Rotations (2D): Definitions and Analytical Expressions

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

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

Covers translations, homotheties, and their analytical expressions, emphasizing stability by composition.

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

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

Explores orthogonal matrices and transformations, emphasizing preservation of norms and angles.

Covers the preservation of isometry by rotations and symmetries.

Covers the concept of orientation in the plane and transformations using matrices.

Covers the equilibrium conditions in 3D, system isolation, free-body diagrams, and constraints.

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