Isometries: Definition and Examples

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

Linear Applications: Matrices and Transformations

Explores linear applications, matrices, transformations, rotations, symmetries, and properties of applications.

Geometric Rotations in 2D

Covers the geometric definition of rotations in 2D and analytical expressions for rotations using matrices.

Isometries and Orthonormal Bases

Discusses isometries and orthonormal bases in mathematics.

2D Transformations: Linear Maps & Matrices

Covers 2D transformations, linear maps, matrices, affine transformations, and orthogonal transformations.

Conformal Transformations: Part 1

Covers the topic of conformal transformations, including translations, dilations, rotations, and the conformal algebra.

Geometric Transformations in R2 and R3

Explores geometric transformations in R2 and R3, including reflections, rotations, and practical applications like billiards.

Introduction to Isometries in Space

Covers isometries in space, reflections, rotations, axial reflections, and geometric constructions.

Symmetry in Modern Geometry

Covers symmetry in modern geometry, reflections, translations, rotations, compositions of isometries, fundamental theorems, configurations of lines and planes, and surface analysis.

Symmetries in Mechanics and Wave Equations

Explores symmetries in Newtonian mechanics and wave equations, highlighting their significance in understanding physical laws.