MATH 170 · Distance is a choice · Norms

Three rulers on one grid L1 · L2 · L∞

Distance is not one thing. Walk the streets and you count blocks; fly and you cut the corner; ask "what was the biggest single step?" and you get a third answer. Move the two points and watch three rulers disagree — then switch modes and see what a circle looks like to each of them.

Drag either point, or focus one and use the arrow keys — everything moves in half units.

Try: put both points in the same row. Which two of the three rulers agree now?