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Prove that while the hyperbolic distance between two points zi-i and z2-ie in the upper half-plan...
Recall that the upper half plane H ((x, y)ly > 0) gives a "model" for hyperbolic space. In this m...
Recall that the upper half plane H ((x, y)ly > 0) gives a "model" for hyperbolic space. In this model, distance decreases as one moves up (i.e. the distance between (0, 1) and (1, 1) is 1, the distance between (0,2) and (1,2) is 1/2, and the distance between (0, y) and (1, y) is 1/y. Draw a picture to see that this is strange.) The geodesics on H are given by (1) half circles with center somewhere on the...
5. Prove that f(z) = (2+1/2) is a conformal map from the half-disc {z = x...
5. Prove that f(z) = (2+1/2) is a conformal map from the half-disc {z = x +iy : 2< 1, y >0} to the upper half-plane. (Hint: The equation f(z) = w reduces to the quadratic equation z2 + 2wz +1 = 0, which has two distinct roots in C whenever w # £1. This is certainly the case if WE H.
Let S denote the sphere x2 y2 2 = 1. Given two points P(1,0,0), (a) Find the distance between P and Q. Lets call this E...
Let S denote the sphere x2 y2 2 = 1. Given two points P(1,0,0), (a) Find the distance between P and Q. Lets call this Euclidean distance. (b) Find the plane that goes through O, P, Q. What is the intersection of this plane with the sphere? (Hint: use OP × OQ as the the normal vector) (c) Observe that the length of the arc PQ is 0 the angle between OP,0Q in radians. (Hint: You know how to find...
Problem 2. (18 points) (a) Find a fractional linear transformation that maps the right half-plane to...
Problem 2. (18 points) (a) Find a fractional linear transformation that maps the right half-plane to the unit disk such that the origin is mapped to -1. (b) A fixed point of a transformation T is one where T(2) = 2. Let T be a fractional linear transformation. Assume T is not the identity map. Show T has a most two fixed points. (c) Let S be a circle and 21 a point not on the circle. Show that there...
(3 points) Two superconducting and frictionless rails a distance I apart are connected by a super...
(3 points) Two superconducting and frictionless rails a distance I apart are connected by a superconducting wire, as shown in Figure 7. A platform of mass m connects the two rails Page 2 and can slide without friction along the rails. The platform has a resistance R between the points where it makes contact with the rails. The rails are infinitely long and a uniform magnetic field is perpendicular to the plane of the rails and the platform at all...
can you just use the formula to explain it (ie. use dA (as the distance between...
can
you just use the formula to explain it (ie. use dA (as the distance
between V2 and V3), etc.)
Find the magnitude E of the electric field vector È for a point A between the V 2 volts and V 3 volts equipotential lines. Repeat for a point B between the V 3 volts and V- 4 volts equipotential lines. Repeat for a point C between the V 4 volts and V 5 volts equipotential lines. Repeat for a...
I he following formula gives the distance between two points (x1, yl) and (02, y2) in...
I he following formula gives the distance between two points (x1, yl) and (02, y2) in the Cartesian plane The main0 function is provided. You should implement the following functions: sqrt [ (x2-x1), (y2-yl) 1. Fi ndRadius... ): This function takes as its parameter four numbers that represent the center and a point on the circle, finds and returns the circle's radius. 2 CircleCalculations(....: This function takes as its parameter a number that represents the radius of the circle and...
Problem 1: 20 Points Two infinite planes of insulating material are arranged like a capacitor, wi...
Relations and equations that you may need:
Problem 1: 20 Points Two infinite planes of insulating material are arranged like a capacitor, with equal and opposite charge densities on them (pR+po and pLP. They are each have a thickness h and are separated by a distance D. Take XY to be the coordinates the planes are infinite in, and Z to be the direction of separation between the planes. a) Prove (any way you like) that A's ti for one...
Q1. Consider these four points: P [,,5| , P2 = 2], P3 = [H]. Plot these...
Q1. Consider these four points: P [,,5| , P2 = 2], P3 = [H]. Plot these three points. (a) Find the Manhattan distance between Pi and P2 (b) Find the Manhattan distance between P1 and P3. (e) Find the Manhattan distance between P2 and P3. Q2. Consider the same points in Q1 and find the Euclidean distances between the points specified in parts (a), (b), and (e). In other words, you will be doing the above question again but now...
