What is Squares: Definition and 400 Discussions

In Euclidean geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, π/2 radian 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



◻


{\displaystyle \square }
ABCD.

View More On Wikipedia.org
Recent contents Top users
  1. B

    Determine the number of Pairwise Non-Isotopic Latin Squares

    Homework Statement Basically, everything's in the title. I'm asked to find the number of pairwise non-isotopic Latin Squares. Homework Equations A non-isotopic Latin Square is one that cannot be created simply by permuting the rows/columns of another Latin Square. The Attempt at a Solution...
  2. R

    Calculating uncertainty using the least squares method.

    Can someone point me in the right direction or give me a rundown on how to use the least squares method in calculating the uncertainty in a gradient of a graph? We have been given a theoretical experiment with data and so on supplied and we need to find the uncertainty of the graph we have...
  3. X

    Least Squares Derivation question

    So I am learning how to use the method of least squares to find the best fit straight line and there is this one part in the derivation I do not fully understand and I was wondering if anyone could help me out. So basically we start out with the residuals of the equation of a straight line...
  4. M

    Difference of two squares under a radical

    This may seem elementary, but it's been awhile since I've done heavy algebra work. I used the quadratic formula to get this equation: \mu = (\pm \sqrt{1 - 8x^{2}} - 1)/2 and I'm trying to simplify to: \mu = (\sqrt{1 + 8x^{2}} - 1)/2 If anyone could just point me to any resources that could...
  5. R

    Interesting way to define a sequence of Squares

    Let A and B be two coprime integers. Find X = zero mod A such that Y = 2*X +1 = 0 mod B. Then 8*(Y +2*N*A*B)*(X + N*A*B) + 1 is a square for all integer N. If A = 5,B = 7, X = 10, Z = 21 then the sequence of square roots of the Squares for N = -3 to 3 is -379, -249, -99, 41, 181, and 321. Of...
  6. D

    Number theory-product of squares

    Number theory--product of squares Homework Statement Suppose a and b are two integers, which can each be written as the sum of two squares. Prove that ab can be expressed as the sum of two squares. Homework Equations The Attempt at a Solution a=c^{2}+d^{2} b=x^{2}+y^{2} I'm...
  7. Vorde

    Number of squares in a grid of dots.

    This is a problem that I just thought of the other day and am intrigued by, let me set it up. You have an n x n grid of dots, so that each dot is 1 away from the four dots closest in each direction. My question is; for a grid of n2 dots, what is the total number of possible combinations of...
  8. K

    Forcing a Least squares Polynomial through a fixed point

    Hi guys, Thanks for taking the time to read the post. I have a question related to curve fitting and polynomials that i was hoping someone might be able to help me with. I have a set of x and y data points, all on a graph. I have then calculated the 4th order least squares polynomial...
  9. V

    Difference of two squares considered to be a quadratic

    Homework Statement is an expression that is a difference of two squares considered to be a quadratic. For example, would x2 - 4 be a quadratic? What about x4 - 4? Homework Equations Ax2 + Bx + C The Attempt at a Solution I know we can factor a DOTS into two binomials like a...
  10. S

    Optimal Filter Coefficients: Correlation versus Least Squares

    I found a claim in a paper (BSSA, Vol 81, No. 6: "A Waveform Correlation Method for Identifying Quarry Explosions", By D.B. Harris) concerning finding filter coefficients. The statement is given without proof. I cannot locate a reference or theorem for the following, and have not been able thus...
  11. I

    Non-linear 2nd ODE involving squares of derivatives

    Homework Statement y''+(1/y)*(y')2=0 Homework Equations The Attempt at a Solution This is another problem I am having trouble with. I have done searches around the internet, but seen that all "non linear" ODE of second order involves a non linear form in a non differential term...
  12. B

    Question about Least Squares Fitting

    Hey, I have a graph for which I am supposed to fit two linear least squares line and minimize the combined residuals (the lines intersect)... I would really appreciate some info about how to do this or what this type of data analysis is called so i can google the step-by-step method. Thanks!
  13. B

    Question about Least Squares Fitting

    Hey, Not sure if this is the right section to post this but ... I have a graph for which I am supposed to fit two linear least squares line and minimize the combined residuals (the lines intersect)... I would really appreciate some info about how to do this or what this type of data analysis...
  14. K

    Can Least Squares be Applied to Matrices for Solving a Complex Equation?

