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. I

    MHB Arrangement of eight people around a square table (problem from Grimaldi's book)

    Hi Here is the statement of the problem from Ralph Grimaldi's discrete math book. a) In how many ways can eight people, denoted A,B,...,H be seated about the square table shown in the figure (see attachment), where Figs 1.6 (a) and 1.6 (b) are considered the same but are distinct from Fig 1.6...
  2. S

    What is the correct function f(x) to use for this limit?

    Hi guys, I'm really new to calculus and limits and have been trying to have a good crack at the following question. Sorry if I haven't written the problem out in the most acceptable format. lim (9-3√x)/(9-x) x→9 Substituting 9 gives you 0/0 and indeterminate. I tried multiplying the...
  3. N

    Square roots by approximate iterations

    Homework Statement hi every one I need to construct a C++ square root program that uses approximate values I've done the first part of the work; ********************************************************************************************************************* prompt the user for two...
  4. E

    How many square centimeters are in 3.39ft^2?

    How many square centimeters are in 3.39ft^2? (use cm^2)
  5. Z

    Square root of a function

    Homework Statement I have the function H^2 + 12756H and I want to find the domain and range of it's square root algebraically. Homework EquationsThe Attempt at a Solution I understand y= √(H^2 + 12756H) is undefined if H^2 + 12756H < 0, however I don't get how to find its domain and range...
  6. C

    Solution to the dirac equation and the square root of a matrix?

    Hi. I'm currently reading about (negative frequency) solutions to the Dirac equations which can be written on the form \Psi = ( \sqrt{p \cdot \sigma} \chi, \sqrt{p \cdot \bar{\sigma}} \chi)^T e^{-i p \cdot x}For any two component spinor Chi. But the dot product with the four vector p and the...
  7. C

    Finding Limit As X Approaches Infinite Of Square Root Function

    Finding Limit As "X" Approaches Infinite Of Square Root Function Homework Statement Homework Equations None that I am aware of. The Attempt at a Solution What I tried to do to solve this problem was first, multiplying the function by its conjugate, and then simplifying the...
  8. nukeman

    F of G function question - Square root inside a square root?

    Homework Statement The image has the question I don't quite understand! Homework Equations The Attempt at a Solution I understand how to get √(√2 - x) but I don't get how they end up with: 4√2 - x ?
  9. H

    Proof by Contradiction || Prove that an equation can never be a square number

    Homework Statement Prove that for any integer n n^2+n+1, can never be a square number. Homework Equations None. The Attempt at a Solution We could put the equation to a^2, (where a^2 is a square number) and solve for n and show that n can not be an integer. I tried quadratic...
  10. R

    Square root within a square root

    Hoping someone can push me in the right direction with this one. Plume snookered. It's to simplify: 2√3(3+√3) Guessing first calculate (a^2 - b^2*c) in the square, though the 2 is throwing this an I'm not sure how the answer is 6√3 + 6, an not 18√3 ?
  11. S

    MHB Quotient rule with square roots

    I have the answer to this problem but I am stumped as how to get there. Here it is h(x)=e^x/5/sqrt2x^2-10x+17, I'm getting stuck moving the square root up. Help
  12. K

    Electric Field in a Square Problem

    Homework Statement I think it would be better if I put the picture. Additional questions: Find the direction of the electric field. Find the magnitude of electric field due at C due to charges A, B, and D. Homework Equations Pythagorean Theorem. E = kq/r^2 The Attempt at a Solution For...
  13. C

    Number Theory. Argue Is not the square of an integer.

    Homework Statement Argue that (17^4)*(5^10)*(3^5) is not the square of an integer. Homework Equations N/A? The Attempt at a Solution Do I break these up, and show that each is not a square? I'm not sure if that would be correct, but sqrt(17^4)=289 * sqrt(5^10)=3125 *...
  14. S

    Inverse Square Law: 1mW laser range?