I need to create the "nnclassifier using the euclidean distance formula to find nearest neighbor. I...
I need to create the "nnclassifier using the euclidean distance formula to find nearest neighbor. I am using the inis dataset from seabom. I have loaded the data and split the database into values and species. I have created a function to find the nearest neighbor by also calculating the euclidean distance and appending them to a distance list. I am able to see the positions of the nearest neighbors. Smart numpy as Import pandas as pd Import seaborn as...
Recall that the upper half plane H ((x, y)ly > 0) gives a "model" for hyperbolic space. In this model, distance decreases as one moves up (i.e. the distance between (0, 1) and (1, 1) is 1, the distance between (0,2) and (1,2) is 1/2, and the distance between (0, y) and (1, y) is 1/y. Draw a picture to see that this is strange.) The geodesics on H are given by (1) half circles with center somewhere on the...
5. Prove that f(z) = (2+1/2) is a conformal map from the half-disc {z = x +iy : 2< 1, y >0} to the upper half-plane. (Hint: The equation f(z) = w reduces to the quadratic equation z2 + 2wz +1 = 0, which has two distinct roots in C whenever w # £1. This is certainly the case if WE H.
Let S denote the sphere x2 y2 2 = 1. Given two points P(1,0,0), (a) Find the distance between P and Q. Lets call this Euclidean distance. (b) Find the plane that goes through O, P, Q. What is the intersection of this plane with the sphere? (Hint: use OP × OQ as the the normal vector) (c) Observe that the length of the arc PQ is 0 the angle between OP,0Q in radians. (Hint: You know how to find...
Problem 2. (18 points) (a) Find a fractional linear transformation that maps the right half-plane to the unit disk such that the origin is mapped to -1. (b) A fixed point of a transformation T is one where T(2) = 2. Let T be a fractional linear transformation. Assume T is not the identity map. Show T has a most two fixed points. (c) Let S be a circle and 21 a point not on the circle. Show that there...
(3 points) Two superconducting and frictionless rails a distance I apart are connected by a superconducting wire, as shown in Figure 7. A platform of mass m connects the two rails Page 2 and can slide without friction along the rails. The platform has a resistance R between the points where it makes contact with the rails. The rails are infinitely long and a uniform magnetic field is perpendicular to the plane of the rails and the platform at all...
can
you just use the formula to explain it (ie. use dA (as the distance
between V2 and V3), etc.)
Find the magnitude E of the electric field vector È for a point A between the V 2 volts and V 3 volts equipotential lines. Repeat for a point B between the V 3 volts and V- 4 volts equipotential lines. Repeat for a point C between the V 4 volts and V 5 volts equipotential lines. Repeat for a...
I he following formula gives the distance between two points (x1, yl) and (02, y2) in the Cartesian plane The main0 function is provided. You should implement the following functions: sqrt [ (x2-x1), (y2-yl) 1. Fi ndRadius... ): This function takes as its parameter four numbers that represent the center and a point on the circle, finds and returns the circle's radius. 2 CircleCalculations(....: This function takes as its parameter a number that represents the radius of the circle and...
Relations and equations that you may need:
Problem 1: 20 Points Two infinite planes of insulating material are arranged like a capacitor, with equal and opposite charge densities on them (pR+po and pLP. They are each have a thickness h and are separated by a distance D. Take XY to be the coordinates the planes are infinite in, and Z to be the direction of separation between the planes. a) Prove (any way you like) that A's ti for one...
Q1. Consider these four points: P [,,5| , P2 = 2], P3 = [H]. Plot these three points. (a) Find the Manhattan distance between Pi and P2 (b) Find the Manhattan distance between P1 and P3. (e) Find the Manhattan distance between P2 and P3. Q2. Consider the same points in Q1 and find the Euclidean distances between the points specified in parts (a), (b), and (e). In other words, you will be doing the above question again but now...
I need to create the "nnclassifier using the euclidean distance formula to find nearest neighbor. I am using the inis dataset from seabom. I have loaded the data and split the database into values and species. I have created a function to find the nearest neighbor by also calculating the euclidean distance and appending them to a distance list. I am able to see the positions of the nearest neighbors. Smart numpy as Import pandas as pd Import seaborn as...
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