: a) If x is in the nullspace of A, then x is in the nullspace of A2 b) If x is in the nullspace of A2, the x is in the nullspace of A. Homework Equations The...
  42. B

    Square Root Indefinite Integral

    Hello everyone.. Homework Statement ∫√((1+(e^-x))^2)dx 2. The attempt at a solution I first tried to do a u sub and then attempt a trig sub however I can't do anything with the e^-x left in the u sub. Does anyone have another way I can integrate this thing?? Thank you for any suggestions/help!
  43. shounakbhatta

    Kepler's planetary motion and inverse square law

    Hello, The inverse square law of Newton's gravitational force, is it somehow related to each other? I mean to say P^2 is directly prop.a^3. Is it from the third law that the derivation of inverse sq.law of G=M.m/R2 is derived? Thanks.
  44. A

    Kinetic Energy in water and the rate carried across each square meter

    [b]1. Consider an ocean current flowing at 2.5m/s a) How much kinetic energy is contained in a cubic volume of water that measures 1m on each side? The density of seawater is about 1030kg/m3 b) If the flow is perpendicular to one of the cube faces, what is the rate at which the current carries...
  45. B

    Pentagonal Bipyramidal and Square Antiprismatic

    What are the bond angles in a pentagonal bipyramidal molecule in general? If they vary from molecule to molecule then just the bond angles for IF7 would be ideal. I'd like the same thing for square antiprismatic molecules (any complex ion with coordination number 8 which is square antiprismatic...
  46. D

    Electric field on each midpoint of square of side L

    θHomework Statement What would be the electric field on the midpoint of each side of a square with point charges of +Q on diagonal corners and -Q on diagonal corners? Homework Equations E=kQ/r^2 Ex=Ecosθ Ey=Esinθ The Attempt at a Solution Considering the midpoint of the side at...
  47. R

    Let G be a finite group in which every element has a square root

    Homework Statement Let G be a finite group in which every element has a square root. That is, for each x in G, there exists a y in G such that y^2=x. Prove every element in G has a unique square root. Homework Equations G being a group means it is a set with operation * satisfying...
  48. M

    Meaning of Square of four vector potential

    The square of the four vector potential. (\phi,A)^2=\phi ^2 - A^2 What's the physical meaning of this lorentz invariant?
  49. A

    Solving a System of Differential Equations: Ants at the Corners of a Square

    Suppose there is an ant at each of the four corners of a square with side length 1, such that (0,0) and (1,1) are at opposite corners of the square. The ant at (0,0) is facing the ant at (1,0) is facing the ant at (1,1) and so forth. Each ant will choose its path such that it is always facing...
  50. L

    Statistics Chi Square test of normally distributed data

    Homework Statement The following data is hypothesized to possesses a normal distribution, is that hypothesis sustained by a Chi-square test at .05 significance: <66...4 67-68...24 68-70...35 70-72...15 72-74...8 >74...4 The Attempt at a Solution 1. I know that I should...
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