    Hello PF! I've got a strange question for you physics boffins; assuming for a moment that lasers obeyed the inverse square law, what range would a typical 1mW red laser have in the atmosphere?
  15. B

    Integration With Completing the Square

    The problem is: \int\frac{1}{\sqrt{1-4x-x^2}}dx I took the expression under the radical and I completed the square, yielding: \int\frac{1}{\sqrt{5-(x+2)^2}}dx Then I figured that I could apply the arcsin formula, where a^2=5 andu^2=(x+2)^2 But by solving for "a" and "u," I would be...
  16. C

    Electric Field at the Center of a Square with Four Charges

    Homework Statement What is the electric field in the middle of the square in magnitude and direction? four charges are arranged at the outer corners of the square in order from left to right , then top top to bottom respectively +q,-2q,-q,+2q.Homework Equations The Attempt at a Solution...
  17. srfriggen

    Reflective symmetry of a Square

    In my abstract algebra course we learned recently of the symmetries D4. Regarding flips/reflections, of which there are 4, it seems for the 2D object that is a square, you would have to "fold it through the 3rd dimension" to obtain a flip/reflection. Couldn't you just invert the square by...
  18. H

    Finding the last corner of a square

    Homework Statement Show that there is a C point to these points A(-2|2|3), B(2|10|4) and D(5|-2|7), so that the quadrangle ABCD a square is. Determine the coordinates of C. The Attempt at a Solution All I have done is measure AC, CD and BC, which are 9, 9 and 12.78. But how do I get the C...
  19. T

    Dimension-analogy square?

    Hi,I m thinking about,what is dimension meaning in physics.Is it any analogy with square or cube,for example?Let have for example the simplest example,distance:s=v*t.Can I draw this equation like rectangle object?Like in geometry,we have for rectangle equation a*b,now we have v*t.I know,it is...
  20. M

    Transforming between square matrices of different order

    I have two known square matrices A and B of different order. Is there any way of constructing a transformation - e.g. a transformation matrix C - that transforms A to B? And, in that case, how do I determine C? Would it be something like this? AC = B Or maybe more general, how to determine...
  21. B

    Why Doesn't My Fourier Series Expansion Look Like a Square Wave?

    for a square wave function, f(x)= { -1, -∞ ≤ x ≤ 0; +1, 0 ≤ x ≤ ∞ Expanding it in Fourier series gives a function like, f(x) = (4/π) * Ʃn=0∞( (sin ((2n+1)x) / (2n+) ) Plotting a graph of the equation gives something like this, http://goo.gl/vFJhL which obviously doesn't look like a...
  22. H

    What is the Correct Value of the Square of a Momentum Operator?

    know I'm missing something obvious. for a momentum operator p = -iħ d/dx if I square the -iħ part I get (+1)ħ2 but I believe the correct value (as in the kinetic energy of the Hamiltonian) is -ħ/2m d2/dx2. how is the value of the term -ħ/2m where the square of -i = +1? Thanks!
  23. M

    Convolution of iid non central Chi square and normal distribution

    Hi, I am doing research and I am stuck at this point I need help to convolute iid non central chi-square with normal distribution.
  24. P

    What is the relationship between area and dimensions?

    I was just wondering the other day about the concept of area...Area to me is the space occupied in 2d by a bounded figure... I wanted to find out WHY the area of a square is s^2 or why area of a rectangle is lxb...Consider the dimensions of a rectangle 7x5. The area can be expressed as 5 strips...
  25. L

    Prove Square Root of 15 is Irrational

    Homework Statement Prove Square Root of 15 is Irrational The Attempt at a Solution Here's what I have. I believe it's valid, but I want confirmation. As usual, for contradiction, assume 15.5=p/q, where p,q are coprime integers and q is non-zero. Thus, 15q2 = 5*3*q2 = p2...
  26. N

    Square or Rectangle 30 psi storage tank

    If I want to make a Square or Rectangle storage tank 5 feet deep and 22 feet long and 1 foot wide. The tank will be under 30 psi and also vacuum. That’s not hard to do what I want is the walls not to deflect more then .001 of an inch. The walls can be plastic, plywood with a steel sheet or...
  27. S

    MHB Proof that the product of 4 consecutive numbers is not a perfect square.

