Geometry
concept
The branch of mathematics that studies spatial form and the properties of figures.
Geometry studies shapes, space, and distance. The concepts in this hub are organized around geometric themes — properties and theorems of lines, triangles, circles, and other basic figures.
Many moving-point optimization problems eventually reduce to one humble fact: a straight line is the shortest path between two points — i.e. [[triangle-inequality]]. Different transformations turn this single fact into a family of named models:
- General Drinking Horse (axial-symmetry shortest path) — fold "two segments" into a single polyline by reflection
- Fermat point — chain "three segments" with a 60° rotation
- Apollonius circle — turn "weighted distance" into an additive form by similarity