Concept

Euclidean group

Related lectures (29)

Isometries and Orthonormal Bases

Discusses isometries and orthonormal bases in mathematics.

Symmetry in Modern Geometry

Delves into modern geometry, covering transformations, isometries, and symmetries.

Isometries in R^n

Explores the standard form of isometries in R^n and the preservation of distances.

Isometries & Orientation: Modern Symmetry

Explores isometries, reflections, rotations, and translations in space, as well as the structure theorem and configurations of planes and lines.

Euclidean Isometries: Properties and Applications

Explores the properties and applications of Euclidean isometries in R^2.

Isometries in Space: Synthesis

Covers the synthesis of isometries in space and the complexities of determining symmetries in 3D objects.

Orientation & Angles in 3D Space

Explores isometries, orientation, and dihedral angles in 3D space.

Isometries in R^2 and R^3

Explores isometries in R^2 and R^3, focusing on symmetries, rotations, and linear compositions, with a glimpse into the Banach-Tarski paradox.

Isometry in Space

Covers the examination of 10 possible isometries in space.

Isometry in Space Synthesis

Examines the synthesis of isometry in space and its differences with the plane.

Bisectrix: Symmetry and Angles

Explores the concept of bisectrix in angles and its symmetries.

Symmetry in Modern Topology

Explores the concept of symmetry in various geometric transformations.

Symmetry in Geometry

Explores modern symmetry in geometry, covering transformations, isometries, orientations, and practical applications.

Mediatrice: Construction and Justification

Covers the construction and justification of the mediatrice as the axis of symmetry for a segment.

Symmetry: Central Symmetry

Introduces central symmetry, an isometry fixing a point and transforming other points.

Rotations: Isometries and Axes

Explores rotations as isometries composed of reflections with common axes and the flexibility in choosing rotation axes.

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.

Rotations and Symmetries

Covers the preservation of isometry by rotations and symmetries.

Embedding Space: AdS and Euclidean Geometry

Covers the concept of embedding space for AdS and Euclidean geometry, discussing AdS isometries and Euclidean Ads.

Geometry: Reflections and Transformations

Explores geometry transformations, emphasizing isometries, point reflections, rotations, and translations to illustrate fundamental geometric principles.