1. C

    Euclidean Geometry

    if AB < CD, prove that 2AB < 2CD
  2. N

    Euclidean Circle Geometry

    I need to calculate the angles A1, O1 and B2. In the diagram I understand that DEF is a tangent to the circle that goes through A, B, C and E. O is the centre. BC=CE, AEC = 105, CEF = 40.
  3. N

    Euclidean Circle Geometry

    In the diagram below, XY is a chord of the circle that goes through X, Y and Z. WZ is a tangent to the circle. XZ = YZ XZW = x-30 degrees XZY = 4x I want to calculate the value of x in order to move on to the next steps. Any advice or tips on where to start?
  4. N

    Euclidean Circle Geometry. Calculating the Radius

    In the diagram below, DE is a chord of the circle that goes through c,d and e. A is the center of the circle. The perpendicular line from centre A intersects DE at B and the circle at C, DE=100cm BC= 10cm AB=X I need to calculate the length of AB / x. Basically i need to calculate the...
  5. N

    HELP! Euclidean Geometry

    Hi everyone! I am struggling with circle geometry and am doing a practice test but can't seem to find the memo. I am stuck on two questions hoping you guys can help? The first question says: In the diagram below, DEF is a tangent to the circle that goes through A<B<C and E. O is the centre of...
  6. Z

    Gradient of a Euclidean function

    Folks - I know this is too basic but I really need your help. I haven't mastered the properties of Matrix Differentiation. Haven't had any Matrix Calculus in college. Please share your knowledge. Thanks! Please help explain the solution, if possibly, in a clear and detailed way Seems like...
  7. Z

    Euclidean Geometric Proof regarding Triangles

    Hello, This is related to altitudes, medians and bisectors in a triangle: I'm struggling to solve this proof - In triangle ABC where AB is not equal to AC, and AH, AD, AM are the altitude, bisector, and median, respectively, prove that point D will always fall between H and M. I've set...
  8. M

    Euclidean Minimum spanning tree and an extra edge

    Consider n points randomly distributed in space. The goal is to find the graph that has the smallest Euclidean length that connects these points. The answer is clearly the minimum spanning tree G_0 which has n-1 edges. Now suppose we are required to use exactly n edges and find the smallest...
  9. H

    Euclidean algorithm: the number gets smaller with complexity log(k)

    Hi there Given the exercise Let 1 \le d \in \mathbb{N} , k=f*d+h , h<f. Firstly show that the variable h has (with respect to basis 2) less digits than k. Then conclude that the euclidean algorithm is (ends) in polynomial time in log_2(k). I don't find a meaningful beginning. I can write...
  10. E

    Linear independence question Euclidean 3-space

    Getting quite confused with how to solve this one, I have 3 vectors v1 (1,1,1) , v2 (1, m , 1) and v3 (1, 1, n) I'm asked to find m and n that makes v1 - v3 linearly independent - any help would be appreciated I want to know if I was on the right track - I was thinking that (putting a value...
  11. R

    Euclidean Geometry Question

    Hi! I attach a file here with a question and suggested solution. All is fine, except I would like to know how there is a sign change on |BE|^2 from the first line to the second line. Thanks in advance for your help. Josh
  12. Educated

    Euclidean algorithm, integer solutions

    So the first thing to do is find the greatest common divisor of the 2 numbers using the Euclidean Algorithm, (I'm going to use the numbers 327, 33 and 18) We have the equation: 33x + 18y = 327 33 = 1 * 18 + 15 18 = 1 * 15 + 3 15 = 5 * 3 + 0 And so the GCD is 3. Using the extended Euclidean...
  13. Z

    Division Algorithm or Euclidean Algorithm

    Hello, i am confused on division algorithm, can anyone give me an understandable example so far for euclidean i have 1188=385(3)+33 385=33(3)+22 33=22(3)+11 22=11(2)+0 and the answer is 11, does this apply to division too? cause i am somewhat dividing numbers.....
  14. M

    Euclidean GCD Algorithm (Proof)

    I'd like to have a formal proof of the following case (case 2) related to the euclidean GCD algorithm: We have M > N, and N > M/2, I'd like to show that M - N > M / 2. Thank you!
  15. S

    Question in Euclidean geometry(Please help)

    Proved that
  16. S

    Euclidean Algorithm, more than two variables

    Hi all, Ok, so im more than comfortable with the Euclidean Algorithm when I have only two numbers so it is of the form an + bm = r But now i have the equation 225a + 360b + 432c + 480d = 3, and i need to find the integers a,b,c and d to satisfy this. So i know the gcd is 3, and I realise how...
  17. O

    Euclidean Algorithm and the Linear Equation Theorem Help

    I am sure this is going to sound trivial to most of you once you figure out what I am asking. Ok, so I am writing a post about the Euclidean algorithm and the linear equation theorem. I wrote out all the steps for the Euclidean algorithm, the steps for the linear equation theorem, and tried to...
  18. S

    For what NEGATIVE values of d is Z[sqrt[d]] a Euclidean domain?

    I was asked to prove that the ring Z[sqrt[d]] is not euclidean for any d <= -3. (Note - The resulting ring it not contained in R!) I proved it for certain d's easily (For example d=-3), by showing that it is not a UFD, but am not sure how to prove it in the more general case. (Or whether...
  19. J

    Euclidean metric vs Taxicab metric?

    Does it matter which metric we use on R^2? Does it change how sequences converge?
  20. fkf

    Transformation in Euclidean vector space.

    Consider the Euclidean vector space R^2 with the basis B = {(2 \quad 0),(1 \quad 1)} and the linear transformation T:x \rightarrow Ax, where A = [1 2 ; 0 1] Find the B-matrix of T, that is find [T]_B I thought that I was just going to find the transform matrix from B to A, but that doesn't...