# Jammer1

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1. ## What is Euclidean Space?

First take *Cartesian space*, that is a coordinate space formed by taking pairs or tuples of real numbers as the coordinates, e.g. [1.0, 2.0] would be a point in 2D Cartesian space. (It's called "Cartesian" because it's formed by taking the *Cartesian product* of real lines). Then add to that a specific *distance function* called the "Euclidean metric" and you have yourself a *Euclidean space*. The Euclidean metric mostly corresponds to the usual notion of shortest straight-line distance between points. Other metrics are "taxicab metric" (imagine measuring walking distance in a city, you can't travel in a straight line through buildings, you have to stick to streets as they are layed out in a grid), or the discrete metric (distance to all other points is 1, otherwise the distance of a point to itself is 0). Don't ask me about Hyperbolic or Elliptic spaces, I think the metric requirements are similar but the underlying geometry is obviously different 😃