    Hey, I was thinking and I realized that this is true and I want to prove it but I have nowhere to start. If anyone knows any way to prove can you give me some advice on where to start.
  28. S

    Is the white region a square or rectangle?

    Is the white region a square or rectangle? See my post below for image
  29. B

    Square roots of complex numbers

    Mod note: These posts are orginally from the thread: https://www.physicsforums.com/showthread.php?t=626545 The square root is not defined everywhere, at least not as a function, but as a multifunction, since every complex number has two square roots. I mean, the expression z1/2 is ambiguous...
  30. S

    Finding magnitude of electric field at center of square

    In each situation below, electric charges are arranged at the corner of a square. Each charge Q has the same magnitude with the signs indicated in the diagrams. Rank the electric potential from most positive to most negative, and the magnitude of the electric field at the center of the square...
  31. C

    When the expression is a square of a rational number.

    Homework Statement I am trying to find when the square root of the expression 25+8a^2 is rational, where the number a also needs to be rational. \sqrt{25+8a^2}=b, where a and b are both rational numbers. I am trying to get an expression for a in terms of some other number m, which would always...
  32. J

    ASTM A500 Grade B Square Tubing: Safely Supporting 180 lbs. Over 12 ft.

    Will 3"od X .250" wall ASTM A500 Grade B square tubing safely carry a single point load of 180lbs. over a 12ft span. Thanks
  33. M

    Taking negative/positive square roots

    Let's say that the variable 'x' is definitely some negative number. So if I wanted to solve: x^2 = 4 I get: \pm \sqrt{x^2} = \pm \sqrt{4} \pm x = \pm 2 I would have to take the positive value of 'x' and the negative value of '2' to make this true...is it okay to only take a positive square...
  34. O

    Question about reducing a square root.

    IDK if this should be in the precalc section, but I was wondering how to reduce \sqrt{(3+\sqrt{5})} / \sqrt{(3-\sqrt{5})} to (\sqrt{5} + 1) /(\sqrt{5} - 1)
  35. A

    Is the Square Root Function Bijective in all Branches of Mathematics?

    In what branches of mathematics is this proven.. I have never seen a proof, so I wonder if anyone can give me the basics of what is done to proove it or got a link to a proof.. Edit: By square root I mean the positive square root.
  36. S

    Calculating Square Roots of an Elliptic Curve

    So there are four square roots for an elliptic curve represented by an equation something like this: y^2 = x^3 + x + 6 (mod 5) How would one go about calculating these?
  37. X

    Trace and its square of mixed state density operator using integral

    Homework Statement I want to show that tr\left(\hat{\rho}_{mixed}\right)=1 tr\left(\hat{\rho}_{mixed}^{2}\right)<1 when \hat{\rho}_{mixed}=\frac{1}{2\pi}\int_{0}^{2\pi}d \alpha \hat{\rho}(\psi) Homework Equations tr\left(\psi\right)= \sum_{n}\langle n|\psi|n\rangle...
  38. D

    Sampling frequency and square waves

    Homework Statement Lets say I have a square wave of 10Hz. I want a good sampling frequency or the Nyquist rate (minimum) to accurately capture its characteristics without aliasing. Is it enough to use 10Hz x 2 as nyquist rate, or must I break it down into harmonic frequencies? and use...
  39. E

    Square integrable functions - Hilbert space and light on Dirac Notation

    Square integrable functions -- Hilbert space and light on Dirac Notation I started off with Zettilis Quantum Mechanics ... after being half way through D.Griffiths ... Now Zettilis precisely defines what a Hibert space is and it includes the Cauchy sequence and convergence of the same ... is...
  40. A

