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Lecture
Relative Positions: Basics
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Related lectures (31)
Relative Positions: Examples
Presents examples of relative positions in space and solving problems with parametric equations.
Isometries & Orientation: Modern Symmetry
Explores isometries, reflections, rotations, and translations in space, as well as the structure theorem and configurations of planes and lines.
Configurations of 3 Plans in Space
Explores the configurations of 3 plans in space and the decomposition of isometries.
Introduction to Euclidean Elements
Introduces Euclidean elements, explores infinity uniqueness, parallel lines, and different geometries like Euclidean, hyperbolic, and spherical.
Introduction to Non-Euclidean Geometry
Explores non-Euclidean geometries, hyperbolic and spherical, challenging the traditional Euclidean geometry with implications for modern mathematics.
Special Cases of 3 Plane Reflections
Explores the configurations and transformations of three planes in space.
Introduction to Euclidean Geometry
Introduces the fundamental concepts of Euclidean geometry, exploring postulates, parallel lines, and non-Euclidean geometries.
Geometry: Introduction to Architectural Geometry
Explores the historical and practical applications of geometry in architecture, emphasizing key geometric principles in architectural design.
Geometric Transformations: Meanings and Applications
Explores geometric transformations, invariant properties, and mean relationships in modern geometry.
Introduction to Euclidean Elements
Introduces the 5th postulate in Euclidean geometry and explores non-Euclidean geometries and their implications.
Theorem of Three Perpendiculars, Shadow of a Point
Explains the Theorem of Three Perpendiculars and shadow casting of points on planes.
Euclidean Geometry: Operations and Constructions
Covers the fundamental operations and constructions in Euclidean geometry, focusing on algebraic interpretations and ruler-and-compass constructions.
Axioms of Connection
Introduces the axioms of connection in Euclidean geometry, emphasizing unique lines and non-collinear points.
Relative Positions in Space
Covers the precise description of the relative positioning of objects in space.
Geometry and Complex Numbers: Circles in the Complex Plane
Explores equations and properties of circles in the complex plane.
Regular Polyhedra in Euclidean Geometry
Explores the historical background and properties of regular polyhedra in Euclidean geometry, including the construction of perfect even numbers and the proportionality of arcs and angles.
Geometry: Modern Interpretation of Symmetry
Introduces a new online format for the geometry course, emphasizing the study of isometries and the modern interpretation of symmetry.
Analytical Study of Space
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Explores the analytical study of space, covering relative positions, angles, and properties of lines and planes.
Isometries & Orientation in Modern Geometry
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Explores true angle magnitude, reflections, isometries, and symmetries in modern geometry, with practical CAD applications.
Geometry II: Modern Geometric Transformations
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Explores modern geometric transformations and invariances, focusing on projective geometry and historical developments.
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