Euclidean geometry

Related lectures (20)

Explores the definitions and symmetries of regular polyhedra, focusing on the five known convex regular polyhedra from ancient times.

Explores the definitions and symmetries of regular polyhedra, shedding light on ancient geometry and modern mathematical formalization.

Explores Euclid's first proposition, ancient symmetria, and Vitruvius' architectural figures.

Explores elementary operations in geometry, including addition, subtraction, multiplication, and division of segments and angles.

Explores angles at the center of a circle and the power of a point relative to a circle, emphasizing their importance in geometry and CAD software.

Delves into the geometric principles of Gothic architecture, focusing on surface curvature and stereotomy techniques.

Explores ellipse construction using the Dandelin theorem and properties of conics in space.

Explores the historical development of approximating ellipses with ovals and the challenges in machining trajectories.

Covers the geometry of the triangle, including inequalities, heights, and centers.

Explains the parametric equations of surfaces of revolution generated by curves in space.

Covers the resolution of triangles using trigonometric functions to find missing sides and angles.

Explores the properties of regular polyhedra, their symmetries, generation, and historical misconceptions.

Covers curvature, osculating circles, and the evolute of plane curves, with examples and equations.

Explores the mediatrix and bisector properties in right-angled triangles through proofs and constructions.

Explores optimization problems to find global extrema of functions over domains.

Covers the introduction to conic sections in space, focusing on ellipses and their properties.

Explores the construction and properties of parabolas, ellipses, and hyperbolas in the plane.

Covers surface integrals with a focus on regular parametrization and the importance of understanding the normal vector.

Explores ellipses, conic sections, Kepler's laws, and geometric reconstruction in architectural modeling.

Covers the topology of Riemann surfaces and the concept of triangulation using finitely many triangles.