    Hi, as no unique unique analytical solution exists to my problem (as another poster pointed out), I have taken to solving it through a least squares method. My equation is as follows: (s1x1 + s2x2 - I).^2 = min. Here s1 and s2 are shift matrices (I know them), and I is a matrix of size...
  15. M

    Least Squares solution and residuals

    Homework Statement Solve the following linear equations simultaneously by the Least Squares solution and calculate the residuals. Homework Equations 3x + 2y + z = 5 x + 6y - z = -7 x - y + 2z = 3 5x - 2y = 1 The Attempt at a Solution This is a question from this guy at...
  16. F

    An efficient way to find perfect squares?

    Hi, I have a problem that I'm a bit stuck on, and need some direction: I need to find \forall_n within a certain domain that can satisfy this equation: \left( 3n-1 \right) \left( n+1 \right) = m^{2} where m,n \in \mathbb{Z} Or, to put it in a different context, I'm looking for...
  17. M

    Puzzle: a cube with Latin squares

    Imagine a cube wrapped in Latin squares and try to solve the following puzzles. Please be aware the symbols at the borders are shared between neighboring cube's sides. Let me know if you like it or not. This is rather straightforward: This is a bit harder
  18. G

    Math Challenges: Find Pairs, Units Digit, Perfect Squares, Last Digit

    1. Find the number of pairs (m, n) such that 2m - 2n = 63 in which m and n are nonnegative integers. 2. What is the units digit of 625 - 324 ? 3. How many perfect squares divide the number 4!*5!*6! ? 4. What is the last digit of the sum 1! + 2! + 3! + ... + 2010! + 2011! ? Thanks!
  19. L

    Weighted least squares fitting

    Hello y'all, If I have n data points (xi, yi) each with error bars in both x and y (xi_err, yi_err), should I use 1/(xi_err^2+yi_err^2) as the weight in a weighted least squares linear fit, or should the weight be a different value that has nothing to do with error bars? I've never used WLS...
  20. K

    Elements of odd-order abelian groups are squares.

    Homework Statement Let G be a finite abelian group, and assume that |G| is odd. Show that every element of G is a square. The Attempt at a Solution So we want to show that \forall g \in G, \exists h \in G, g = h^2 . Let g \in G be arbitary, and consider the subgroup generated by g, denoted...
  21. G

    Sum of squares of prime factors

    I recently got interested in number theory and have been fiddling around with Scilab trying to find interesting things. I came across the following mildly interesting property, which I couldn't find much about on Google. Form the difference d_n between the sum of the squares of the prime...
  22. D

    Weighted least squares best fit plane

    I know that the plane through the center of mass whose normal is the eigenvector corresponding to the smallest eigenvalue of the scatter matrix of a set of points is the best fit plane. I now want to do a "weighted least squares" - would I simply multiply the...
  23. L

    How many ways to express a prime (= 1 mod 4) into sum of 2 squares ?

    I know that any prime p = 1 mod 4 can be expressed as sum of 2 squares. But how many different pairs of integers a,b such that p = a^2+b^2? (with a>b!) It seems there is only one pair. How to prove it? I try in this way: assume p = a^2+b^2 = c^2+d^2 (with a>c>d>b) and try to show it has...
  24. P

    How do I perform a weighted least squares fit with error bars?

    Hi, I am trying to do a best least-squares fit to a set of data which is described by the following equation: y=a\exp(-b\ln^2(c/x)) Where a,b,c are constant parameters I am trying to find values for. Any advice on how to proceed?
  25. S

    Linear Algebra - Least Squares

    Homework Statement Test these two equations, using least-squares fitting of the data (ti, bi), i = 1, 2, . . . , 100:1. b(t) = d_{1} + d_{2}te^{-t} + d_{3}t^{2}e^{-2t}2. b(t) = d_{1} + d_{2}\sqrt{t}e^{-\sqrt{t}} + d_{3}te^{-2\sqrt{t}} where d1, d2, d3 in R are unknown. For both theories...
  26. fluidistic

