Metric Geometry Flashcards
1
Q
Metric Space
A
2
Q
Open Ball
A
3
Q
Convergence in Metric Space
A
4
Q
Compactness
A
5
Q
Lipschitz Function
A
6
Q
Hausdorff Distance
A
7
Q
Closed Ball
A
8
Q
Isometry
A
9
Q
Hausdorff Distance
A
10
Q
Bounded Set
A
11
Q
Application of Euclidean Distance
A
Examples:
Computer Graphics: Calculating the distance between pixels in image processing.
Machine Learning: Measuring similarity between data points.
Robotics: Navigating the shortest path between points.
Geography: Calculating the straight-line distance between two locations on a map.
12
Q
Properties of Euclidean Distance
A
13
Q
Taxicab (Manhattan) Distance
A
14
Q
Taxicab Distance in 2D
A
15
Q
Taxicab Distance in 3D
A
16
Q
Taxicab Distance in n-Dimensional Space
A
17
Q
Properties of Taxicab Distance
A
19
Q
Open and Closed Balls in Taxicab Geometry
A
20
Q
Comparison with Euclidean Distance
A
