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



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{\displaystyle \square }
ABCD.

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  1. K

    Squares, subsquares and arrangement puzzle

    Substitute each of the capital letters in this 3x3 square by a different digit from 1 to 9 such that the sum of digits in each of the four 2x2 subsquares is equal to 6*E. A B C D E F G H I What will be the arrangement(s), if keeping all the other conditions unaltered, the...
  2. R

    Error propagation in least squares

    I am doing a calculation involving taking three or more temperature measurements and then plotting them against another quantity (dependent). I get a relationship that is pretty linear, so I take the line of best fit to obtain an equation with a slope and an intercept. Now, my question is...
  3. P

    Conditional expectation and Least Squares Regression

    Hello everybody, I have two questions on conditional expectation w.r.t (Polynomial) OLS: Let X_t be a random variable and F_t the associated filtration, Vect_n{X_t} the vector space spanned by the polynomials of order {i, i<=n }, f(.) one function with enough regularity. I am wondering how...
  4. A

    How Many Squares Fit in 1000.25mm Square? Ask Aaardvark!

    Hi, does anyone know how many squares of side 1 millimeter can fit in a big square of side 1000.25 millimeters ? Cheers, Aaardvark.
  5. C

    Ax + b Least Squares Minimization Standard Form

    All - Given a set of data {(xi, yi)| i = 1,2,...,m} and the regression equation f(x) = ax + b, I want to use the simplex method to minimize the equation Sigma [(yi - f(xi))/f(xi)]^2. However, I am stuck on how to initially organize the problem. I am not sure whether the equation, Sigma [(yi -...
  6. D

    Solving the Overlapping Squares Puzzle

    I'm kind of lost on this one. Could someone please help me. Two equally big squares with the sides 12 cm partly covers each other as the figure shows. One of the squares corner is in the other squares center. Decide the area of the shadowed part...
  7. E

    So the obvious guess is 1999 or 2006.

    Homework Statement Find A: A2 = (4/5)(18292 + 12982) in about 3min, because this comes at the end of a rather difficult geometry problem with 6 min for the entire question. (edit: Yes, calculators weren't allowed because it was a competition. I have verified that everyone comes to this step...
  8. B

    Simple least squares regression problem. Am I doing anything wrongly?

    Least squares regression of Y on A-D based on sample size of 506. Reported results with standard errors are: Y = 11.08 - 0.954*A - 0.134*B + 0.255*C - 0.052*D s.errs (0.32) (0.117) (0.043) (0.019) (0.006) R^2 = 0.581 problem A. Test null that coefficient on D is equal to 0 d =...
  9. B

    Simple least squares regression problem. Am I doing anything wrongly?

    Least squares regression of Y on A-D based on sample size of 506 Y = 11.08 - 0.954*A - 0.134*B + 0.255*C - 0.052*D s.errs (0.32) (0.117) (0.043) (0.019) (0.006) R^2 = 0.581 problem A. Test null that coefficient on D is equal to 0 d = coefficient on D null: D ~ N(0, 0.006) Pr(d...
  10. B

    Simple least squares regression problem. Am I doing anything wrongly?

    Least squares regression of Y on A-D based on sample size of 506 Y = 11.08 - 0.954*A - 0.134*B + 0.255*C - 0.052*D s.errs (0.32) (0.117) (0.043) (0.019) (0.006) R^2 = 0.581 problem A. Test null that coefficient on D is equal to 0 d = coefficient on D null: D ~ N(0...
  11. J

    Proof of least Squares estimators

    Hey guys, long time lurker, first time poster! Just having some trouble with something..Im probably just looking at it the wrong way, but I was wondering if anyone could help me with this.. Im trying to prove that by choosing b0 and b1 to minimize...
  12. N

    Exploring the Relationship Between Telescoping Sums and Squares

    the proof in my text starts with what's called a telescoping sum (1+i^3)-i^3 what is the relevence of this to i^2
  13. C

