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. M

    Understanding the Solution for Finding the Sum of Digits of m

    Homework Statement Let m be the number of numbers fromantic the set {1,2,3,...,2014} which can be expressed as difference of squares of two non negative integers. The sum of the digits of m is ... Homework EquationsThe Attempt at a Solution I got a solution from a magazine but I didn't under...
  2. J

    What is the Optimal Wall Thickness for a Square Tube Supporting a Static Load?

    I need to make a steel beam ( or aluminum) of square tube ( box beam) 10 feet long with a balance point 2 feet from one end. The short end will have 60 lbs on it and the long end will have 30 lbs. how thick of a wall will the square tube need to be to hold the static load?
  3. S

    MHB How to Create 4-by-4 Magic Square w/Sum 34

    If you ever need a 4-by-4 Magic Square, here's an easy way to construct one. Draw a 4-by-4 grid and consider the cells on the two diagonals. $\quad\begin{array}{|c|c|c|c|} \hline * &&& *\\ \hline & * & * & \\ \hline & * & * & \\ \hline * &&& * \\ \hline \end{array}$Starting at the...
  4. kaliprasad

    MHB Square Numbers Satisfying $3x^2+x=4y^2+y$

    show that for x,y positive integers satisfying $3x^2+x= 4y^2+y$ each of x-y , 3x+3y+ 1 and 4x + 4y + 1 are squares. ( above equation has atleast one solution x= 30 and y = 26)
  5. Berlin

    Does the Square Root of the Inverse Metric Unify Geometry and Physics?

    Anyone noticed this paper: Square Root of Inverse Metric: The Geometry Background of Unified Theory? Authors: De-Sheng Li, arXiv:1412.2578 ? The author tries to construct the square root of the inverse metric, based on a product of a fermion field and a framefield. Somehow the Standard model...
  6. ELB27

    A strange inconsistency with square roots

    Hi, I have a question that came into my mind while solving some problems. If I have a constant times an expression in a square root like ##4\sqrt{16}## I can square the constant and push it into the square root: ##4\sqrt{16}=\sqrt{4^2 16} = 16##. But what if the constant outside of the square...
  7. Greg Bernhardt

    Can distinct integers with 8 subsets of 3 always form a magic square?

    This challenge has been provided by @Joffan A magic square has rows, columns and diagonals summing to the same number. For a 3x3 magic square there are 8 such sums. Given a set of 9 distinct integers which has at least 8 subsets of 3 all with a common sum, is it always possible to make a magic...
  8. D

    Problem 2.4 Griffiths E&M 3rd ed -- E-field above a square loop

    Homework Statement The problem states, "Find the electric field a distance z above the center of a square loop (sides of length a) carrying a uniform line charge λ. " The hint says to use the result of example 2.1. Example 2.1 is a similar problem, but instead of a square loop you are asked...
  9. C

    What is the Threshold for Interband Optical Transitions in a 2D Square Lattice?

    Homework Statement A two dimensional solid has two electrons per unit cell and has a Bravais lattice with primitive vectors ##\vec a = \ell \hat x## and ##\vec b = \ell \hat y##. The crystal potential is weak and the solid behaves like a free electron metal. a)In a reciprocal space diagram...
  10. AdityaDev

    Permutations and combinations - is square a rectangle?

    I was going through a p and c problem where I had to find the number of non congruent RECTANGLES. Answer includes number of squares as well. SHOULD SQUARE BE TAKEN AS A RECTANGLE?
  11. B

    High precision square roots

    Hello, i'm having trouble evaluating my gamma factor for my special relativity homework, because I need to compute 1 minus a very small number (8.57*10^-13). My calculator treats this value as simply 1, as does Mathematica. Although I don't know much about it, and maybe there's a way to force...
  12. V

    Estimating irradiance on a square planar surface

    Hi, I have a simple problem. A Lambertian emitter has the shape of a square planar surface, with area Ae=4mm2, total power P=1mW, and is located in yz plane. Another square planar surface, with area Ad=6mm2, is located in the xy plane, at a distance d=10cm to the Ae, and is tilted 20 Degrees...
  13. 2

    Variance in position for the infinite square potential well?