    Least Squares Fitting for ax²+bx+c with Given Points: Homework Solution

    Homework Statement I must find the best fitting function of the form ax²+bx+c using least squares. The points are (-1,6.1), (0,2.8), (1,2.2), (3,6) and (6,26.9). 2. Homework Equations + attempt at a solution A\vec x= \vec b, I'm looking for \vec x =\begin {pmatrix} a \\ b \\ c \end {pmatrix}...
  27. Simfish

    MATLAB Linear Least Squares Fit with Error Bars: A MATLAB Tutorial

    With MATLAB or something. Basically, I just have a bunch of data points where I should do a linear least squares fit, but each of the points have error bars around them.
  28. E

    Every element of a finite field is a sum of 2 squares?

    Hi everyone, I have to prove that every element z of a finite field F is a sum of 2 squares. Really not sure how to go about proving this, though I've done some research and it is suggested to start with a function that maps F* to itself, defined by f(x) = x^{2} . I guess if I could show...
  29. P

    Finding the Curl at a point with three squares

    Homework Statement Three small squares, S1, S2, and S3, each with side 0.1 and centered at the point (4,5,7), like parallel to the xy, yz, and xz planes respectively. The squares are oriented counterclockwise when viewed from the positive z, x, y axes respectively. A vector field G has...
  30. B

    Fourier Series as (Generalized)Least Squares?

    Hi, All: Given a normed vector space (X,||.||), and an inconsistent system Ax=b, the generalized least squares solution x^ to Ax=b is the point in the span of Ax that is closest to b, i.e., given a fixed matrix A, we define AX={Ax: x in X}, and then: x^:={ x in AX...
  31. C

    Solve Least Squares Problem for Matrix A and B | Homework Equations

    Homework Statement Let A= |2 -1 -1| |-1 2 -1| |-1 -1 2| and B= |1| |2| |3| Homework Equations Find the x in which minimizes ||Ax-b||2 The Attempt at a Solution I tried to solve it by using this formula (A**A)-1A**b=x but i get the inverse of A*A equal 0
  32. S

    Nonlinear Least Squares Minimization

    How should I go about solving this problem? This is only to get a better understanding of how NLLS works. F(x;a) = (1+a1*x)/(a2+a3*x) (so n = 3) I am choosing a1,a2,a3 to be 2,3,5 respectively. I am also picking 6 data points (so m = 6): (0, 0), (-1/4, 1/4), (-1/2, 1/10), (1/4, 1/4)...
  33. S

    Sum of Two Squares: Is There a Relation?

    sum of two squares? If an Even number could be expressed in the form a2 + b2 . And if there exits two other numbers m,n such that a2 + b2 = m2 + n2 then , my question is is there any relation between (a,b) and (m,n) apart from a2 + b2 = m2 + n2 ??
  34. H

    Comp Sci How to Test if a Matrix is a Magic Square in Java?

    Homework Statement Magic squares. An n × n matrix that is filled with the numbers 1, 2, 3, ..., n2 is a magic square if the sum of the elements in each row, in each column, and in the two diagonals is the same value. Write a program that reads in n2 values from the keyboard and tests...
  35. Evo

    Medical Experiencing Purple Squares and Hot Pink Circles in Vision

    Now that this has happened a second time, I'm really puzzled over what I am experiencing, just wondering if any of you have heard of this. The other day I was lying in bed and I noticed that there was a large circle about 1 inch in diameter made of bright hot pink filaments in my vision. It...
  36. S

    Linear Least Squares Minimization

    I'm going through some methods to solve the LLS method of minimization and have come upon 3 general methods to solve the problem. The 3 methods I am looking at are normal equations, QR factorization, and SVD. I've come upon a fact that I can't find an explanation for: Can anyone explain why...
  37. K

    Are 0 and 1 Considered Perfect Squares?

