Squares Definition and 400 Threads

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



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{\displaystyle \square }
ABCD.

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  1. E

    Eviews 3 stage least squares near singular matrix

    I'm doing a replication paper and having a bit of issues. The author uses 2 instruments and has 4 endogenous variables. Since he is under-identified, he runs 4 separate regressions, so that each equation has 1 overidentifying restrictions. I want to extend this and run the four equations as a...
  2. I

    Optimizing H for Accurate Outlier Detection in Weighted Linear Least Squares

    I have the following problem: I have a set of m measurements $\mathbf{\phi}$ and I estimate a set of 3 variables $\mathbf{x}$ The estimated value for $\mathbf{\phi}$ depends linearly on $\mathbf{x}$ : Hx=\Tilde{\phi} The solution through weighted linear least squares is: $\mathbf{x}$ =...
  3. A

    How Can a Number Be Written as a Sum of Squares or Primes?

    Hi All, So I was just wondering if there is a formula for the number of ways a number can be written as a sum of squares?(Without including negatives, zero or repeats). For example 5=2^2+1^2. (There is only one way for 5). Second question along this line is: In how many ways can a number...
  4. T

    Geometry with circles, triangles and squares

    Homework Statement The diagram below shows four congruent circles whose centres are the vertices of the square DEFG and whose circumference touch the sides of an isosceles triangle. Area of triangle ABC is 10000 units square. What is the radius of the circles, to the nearest unit...
  5. S

    Finding the General Term for Perfect Squares

    a1=22+32+62 a2=32+42+122 a3=52+52+202 Using these, gIve a general term for an such that an is always a perfect square
  6. V

    Prove the sum of two even perfect squares is not a perfect square

    Homework Statement For all natural numbers, a and b, if a and b are both even, then (a^2+b^2) is not a perfect square. (prove this) Homework Equations The Attempt at a Solution I tried proving by contradiction and got (2s)^2 +(2t)^2 =k^2. which translates to 4s^2 +4t^2=k^2. I...
  7. T

    Factorials and Squares: Finding Solutions to a Unique Equation

    Homework Statement For some natural N the no of positive integers x satisfying the equation 1! + 2! + 3! + ... + x! = (N)2 is: A)one B)two C)infinite D)none The Attempt at a Solution I have no idea of how to start.. never came across such problems. By trial i have got two values...
  8. E

    Negative squares using the space time interval invariance

    Hallo I'm new to this (wonderful) forum, and to SR too... I've a general question about the space time interval invariance. Say we have two points A and B, at rest each other, at distance AB. Now A and B simultaneously in their reference frame emit a flash of light. The space time interval...
  9. S

    Sum of Squares: Get the Answers You Need

    noope
  10. J

    Algebra proof involving perfect squares

    The problem states, if c^2 = ab and (a,b) = 1, prove that a and b are perfect squares. ( the notation (a,b) means the GCD of a and b) So i have a lot of thoughts on this problem but i am getting stuck. 1) if c^2 = ab then c(c) = ab which says c divides ab. 2) the only real theorem...
  11. L

    Limits and difference of squares help

    Homework Statement find the limit as x tends to 3 of [sqrt(2x+3)-x] / (x-3) Homework Equations The Attempt at a Solution This is from an old Protter textbook I am working through. I started with the difference of squares which results in [2x + 3 - x^2]/ [(x-3)*sqrt(2x+3)+x]...
  12. S

    Linear algebra least squares solution

    Homework Statement Suppose you have a set S of three points in R^2, S1 = {(1, 12), (2, 15), (3, 16)} S2 = {(1, 12), (1, 15), (3, 16)} S3 = {(1, 12), (2, 15), (2, 15)} which you seek to interpolate with the quadratic polynomial p(t) = a_0 + a_1t + a_2t^2. Problem: Least-Squares...
  13. D

    How to know whether the least squares approximation exitsts.

    How would one know when to find the least squares approximation?
  14. M

    Nonsingularity of matrix of squares (help)

    Need help to prove (or disprove, hope not) this result: Let Q=[q_ij] be a orthogonal matrix (Q^T*Q=Identity) and let Q2 be the matrix of the squares of the entries of Q, that is Q2=[q^2_ij]. I need to prove that Q2 is nonsingular. Been trying with some results about the Hadamard or Schur...
  15. T

    Sum of squares equation problem

    Homework Statement Prove only solution in integers of the equation x2 + y 2 + z2 = 2xyz is x = y = z =0 2. The attempt at a solution Well, using common sense got the idea but don't exactly know how to prove it! Can anyone please help as how to start ...? Thanks!
  16. T

    How can I solve this Least Squares Regression problem?

    Homework Statement http://img683.imageshack.us/img683/4744/leastsquares.jpg [PLAIN][PLAIN]http://img149.imageshack.us/img149/4793/graphwd.jpg Homework Equations The Attempt at a Solution So would these be the points? (-41,51),(-22,62),(23,63),(44,24) I'm not too sure how...
  17. clope023

    Method of Least Squares question

    Homework Statement for vector space C[-1,1] with L^2 inner product <f,g> = \intf(x)g(x)dx find the best least squares approximation for function x^(1/3) on [-1,1] by a quadratic function q(x) = c0 + c1x + c2x^2 Homework Equations s+r = n <t^s, t^r> = \intt^ndt = { 2/(n+1)...
  18. Fredrik

    Software for drawing lines, squares, curves etc.