    [Note from mentor: this thread originated in a non-homework forum, therefore it doesn't use the standard homework template] ------------------------------------------ This exercise pops up in the Cavendish Quantum Mechanics Primer (M. Warner and A. Cheung) but I can't seem to figure it out. So...
  14. H

    Complex numbers and completing the square

    Homework Statement let z' = (a,b), find z in C such that z^2 = z' Homework EquationsThe Attempt at a Solution let z = (x,y) then z^2 = (x^2-y^2, 2xy) since z^2 = z', we have, (x^2-y^2, 2xy) = (a,b) comparing real and imaginary components we have; x^2-y^2 = a, 2xy = b. Now, this...
  15. K

    Electric charges at the corners of a square

    Homework Statement 3 point charges, q1=+2E-9[Coulomb] are placed at the corners of a square of 0.2[m] edge. what is the potential at the center. Homework Equations The potential of a point charge at distance r: $$V[Volt]=K\frac{q}{r}$$ ##K=\frac{1}{4\pi\varepsilon_0}=9\times 10^9## The...
  16. T

    Fourier Series for f(x) = sin(3x/2) and Evaluating Series for (1/(4n^2-9))^2

    Homework Statement Evaluate following series: \sum_{n=1}^\infty \frac{1}{(4n^2-9)^2} by finding the Fourier series for the 2\pi-periodic function f(x) = \begin{cases} sin(3x/2) & 0<x<\pi \\ 0 & otherwise \end{cases} Homework Equations a_n = \frac{1}{\pi}\int_{-\pi}^{\pi}...
  17. C

    Solving Antiferromagnetic Ising Model on Square Lattice

    Hello, I am trying to work out a mean field theory for an antiferromagnetic Ising model on a square lattice. The Hamiltonian is: ## H = + J \sum_{<i,j>} s_{i} s_{j} - B \sum_{i} s_{i} ## ## J > 0 ## I'm running into issues trying to use ## <s_{i}> = m ## together with the self-consistency...
  18. G

    Calculating strength of steel square tubing

    Hello, I'm enrolled in College in the civil engineering program and am looking for guidance with calculating strength of steel square tubing. We are making a project that has parameters. 1- Must be made of steel 2- 4"x6"x36" is maximum OD of section. 3- 14 lbs is maximum weight 4- the load...
  19. anemone

    MHB Find X, a 4-digit perfect square

    X is a 4-digit perfect square all of whose decimal digits are less than seven. Increasing each digit by three we obtain a perfect square again. Find X.
  20. JasonHathaway

    The area of a square with right triangle inside it

    Homework Statement I need to find the area of the square in the following figure: Homework Equations Basic Trig relations. The Attempt at a Solution I aimed to find the length of BC, but first I had to find the unknowns of the right triangle CDE, which are EC=5m, <DCE=36.86ْ , <DEC=53.13ْ ...
  21. B

    How to show the inverse square law from a data set

    Homework Statement Hi there! I have a data set of r (independent variable) and E (electric field strength) (dependent variable). The question asks for a non graphical method to show if there is an inverse square law relationship between the two data sets. -- My attempt: I picked the equation...
  22. A

    MHB Concept of contour integration and integration along a square

    Hello, My question is, there is a concept of contour integration. Which is choosing a circular contour space sort of, and integrating along that. How do you do contour integration? Secondly, there is something going around called integrating along a square. I tried searching only, a lot...
  23. R

    Finding Torque in a Square: How to Determine the Distance for Calculating Torque

    Homework Statement So image we have a square. And the center of mass is, well in the center. If I choose the pivot to be the bottom left corner, would the distance used to calculate torque be from the bottom left to the center or to the middle on the same axis? I have a picture since it's kind...
  24. S

    What is the energy of the following state (quantum square)?