    Find Phase Shift & # Squares to Move Trig Graphs

    Hi i was just wondering if someone could tell me how one can find the phase shift and the number of squares to move the graph over by from an equation?. We are doing cosine and sine graphs and my teacher has been away for a few days so the supply teachers haven't been really that great in...
  14. S

    Least Squares Regression Analysis - No Idea

    Hello, I am a first year undergraduate university student majoring in Engineering and Computing Sc. One of my courses is Linear Algebra. We have been given an assignment in which question no. 2 is out of syllabus. It is on Least Squares Regression Analysis. This has not been taught to us. We...
  15. S

    Unable to find the nonlinear least squares

    Homework Statement We have the following x, y values x ||| y 1.0 -0.15 1.5 0.24 2.0 0.68 2.5 1.04 3.0 1.21 3.5 1.15 4.0 0.86 4.5 0.41 5.0 -0.08 How can you find the equation y(x) = ax^2 + bx + c by least squares? The Attempt at a Solution I know how to...
  16. D

    Prove Least Squares Equation Has Solution

    Homework Statement In the least squares method the vector x* that is the best approximation to b statisfies the Least squares equation: A^T A x^*= A^T b Prove that there's always a solution to this equation. Homework Equations - The Attempt at a Solution I distinct 2...
  17. K

    Getting perfect squares with four cryptarithmetic numerals

    Each of CEM, NOVE, UM and ZERO is a decimal perfect square. Each letter represents a different decimal digit from 0 to 9, but the same letter always denotes the same digit. None of the four numbers can contain any leading 0. What numbers do CEM, NOVE, UM and ZERO represent?
  18. D

    Proving Perfect Squares: A Study in Number Theory

    Homework Statement If C^2 = ab and the greatest common divisor of a and b is equal to 1, prove that a and b are perfect squares Homework Equations I know that if (a,b)=1, then there exists integers u and v where 1=au+bv (even though i don't think this is necessary in this proof)...
  19. C

    Is This a Sufficient Proof for Perfect Squares with Even Exponents?

    n=p1r1...pkrk In order for p to be a perfect square, r must be even. Therefore n=p12h1...pk2hk taking the square root of both sides I'm just left with n=p1h1...pkhk Does this work as a proof that n is a perfect square if r is even? It's a homework problem and I'm not sure if this...
  20. S

    NEED understanding, binomial squares

    Homework Statement x^2 = 2/11x + 99/121 Homework Equations The Attempt at a Solution x^2 = 2/11 x + 99/121 x^2 - 2/11x - 99/121 = 0 x^2 - 2/11x =99/121 I understand that (b/2)^2 must be added to each side to become a perfect square trinomial...But HOW I do it...
  21. K

    Decimal and nondecimal almost perfect squares of the form aaabbb

    Determine all possible positive decimal integer(s) of the form aaabbb, each with no leading zeroes, that becomes a perfect square when 1 is added to it. What are the positive nondecimal integer base(s) S, with S<=16, such that S admits at least one valid solution in conformity with the given...
  22. D

    Conic Sections: Graphing with Multiple Squares

    Homework Statement graph the following Homework Equations 9x^2+4y^2+36x-8y+4=0 The Attempt at a Solution I think I need to get it into \frac{(x-x0)^2}{a^2}+\frac{(y-y0)^2}{b^2} but I'm not sure. I have \frac{9x^2}{-4}-8x+y^2-2y=1 and now I'm stuck
  23. N

    Let (a,b)=1 and ab=c^2. Show that a and b are perfect squares.

    hi all I need some help with this question Let (a,b)=1 and ab=c^2. Show that a and b are perfect squares. Thank you
  24. K

    Sum the squares cryptarithmetically, get square

    Substitute each of the letters by a different decimal digit from 0 to 9 to satisfy this cryptarithmetic equation: (PQR)2 + (STUQ)2 = (SVWX)2 Note: None of P and S can be zero.
  25. K

    Solving 3x3 Magic Squares: 4/6-Folder Reflection & Found

    3x3 magic squares * updated http://en.wikipedia.org/wiki/Magic_square#Types_of_magic_squares_and_their_construction given a 3x3 block with 3 numbers inserted e.g. |2|_|_| |_|_|6| |_|3|_| How would I solve this magic square? Is there a pattern for this? The method in wikipedia...
  26. P

    Modular Congruences of Integer Squares

    prove that for any integer n, n^{2} \cong 0 or 1 (mod 3), and n^{2} \cong 0,1,4(mod 5)
  27. J

    Deriving The Quad. Eq. Using least squares.

