Difference between distance and Euclidean distance? - Answers

There are many ways to measure distance in math. Euclidean distance is one of them. Given two points P1 and P2 the Euclidean distance ( in two dimensions, although the formula very easily generalizes to any number of dimensions) is as follows: Let P1 have the coordiantes (x1, y1) and P2 be (x2, y2) Then the Euclidean distance between them is the square root of (x2-x1)2+(y2-y1)2 . To understand some other ways of measuring "distance" I introduce the term METRIC. A metric is a distance function. You put the points into the function (so they are its domain) and you get the distance as the output (so that is the range). Another metric is the Taxicab Metric, formally known as the Minkowski distance. We often use the small letter d to mean the distance between points. So d(P1, P2) is the distance between points. Using the Taxicab Metric, d(x, y) = |x1 - x2| + |y2 - y2|