Distance calculation and Pythagoras' theorem

Two points in a coordinate system: (1, 2) and (4, 6). How far apart are they?

Draw a right-angled triangle: the horizontal side is 4 − 1 = 3, the vertical side is 6 − 2 = 4.

Pythagoras' theorem: a² + b² = c² → 3² + 4² = 9 + 16 = 25 → c = √25 = 5.

The general formula:

d = √((x₂ − x₁)² + (y₂ − y₁)²)

import math

def avstand(p, q):
    return math.sqrt(sum((a - b) ** 2 for a, b in zip(p, q)))

print(avstand((1, 2), (4, 6)))          # 5.0
print(round(avstand((0, 0), (1, 1)), 3))  # 1.414 = √2

# The same formula works in any number of dimensions:
print(round(avstand((1, 2, 3), (4, 6, 3)), 1))    # 5.0

Why this matters in AI: when words, images, or users are described as points (vectors), “resembling each other” is the same as “being close to each other”. Nearest neighbour, recommendations, and semantic search are all distance calculations — just in hundreds of dimensions instead of two. The formula is exactly the same.