    Calculating Torsional Capacity of Square HSS

    I have having dificulty in determining the torsional capacity of a square HSS section. I am designing a shaft for 9.5 cubic yard mixer powered by a 80hp drive at 6 rpm output. I have calculated the applied torque to be 70,000 ft-lbs (95 kNm). I would like to determine the size of HSS...
  41. S

    Calculate Dead Load of Beam w/ Solid Square Cross Section

    Homework Statement A beam has a solid square cross section of 100mm and is simply supported by two supports 3m apart. Calculate the dead load that can be safely supported when applied to the middle of the beam. Homework Equations Solid square cross section of beam: 100mm Material...
  42. J

    Electric field question involving 4 charges on a square

    Four charges are placed at the vertices of a square, centered at the origin, as shown in the diagram. If each side of the square has a length of 0.224 m, what is the strength and direction of the net electric field at the origin? Express your answer in terms of the charge magnitude q...
  43. J

    Creating a square wave pulse at the peak of a sin wave

    Hi all, I am trying to create a square wave pulse that lasts for a relatively small amnount of time which corresponds (as close as possible) to the peak of a sin wave input of period about 1 second. The only way that I can think of doing this is via a programmable device such as an arduino...
  44. P

    Moment of Inertia for a Square and a pipe of variable density

    Homework Statement First, there's a slender rod with length L that has a mass per unit length that varies with distance from the left end, where x=0, according to dm/dx = yx where y has units of kg/m^2. (a) Calculate the total mass of the rod in terms of y and L (Which I've already done and...
  45. B

    Find the wave function of a particle bound in a semi-infinite square well

    Homework Statement Consider the semi-infinite square well given by V(x) = -V0 < 0 for 0≤ x ≤ a and V(x) = 0 for x > a. There is an infinite barrier at x = 0 (hence the name "semi-infinite"). A particle with mass m is in a bound state in this potential with energy E ≤ 0. Solve the Schrodinger...
  46. H

    MHB Manipulation of negative square root of a negative term/#

    Suppose I have to solve for y: x\leq 1 (x - 1)^{2} = y So I know that (x - 1) will always be 0 or a negative, therefore I must take the negative square root of (x - 1): -\sqrt{(x - 1)^{2}} = -\sqrt{y} Am I to understand that this is the same as: -1 \cdot \sqrt{(x - 1)^{2}} = -1 \cdot...
  47. caffeinemachine

    MHB Square root in Q(root 2) means its in Z[root 2]

    Let $a,b \in \mathbb{Z}$, and if $a+b\sqrt{2}$ has a square root in $\mathbb{Q}(\sqrt{2})$, then the square root is actually in $\mathbb{Z}[\sqrt{2}]$. Only one approach comes to my mind. Let $r_1, r_2 \in \mathbb{Q}$ such that $a+b\sqrt{2}=(r_1+r_2\sqrt{2})^2$. This gives $a=r_1^2+2r_2^2...
  48. J

    MHB Master the Magic Square: Tips for Solving the 3x3 Puzzle in Just 4 Hours

    HI In a square 3 x 3 using the numbers 1 to 9 once only put the numbers so that: the numbers on the top row minus the numbers in the 2nd row = the numbers on the 3rd row. trying this for about 4 hrs and am always 1 number out.
  49. R

    Constructing a Tri-Axial Square Helmholz Coil

    Homework Statement I'm a summer REU student tasked with building a tri-axial square helmholtz coil setup. My frame will be made of aluminum while the wire used will be copper. I've been researching for days, having actually never studied these coils before, and I'm having serious trouble...
  50. S

    Center of mass of half square without a half circle

    Homework Statement Find the position of the center of mass for a thin sheet and homogeneous, with sides R and 2R ,from which has been subtracted a half circle of radius R. [Xcm=(2/3)*R*(4-pi)]Homework Equations Rcm=(1/M)*∫rdm The Attempt at a Solution By symmetry we know Ycm=0. For de...
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