    I need something that I can use to draw a few simple 2D images, that don't have to look pretty. I really mean "draw" (with the mouse) and not generate from a formula, and a minimum requirement is that the program can at least let me try to draw a smooth curve with the mouse and then smooth it...
  19. K

    Product equality and sum of squares equality puzzle

    Substitute each of the capital letters by a different digit from 0 to 9 to satisfy this set of cryptarithmetic relationships. None of the numbers can contain any leading zero. ABCD*EF=GHJB*KE, and: (EH)2 + (KC)2 = (KH)2
  20. H

    Can you give me a least squares example?

    Can you give me a "least squares" example? Assume that, I have a function to estimate like below: f(x) = a3x3 + a2x2 + a1x1 + a0x0 After several experiments I have obtained these (x, f(x)) pairs: (x1, y1) (x2, y2) (x3, y3) (x4, y4) (x5, y5) (x6, y6) How can I estimate a0, a1, a2...
  21. K

    Prove the sum of squares of two odd integers can't be a perfect square

    Homework Statement x^2+y^2=z^2 Homework Equations The Attempt at a Solution assume to the contrary that two odd numbers squared can be perfect squares. Then, x=2j+1 y=2k+1 (2j+1)^2 +(2k+1)^2=z^2 4j^2 +4j+1+4k^2+4k+1 =4j^2+4k^2+4j+4k+2=z^2 =2[2(j^2+K^2+j+k)+1)]=2s the...
  22. S

    Multi-objective recursive least squares

    Is this possible? I've computed a multiobjective least squares solution and want to make it able to be updated recursively but I get stuck at applying the woodbury matrix identity since it's no longer a rank 1 udpate. Are there any derivations of this anywhere or is this not possible? Thanks
  23. T

    Prove 3-Square Prime Sum Equals One of Primes = 3

    Homework Statement Prove that if a prime number is a sum of three squares of different primes, then one of the primes must be equal to 3. Homework Equations The Attempt at a Solution I really have no idea where to start this one.
  24. M

    Prove two squares and a cube equal an integer

    Homework Statement Disprove or prove the statement that every positive integer is the sum of at most two squares and a cube of non-negative integers.2. The attempt at a solution I'll call the numbers that can be squares a and b. C will be the cube. The easiest way to disprove something is to...
  25. D

    Can this be done in a simplier way? Magic Squares

    Proving Axiom 1 of all 3 x 3 magic squares. I used summation notation to do so but it is extremely long and cumbersome. I attached the pdf file with the work. Is there a way to do this in a simpler more concise manner?
  26. D

    Exploring the Generalization of 3 x 3 Magic Squares: A Mathematical Puzzle

    How would I generalized the set of all 3 x 3 magic squares? I don't know what to do this at all for this.
  27. M

    3D Least Squares Fit and some Linear Algebra

    Hello, I am trying to write an algorithm to calculate the Least Squares Fit Line of a 3D data set. After doing some research and using Google, I came across this document, http://www.udel.edu/HNES/HESC427/Sphere%20Fitting/LeastSquares.pdf (section 2 in page 8) that explains the algorithm for...
  28. M

    MATLAB Calculating 3D Least Squares Fit with SVD in MATLAB

    Hello, I am trying to write an algorithm to calculate the Least Squares Fit Line of a 3D data set. After doing some research and using Google, I came across this document, http://www.udel.edu/HNES/HESC427/Sphere%20Fitting/LeastSquares.pdf (section 2 in page 8) that explains the algorithm for...
  29. N

    What is the best estimate for B in Least Squares Fitting?

    1. Homework Statement Suppose two variables x and y are known to satisfy a relation y=Bx. That is a graph of x vs. y is a line through the origin. Suppose further that you have N measurements (xi,yi)and that the uncertainties in x are negligible and those in y are equal. Prove the best...
  30. N

    Determine g from least squares fit line?

    I did a least squares fit project for physics and now i have to say the value of G and the slope. I know that slope is m from the equation y = mx+b but how do i determine G?
  31. S

    [Remember Your Squares] Something I Found

    Let x = 1. Let n = Next Odd Number Let y = Previous Sum x2 = x +3 = 4 = (1+x)2 +5 = 9 = (3+x)2 +n = n+y = (n-2 + x)2 You could make a program to list all the squares without invoking the multiplication function or squaring function using a simple loop. C++ Example: #include...
  32. M

    Method of Weighted Residuals - Least Squares

    I am having a problem applying the Least Squares method in the case where I have 2 fundamental solutions and therefore 2 unknown wieghts to find. I=\int_{\Gamma} |\varphi + 1/2|^2 \mathrm{d}s}_{1} + \underbrace{\int_{\Gamma_{in}} |\varphi + 1/4|^2 \mathrm{d}s (im not sure if this...
  33. T

    What happens to the inequality sign when taking the square of an equation?