    Could someone show me exactly how to derive the quadratic equation from the least squares method? I have no idea where to start. I will appreciate it very much. Thankyou.
  28. A

    Linear least squares, condition number

    Hi, I am trying to learn some numerical algebra. Now I don't understand the following. I'm finding the solution to the Linear Least Squares problem min||A\lambda-y||_{2}, which turns out to be (1,1). I did this by doing a QR factorization using Givens rotations. with: A= \[...
  29. S

    Does least squares regularization have to be iterative?

    Does a http://en.wikipedia.org/wiki/Tikhonov_regularization" solution for least squares have to be iteratively solved? Or is there a way to perform regularization via linear algebra, the way linear regression can be done by solving the (XTX)B=XTy normal equations?
  30. S

    C/C++ Least Squares source code in C++?

    Does anyone know where to find source code for a simple and fast least squares solver written purely in C++?
  31. C

    Tiling squares on the plane, methods

    Hm, is this the right place to ask this? It's kind of a topology question, I guess. Let's say I've got a square. It's got four sides. ______ | 1 | |2 3| | 4 | ------ And I want to tile this over and over on the plane. ________________________ | 1 | 1 | 1 | 1 | |2 3|2 3|2...
  32. R

    Proving the Unsolvable: Lagrange's Theorem and 4 Squares

    Hi everybody :smile: I'm currently reading Burton's Elementary Number Theory (almost done!) and in the chapter about Lagrange's Theorem about the sum of four squares, there is a supposedly easy question which I can't solve for some reason :blushing:. I'd really appreciate a hint or two...
  33. C

    Nonlinear least squares problem

    Dear all, Apologies if this is in the wrong forum. I have a bit Nonlinear least squares fit problem. I have a pair of parametric equations (see attached, fairly nasty :frown: ). in it, a b c x0 y0 z0 are all constant, and they are the values I want to determine from a nonlinear least...
  34. E

    Finding Remainder of Shaded Squares in 6x4 Grid

    Homework Statement In a 6 x 4 grid (6 rows, 4 columns), 12 of the 24 squares are to be shaded so that there are two shaded squares in each row and three shaded squares in each column. Let be the number of shadings with this property. Find the remainder when is divided by 1000. There is a...
  35. K

    Relatively Prime & Perfect Squares

    1) Suppose that a and b are relatively prime natural numbers such that ab is a perfect square (i.e. is the square of a natural number). Show that a and b are each perfect squares. a=(a1^p1)(a2^p2)(a3^p3)...(a_n^p_n), a_i distinct primes b=(b1^q1)(b2^q2)(b3^q3)... (b_m^q_m), b_j distinct...
  36. C

    Biology Genetics problems- punnett squares

    I need help with these: 1. Charles was married once before, & he and his first wife had a child who suffers from cystic fibrosis. His current wife Elaine's brother died of cystic fibrosis. What is the probability that Charles & Elaine will have a baby with cystic fibrosis? Let's say A=...
  37. L

    Why Do We Square Errors in Least Squares Regression?

    You must have used it couple of times while solving an engineering problem. For example in line fitting, why do we have to square? Can't we just pass the line thru the max number of points. Can someone explain. Thanks in advance.
  38. D

    Curve fitting and least squares method.

