Lectures related to Main Lines of a Plane: Sketch and Properties

Intersection of Line and Plane: Geometric Descriptive

Explains the intersection of a line and a plane using auxiliary planes and projectants.

Intersections and Parallel Planes in Descriptive Geometry

Explores intersections between lines and planes, parallel planes, and relative positions of lines and planes.

Covers the concept of finding the distance between two lines in a plane.

Introduces Euclidean elements, explores infinity uniqueness, parallel lines, and different geometries like Euclidean, hyperbolic, and spherical.

Affinity and Ellipses in Descriptive Geometry

Explores affinity in geometry, segment construction, ellipses, and circle projections.

Perpendicular Lines and Planes

Explores perpendicular lines and planes in descriptive geometry, focusing on orthogonality and intersection points.

Introduction to Non-Euclidean Geometry

Explores non-Euclidean geometries, hyperbolic and spherical, challenging the traditional Euclidean geometry with implications for modern mathematics.

Introduction to Euclidean Elements

Introduces the 5th postulate in Euclidean geometry and explores non-Euclidean geometries and their implications.

Vector Study: Equations and Observations

Explores vector equations, observation points, and normal equations in a plane.

Stereographic Projection: Sphere Parameterization

Explores stereographic projection and sphere parameterization, emphasizing regularity and line independence.

Geometric Transformations: Meanings and Applications

Explores geometric transformations, invariant properties, and mean relationships in modern geometry.

Theorem of Three Perpendiculars, Shadow of a Point

Explains the Theorem of Three Perpendiculars and shadow casting of points on planes.

Green's Theorem in 2D: Applications

Explores the applications of Green's Theorem in 2D, emphasizing the importance of regular domains for successful integration.

Introduction to Euclidean Geometry

Introduces the fundamental concepts of Euclidean geometry, exploring postulates, parallel lines, and non-Euclidean geometries.

Barycenters: Examples

Covers examples of barycenters and expressing points as barycenters of given points.

Analytical Geometry: Mixed Product and Determinant

Covers the analytical expression of the mixed product and its applications.

Isometries & Orientation in Modern Geometry

Explores true angle magnitude, reflections, isometries, and symmetries in modern geometry, with practical CAD applications.

Non-Euclidean Geometries

Explores non-Euclidean geometries, including hyperbolic geometry and the tractricoid model, challenging Euclidean principles and introducing projective geometry.

Symmetries in Plane Geometry

Explores symmetries in plane geometry, including isometries, reflections, and practical applications in design.

Isometries: Final Panorama

Explores the synthesis of plane isometries and their composition through axial reflections, rotations, translations, and glided reflections.