Mathematics // Domain_02
GEOMETRY
Euclidean
Axiomatic / Flat
The geometry of flat surfaces. Triangles add to 180°. Parallel lines never meet.
Non-Euclidean
Hyperbolic / Elliptic
Curved space where parallel lines diverge or intersect. The geometry of gravity.
Trigonometry
Ratios / Cycles
The bridge between angles and lengths. Sine waves and circular motion.
Structure of Space
Analytic
Coordinate Systems
Descartes' grid. Translating shapes into algebraic equations (y = mx + b).
Topology
Deformation
Geometry without distance. Properties preserved under stretching and bending.
Fractal
Recursion / Chaos
Self-similar structures. Fractional dimensions found in nature (coastlines, ferns).