    Homework Statement [/B] What is the energy of an STM tunneling electron in the following state? This "quantum square" model can be seen as a "particle in a 2-D box" problem. <Refer to the picture below> The protrusions are Fe atoms and the surface is Cu(111). Given that the radius of an Fe atom...
  25. L

    Finding the Critical Point(negative square root)

    Homework Statement Find the critical points for the function g(x, y, z) = x3+xy2+x2+y2+3z2. Homework EquationsThe Attempt at a Solution I've come up with the following 3 equations (derivatives set so that they are equal to 0) (1) 3x2+y2+2x=0 (2) 2xy+2y=0 (3) 6z=0 From (3), z=0 From (2)...
  26. C

    Equation of SNR versus sigma square for BPSK

    I would like to know in the following equation (attached) how can I incorporate BER for BPSK? is BER the same as Rc? The equation is relation between SNR and sigma square.
  27. M

    Squared numbers and square root (Need help with explaination)

    Can anyone tell me why for example the speed of light is squared in "E=mc^2" ? Also what does square root mean and why is it in certain equations like for example time dilation? What happens if you exclude the square root and the y^x in a equation? I am still studying high school physics, but...
  28. T

    MHB How can you factor out x from the original term?

    In a text, We have this: $\sqrt{2x^2 + 1}$ is equal to $x \sqrt{2 + \frac{1}{x}}$ I am confused as to how to factor out x from the original term.
  29. C

    MHB What is the Square Root Property in Mathematics?

    Dear everyone, I have a question about a property of square root. $${\frac{1}{x}\sqrt{x^2}}$$$\implies$ $\sqrt{\frac{x^2}{x^2}}$=$\left| 1 \right|$ Is that property of a square root? Since $$\sqrt{x^2}$$= $\left| x \right|$.
  30. PcumP_Ravenclaw

    Square root of 2 divided by 0 is rational?

    Dear All, Please help me understand how ## \sqrt{2} ## divide by 0 is rational as stated in the excerpt from alan F beardon's book?
  31. J

    Solve Infinite Square Well: Homework Statement

    Homework Statement The wording of the question is throwing me off. It is a standard inf. pot. well problem and we are given the initial position of the particle to be in the left fourth of the box, \Psi(x,0)=\sqrt{\frac{4}{a}} We are asked to a) write the expansion of the wave function in...
  32. D

    Best way to pulse a constant microcurrent square wave signal?

    I have a constant 100 uA square wave DC 10Hz signal that needs to have a pulse width of 50ms. I was reading up on using an electronic timer relay (recycle type) or a solid state relay controlled via PWM. I need some help choosing which route to take, or if there are better/easier ways to...
  33. R

    MHB Show that Q adjoin square roots of 2, 3 is a vector space of dimension 4 over Q

    Let \mathbb{Q}(\sqrt{2},\sqrt{3}) be the field generated by elements of the form a+b\sqrt{2}+c\sqrt{3}, where a,b,c\in\mathbb{Q}. Prove that \mathbb{Q}(\sqrt{2},\sqrt{3}) is a vector space of dimension 4 over \mathbb{Q}. Find a basis for \mathbb{Q}(\sqrt{2},\sqrt{3}). I suspect the basis is...
  34. S

    CHI square independent test (small expected frequency)

    Homework Statement the expected frequency for the age of (21-30, 31-36, more than or equal to 37) for operation is less than 5 , so combination of these numbers are required for the expected frequency to be more than or equal to 5 . my question is which numbers should i combine? would my ans...
  35. D

    Minimum mean square error for two random variables

    Homework Statement Determine the minimum mean square error for the joint PMF. You will need to evaluate ##E_{X, Y}[(Y - 14/11\cdot X - 1/11)^2]##. Homework EquationsThe Attempt at a Solution The answer is ##\frac{3}{22}##, but when I work it out, I get ##\frac{203}{484}##. From my values, I...
  36. J

    Homework, electric field strength at centre of a square

    Homework Statement 4 charges of +5µC, +3µC, -4µC and +2µC form the 4 points of a square of side length 2m. Calculate the field strength and potential at the centre of the square. Homework Equations F=1/4πhttp://upload.wikimedia.org/math/d/3/c/d3c305fc416b971cd6d284564e51bf85.png0 X Q1Q2/r2 E=...
  37. P

    Finite square well, excited states

    Homework Statement Consider a particle of mass m in the ground state of a potential well of width 2 a and depth. the particle was in the ground state of the potential well with V0 < Vcritical, which means the well is a narrow one. At t = 0 the bottom of the potential well is shifted down to Vo'...
  38. G

    CHI square test - finding degree of freedom

    Homework Statement i have problem of finding the degree f freedom for this question. the ans for v is 3 , but my ans is v=n-1 , where n = 6 , so my v=5... Homework EquationsThe Attempt at a Solution
  39. Z

    MHB How can we simplify this expression involving square roots?