    Homework Statement I have an equation as a function of time. (eq1) C(t) = Css + a(e^.5t) + b(e^.9t) t>0 Where, Css is a constant. then I have 6 data points of time and C (Concentration of a liquid) 1. I have to find an equation to find the maximum time and contains a, b and Css...
  39. S

    Artin's Conjecture on Primitive Roots: Perfect Squares

    If a is a perfect square then a is not a primitive root modulo p (p is an odd prime). (from Artin's conjecture on primitive roots) http://en.wikipedia.org/wiki/Artin%27s_conjecture_on_primitive_roots This is what I know: suppose a = b^2 a is a primitive root mod p when , a^(p-1) congruent to 1...
  40. R

    Infinite sum of squares converges

    Homework Statement So, L2 is defined to be the set of all infinite sequences of real numbers, s.t. the sum of their squares converges: L2 = {x=(x1,...,xn,...) | \Sigmaxi < \infty} we have d(x,y) = \sqrt{\Sigma (xi-yi)^2} I need to show that this is a metric, starting by showing that if...
  41. X

    Can linear least squares be used for inverse function approximation?

    Hi, Forgive me if the subject of this post is not accurate, I'm not quite sure what the correct terminology would be for what I'm trying to figure out. Currently I am using linear least squares via SVD to find the coefficients of a ten term polynomial, say f. This model allows me to...
  42. M

    Proving that (2^n) - 1 is Not Prime for Perfect Squares

    Prove that if n is a perfect square, then (2^n) -1 is not prime. All I can get is that 2^n is some even number. I can't work in the perfect square part.
  43. M

    Condition for finite series: sum of squares finite + ?

    Let u_n be a sequence of positive real number. If \sum_{n=1}^{\infty}u_n^{2} finite + (condition??) then \sum_{n=1}^{\infty}u_n finite. I want to find the condition.Please help me.
  44. rocomath

    Discovering Patterns in the Difference of Squares Equation

    I'm looking for patterns and if you can add to things I noticed before working it out, that would be good :-] 1. (a+b+c)(a+b-c)=a^2+b^2+c^2+2ab I noticed that b+c and b-c compensated for each other. 2. (a+b+c)(a-b-c)=a^2-b^2-c^2-2bc a+b and a-b compensated for each other and the fact that...
  45. R

    Prove Convergence of Positive Series Squares

    Homework Statement The infinite series defined by \Sigma a_{n}, with a_{n}>0 are convergent. If then the series defined by \Sigma a_{n}^{2} coverges, prove it! Homework Equations The relevant equations has been stated above. The Attempt at a Solution Since every term in the first...
  46. E

    Prove: No Prime 3+4n is Sum of 2 Squares

    Homework Statement Prove that no prime three more than a multiple of four is a sum of two squares. (Hint: Work modulo 4.) Homework Equations The Attempt at a Solution a^2+b^2=4n+3=3 mod 4 is impossible if you look at the possibilities of a^2 and b^2. I did not use the fact...
  47. M

    Which Averages Determine the Linear Least Squares Fit in Physics Experiments?

    I am currently working on a lab report for my physics class. During the lab, we used air tracks, gliders, and a photogate to measure the value of 'g'. Basically, we would raise one end of the air track to a certain height and let the glider slide down the frictionless track and the timer would...
  48. S

    Reimann Integration, squares and cubes of functions

    I took a short break from the rudin-crunching. I'm now doing reimann's integral. Anyhow here's a question I've having trouble with. Does f^2 is integrable imply that f is integrable? -No, take f=1 on rationals, f=-1 on irrationals on [0,1]. Does the integrability of f^3 imply that f...
  49. L

    Solve Squares & Numbers Homework: Diff > 5

    Homework Statement A square is divided into 81 smaller squares by lines parallel to its sides. The numbers 1, 2, ..., 81 are entered in an arbitrary fashion, one in each square. Show that, however the numbers are entered, it is possible to find two small squares with an edge in common whose...
  50. G

    Normal assumption with least squares regression

    My google search just turns up results telling me that one of the assumptions I have to make is that each Y is normal. My question is why do I have to assume its normal. Why does it follow that it has to be normal as opposed to some other distribution? Hope that makes sense. Edit: I thought...
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