Data become vectors; similarity becomes geometry

Data become vectors; vectors become points; similarity becomes geometry — dot product u·v, cos θ = u·v / (|u| |v|)

Click two items. Similar things point the same way — the angle between their arrows (and the dot product that measures it) is small. Each dish is just two measurements: weight and fried-crunch.

normalize vectors (rescale each to unit length, |u| = 1) — then the dot product IS the cosine similarity