# euclidean

1. ### Euclidean Geometry

if AB < CD, prove that 2AB < 2CD
2. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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!

Proved that
16. ### 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. ### 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. ### 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. ### Euclidean metric vs Taxicab metric?

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