    4\sqrt{n^{2}}+\sqrt{m^{2}n-\sqrt{4n^{2}}}-\sqrt{mn^{2}} I don't even know where to start, I know the teacher said to distribute but distibute what?
  40. R

    Does there always exist primes in between square of two consecutive prime.

    Does there always exist primes in between square of two consecutive prime i.e Pn-1 and Pn where Pn-1 and Pn are consecutive prime. That is, in other words, does all the odd places between Pn-1 and Pn, are not divided, by primes less than Pn or by all primes upto Pn-1.I can only check randomly...
  41. O

    MHB Simplifying a square root in a fraction, part of midpoint formula

    I have: sq rt 2 +sq rt 2 over 2 , sq rt 5 + sq rt 5 over 2 I got (sq rt 4 over 2, and 0) = 1, 0 but the answer is actually (sq rt 2, 0) so is my answer still wrong?
  42. T

    MHB Finding limit of a funciton with square roots.

    I have to find this: $$\lim_{{x}\to{3}}\frac {\sqrt{6x - 14} - \sqrt { x+1}}{x-3}$$ So I do this: $$\lim_{{x}\to{3}}\frac {\sqrt{6x - 14} - \sqrt { x+1}}{x-3} * \frac{\sqrt{6x + 14} + \sqrt{x+1}}{\sqrt{6x + 14} + \sqrt{x+1}}$$ The top part is easy since $$(\sqrt{a} - \sqrt{b})(\sqrt{a} +...
  43. V

    How do I linearize a square root graph?

    Homework Statement These are the Points. X values: 0, 1.98, 3.96, 5.94, 7.92, 9.9 Y values: 1.98, 7.13, 9.08, 11.04, 12.57, 14.51 I need to find the original equation and the linear equation. I can't seem to find the line for square root graphs. 2. The attempt at a solution I know it's a...
  44. T

    MHB Finding domain of a function with square root in bottom of fraction\infty

    I need to find the domain of this function.$$h(x) = 1 / \sqrt[4]{x^2 - 5x}$$ So, I understand that I need to set $$x^2 -5x > 0$$ from that I get $$ x(x-5) > 0$$ and $$ x > 5$$ However, the answer in the textbook is given: $$ ( \infty, 0) \cup (5, \infty)$$ Which mean that the graph has a...
  45. Albert1

    MHB Calculate Square of Sum ∑1..9999

    \left(\sum_{n=1}^{9999}\frac{\sqrt{100+\sqrt{n}}}{\sqrt{100-\sqrt{n}}}+\sum_{n=1}^{9999}\frac{\sqrt{100-\sqrt{n}}}{\sqrt{100+\sqrt{n}}}\right)^2
  46. F

    Close Packing of Spheres in Regular Tetrahedral vs. Square Pyramidal C

    The full title of this post is "Close Packing of Spheres in Regular Tetrahedral vs. Square Pyramidal Container" I'm not sure where this post belongs, but Greg Bernhardt suggested I just post it where I thought best, and he would find a place for it. So here goes: In 1611, Johannes Kepler...
  47. O

    MHB Solving Square Root Questions: A Math Tutorial for Beginners

    How does this work? (Also, I am very math illiterate and do not understand even the most basic terms, if you could kindly speak as you would to a child I would GREATLY appreciate it.) sq rt sign over 13^2 - 12^2 (over both of it together) Now the answer is 5, because (13)(13) - (12)(12)...
  48. E

    Units square root of a Newton

    I have a table with several quantities in it, and one of them is \sqrt{T} (T is tension) I have values for this table, and want to put the units next to the values. Something seems off to me about doing this, I guess because they're not integers. Is it correct to say the units are kg1/2m1/2s-1...
  49. 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) ...
  50. 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...
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