Lectures related to Normal Equations in Square Geometry

Analytical Geometry: Mixed Product and Determinant

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

Explores vector and normal equations, covering lines, intersections, and distances in 2D and 3D geometry.

Analytical Geometry: Intersections and Medians

Covers Analytical Geometry, focusing on intersections and medians, providing step-by-step solutions for various cases.

Isometries & Orientation in Modern Geometry

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

Geometric Surfaces: Paraboloids and Hyperboloids in Architecture

Explores the geometric properties of paraboloids and hyperboloids in architecture, emphasizing their design implications and practical applications.

Intersections of Lines and Medians

Explores intersections of lines and medians in a square geometry context.

Analytical Geometry: Midpoint, Equations, Projections

Explores midpoint, equations, angles, and projections in analytical geometry.

Geometric Surfaces: Paraboloid and Hyperboloid Concepts

Covers the geometric properties of hyperbolic paraboloids and hyperboloids, focusing on their construction and curvature characteristics.

Perpendicular Lines and Planes

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

Geometric Transformations: Meanings and Applications

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

Intersection Numbers: Algebraic Counting Solutions

Explores intersection numbers for counting solutions to polynomial equations algebraically and their geometric significance in intersection theory and enumerative geometry.

Surfaces in Geometry

Explores surfaces with constant curvature, rules between geometric elements, and the generation of sections in geometry.

Stereographic Projection: Sphere Parameterization

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

Intersections and Parallel Planes in Descriptive Geometry

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

Spatial Curves: Intersections and Singularities

Explores spatial curves, focusing on intersections and singularities in architectural contexts.

Relative Positions in Space

Covers the precise description of the relative positioning of objects in space.

Vector Operations: Planes and Lines

Explores vector operations in 3D space, including plane intersections and distance calculations.

Dandelin Theorem: Ellipse Construction

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

Analytical Geometry: Triangle Properties

Explores triangle properties like inequalities, medians, and orthocenters using analytical geometry.

Theorem of Three Perpendiculars, Shadow of a Point

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