the.com/geometry

the ancient art of being right about triangles since before you were born

means The branch of mathematics concerned with the properties, measurement, and relationships of points, lines, angles, surfaces, and solids in space.

from From Greek geōmetria, literally 'land-measuring' — geō ('earth') plus metron ('measure'). The name remembers its practical roots: surveyors pacing out fields and re-marking property lines after the Nile's annual floods erased them, long before the subject became a temple of abstract proofs.

Etymology: Greek for measuring the earth, literally
Euclid: His textbook ran 2000 years undefeated
No royal road: Euclid told a king to study harder
Pi: Irrational, infinite, and weirdly everywhere
Non-Euclidean: Parallel lines can meet; reality got weird

for instance

euclid's elements — foundational mathematics text written ~300 bce, defined geometry for 2000 years

non-euclidean geometry — developed by lobachevsky and riemann in 1800s, curved space that contradicts euclid's parallel postulate

fractals — self-similar patterns discovered by mandelbrot in 1975, appear in nature and mathematics infinitely