Explore the branch of mathematics concerned with properties of space, including distance, shape, size, and relative position of figures. From classical Euclidean foundations to modern differential and computational approaches.
A comprehensive examination of Euclid's Elements, exploring the five postulates, parallel line theorem, and the historical development of axiomatic reasoning in mathematics.
How algebraic equations map to geometric shapes. Covers Cartesian coordinates, conic sections, transformations, and real-world engineering applications.
An in-depth look at calculus-based geometry, exploring curvature of curves, surfaces, geodesics, and the foundational concepts of Riemannian manifolds.
Understanding homeomorphisms, Euler characteristics, genus, and how topological invariants classify spaces beyond rigid geometric measurements.
Tracing the use of geometric proportion, the golden ratio, and fractal-like structures in ancient temples, Islamic tessellations, and Renaissance design.
Exploring curved spaces where Euclid's parallel postulate fails. Covers Poincaré disk models, spherical trigonometry, and connections to general relativity.
Voronoi diagrams, convex hulls, triangulation, and collision detection. How computers solve geometric problems efficiently in graphics, GIS, and robotics.
Dimensionality beyond integers. Mandelbrot sets, Koch snowflakes, and how fractal geometry models coastlines, biological structures, and financial markets.