    I know this may sound dumb, but is zero and one perfect squares? I have no idea.
  38. I

    Least squares problem - Leon Ch 5, sec.3, prob.3

    Homework Statement For the system Ax = b, find least squares solution. A = (1 2) ; b = (3, 2, 1)T ----(2 4) ----(1 -2) Homework Equations I know if A is an m x n matrix of rank n, the normal equations ATAx = ATb have a unique solution x =...
  39. A

    Field Plots forming curvilinear squares

    Homework Statement Drawing a field plot (using curvilinear squares) between a small sphere within a larger sphere, indicating lines of force and equipotentials. I've been trying to find a software solution to draw the diagram perfectly, but haven't had any luck in finding one. I think it...
  40. F

    Linear Algebra Least Squares Question

    Homework Statement Suppose the columns of A are not independent. How could you find a matrix B so that P=B(BTB)^-1BT does give the projection onto the column space of A? (The usual formula will fail when AT A is not invertible). T is transpose. Homework Equations The Attempt at a Solution I...
  41. J

    What Formula Determines the Squares Producing a Specific Difference?

    Hello, Sorry if this is in the wrong forum, I wasn't sure so I just picked General. Is there a formula to determine the squares that will produce a given difference. For example x^2 - y^2 = 21. From a little experimentation it seems that for odd numbers the problem can be solved with this...
  42. S

    Critical values and linear least squares

    I have a question about Linear least squares: In Linear least squares, For any critical point "x" it must follow the linear system: A(Transpose) * Ax = b * A(Transpose) where x is the critical point. But here x is an n vector, so does that mean there are as many critical points (x) as...
  43. S

    Linear Least Squares: Critical Points & Quadratic Polynomials

    I have a question about Linear least squares: In Linear least squares, For any critical point "x" it must follow the linear system: A(Transpose) * Ax = b * A(Transpose) where x is the critical point. But here x is an n vector, so does that mean there are as many critical points (x) as...
  44. C

    Proof using primes, divisibility, and sum of squares

    Homework Statement I have to prove or disprove the following: Part a) If p is prime and p | (a2 + b2) and p | (c2 + d2), then p | (a2 - c2) Part b) f p is prime and p | (a2 + b2) and p | (c2 + d2), then p | (a2 + c2) Homework Equations The Attempt at a Solution Part a)...
  45. J

    Probability - Sum of Squares of Rolls of a Die

    Homework Statement Roll a fair die n times. Let Sn denote the sum of squares of the rolls. Thus, Sn is the sum of Xi^2, where Xi represents one roll. What are the mean and variance of sqrt(n) * (Sn/n - u), where u is the mean of Yn/n Homework Equations The Attempt at a Solution No...
  46. H

    Find the least squares approximation

    Homework Statement Suppose a set of N data points {(xk,yk)}Nk=1 appears to satisfy the relationship for some constants a and b. Find the least squares approximations for a and b. Homework Equations The Attempt at a Solution I really have no idea about this problem.
  47. W

    Least Squares With Multiple Quadratic Constraints

    Problem: A = n by m matrix x = m by 1 vector y = n by 1 vector C = c by m matrix E = e by m matrix Alpha, gamma and theta are constants. norm(Ax-y) = min subject to: norm(Cx) = alpha norm(Ex) = gamma transpose(Cx)*Ex = (alpha^2)*(gamma^2)*cos(theta) I read a paper on how to do this with 1...
  48. L

    Linear Least Squares: Solving 3D Data Points in C++

    I have a simple problem. I have a set of 3D data points and I want to fit a line through them using linear least squares. I understand the basic approach required: set up two matrices such that Ax = b, then make it a square matrix A^t*Ax = A^t*b, then solve for x using a Cholesky decomposition...
  49. Z

    How Can MATLAB Solve Least Squares for Predicting Comet Distances?

    Homework Statement The distance traveled by a comet is described with the following equation: r = B + re cos (θ) B (Beta) and e are constants θ 0.88 1.10 1.42 1.77 2.14 2.91 3.85 r 8.27 5.49 3.53 2.50 1.95 1.52 5.21 These were some of the measurements, which can be written in...
  50. S

    Existence and Uniqueness of a Linear Least Squares Solution

    I'm studying for my numerical analysis final on tuesday, and I know this is going to be one of the problems, so any help is greatly appreciated. Homework Statement State and prove existence and uniqueness for the solution of the linear least squares problem. Homework Equations y \approx...
Back
Top