    Alright let's just say (x-2)^2>12, find x can someone tell me what happens to the inequality sign when you take the square of the left hand side to the right hands side? does it swap?
  34. N

    Least squares fit to a straight line?

    I was wondering if someone could explain how to compute the Least squares fit to a straight line
  35. N

    Least squares fit to a straight line?

    I was wondering if someone could explain how to compute the Least squares fit to a straight line
  36. K

    Sum of Four Squares and Digits Puzzle

    Substitute each of the small letters by a different base ten digit from 1 to 9, with a<= b<=c<=d, to satisfy this equation. a2 + b2 + c2 + d2 = e2
  37. M

    How to Convert Least Squares Problems into Independent Equations

    I think that this is best suited here as it is linear algebra specific... sorry if I'm wrong. Please look at: I can do parts a,b and c. But I can't do part d. I've been trying to turn it into n independent least squares equations. Let me know if this is not the way to go or you have...
  38. J

    Least Squares Approx. for Life Expectancy

    This test question is really boggling me and my math group. Any help would be appreciated. We know that AT*x=AT*b is the setup, but we're not so sure how to approach the problem most effectively. Here's the question: Use the data below to find an approximate formula for the life expectancy in...
  39. R

    Least Squares Fit for h(x)=ae^x+be^(-x) Homework

    Homework Statement For the following data, find the least squares fit of the given form x=1,2,3,4,6 y=14,10,8,6,5 h(x)=ae^x+be^(-x) Homework Equations The Attempt at a Solution So I tried to linearize the equation by taking the natural log of everything...
  40. icystrike

    Sum of reciprocal of squares <Logic>

    Homework Statement https://www.physicsforums.com/attachment.php?attachmentid=21977&stc=1&d=1258886072 I think my proof is lousy and may be wrong. Please help me with it (= Thanks in advance Homework Equations My proof is of below. The Attempt at a Solution
  41. C

    Prove 2/5 perfect squares must be even to have their sum equal odd

    Homework Statement given the equality a2+b2+c2+d2+e2=f2 prove 2 out of the the 6 variables must be even.Homework Equations can use quadratic residues and primitive roots if it helps but don't think i need them. The Attempt at a Solution assume f is even. then f2 is even. and not all 5 numbers...
  42. J

    Can Dyadic Squares Approximate the Area of a Unit Disc with Minimal Overlap?

    Homework Statement Given \epsilon > 0 , show that the unit disc contains finitely many dyadic squares whose total area exceeds \pi - \epsilon , and which intersect each other only along their boundaries. Homework Equations The Attempt at a Solution I've tried to solve this...
  43. P

    Comp Sci Maximizing Rectangle Surface Area with Fortran Squares

    Homework Statement Hi, I have to do a project in Fortran based on solving a system. My professor mentioned one idea to me, I am trying to see if this idea is even feasible and some potential ways to progress through it before I submit a project proposal to do it. The problem is based on...
  44. H

    Understanding Dirac Delta Squares: Clarifying Doubts

    hi, may someone help me to clarify my doubts... in my work, i encounter diracdelta square \delta(x-x_1)\delta(x-x_2) i am not sure what it means... it seems if i integrate it \int dx \;\delta(x-x_1)\delta(x-x_2) = \delta(x_1-x_2) is either zero of infinity. is this correct? thanks
  45. S

    Max Squares Fitting in a Circle: Proof & Formulas

    Hi, Given that the radius of a circle is X, and the side length of a square is Y, what is the maximum number of squares you can fill inside this circle, provided that the squares do not overlap? If you know of a general formula or something, can you please tell me the proof or give me a link...
  46. mnb96

    Plane Fitting with Linear Least Squares

    Hello, I am trying to figure out how to fit a plane passing through the origin in \mathbf{R}^3, given a cloud of N points. The points are vectors of the form (x_1^{(k)}, x_2^{(k)}, x_3^{(k)}) , where k stands for the k-th point. I want to minimize the sum of squared distances point-plane. What...
  47. P

    When and how do you use perfect squares on integrals?

    So when using a perfect square I would divide the linear middle term by 2 and put the x in squared ( ) along with that term?
  48. A

    Pretty easy question about squares of square roots

    If you know \sqrt{(a^2+b^2)} < \epsilon, do you know a < \epsilon and b < \epsilon? If so, how?
  49. U

    Exploring the Difference of Two Squares: A Scientific Analysis

    Homework Statement 1) Find all pairs of natural numbers whose squares differ by 75. 2) Find all pairs of natural numbers whose squares differ by 79. 3) Prove that there can only be 1 pair of numbers with a prime number differenceHomework Equations none The Attempt at a Solution from...
  50. M

    Least squares solution to simultaneous equations

    I am trying to fit a transformation from one set of coordiantes to another. x' = R + Px + Qy y' = S - Qx + Py Where P,Q,R,S are constants, P = scale*cos(rotation). Q=scale*sin(rotation) There is a well known 'by hand' formula for fitting P,Q,R,S to a set of corresponding points. But I...
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