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Concept

Isometry group

Related lectures (29)

Isometries and Orthonormal Bases

Discusses isometries and orthonormal bases in mathematics.

Isometries in Euclidean Spaces

Explores isometries in Euclidean spaces, including translations, rotations, and linear symmetries, with a focus on matrices.

Conformal Symmetries in Euclidean and AdS Spaces

Explores conformal symmetries in Euclidean and AdS spaces, isometries, induced metric, Poincaré coordinates, and boundary structure.

Isometries & Orientation: Modern Symmetry

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

Isometries in Space: Synthesis

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

Mediatrice: Construction and Justification

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

Orientation & Angles in 3D Space

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

Symmetry: Central Symmetry

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

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.

Conformal Field Theory Basics

Covers the basics of Conformal Field Theory, focusing on Large N CFTs and correlation functions.

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Embedding Space: AdS and Euclidean Geometry

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

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.

Isometries: Final Panorama

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

Isometries and Group Homomorphisms

Explores isometries, group homomorphisms, linear transformations, and group generation by similarities.

Symmetries in Plane Geometry

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

Geometry: Reflections and Transformations

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