202411291941
Status: #idea
Tags: Elementary
State: #nascient

Euclidean distance

This is the basic and most natural measure of distance, also called the $L_2-norm$.
It measures distance in terms of Pythagorean theorem and straight lines through space.

I don't know what much to say here because if you've ever walked anywhere in a straight line and cut a line to walk diagonally, you made use of the Euclidean distance.

As a norm it respects the triangular inequality $||a|{|}_2+||b|{|}_2\ge ||a+b|{|}_2$ and is always positive.

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