Introduction to Isometries in Space

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Explores the fundamental theorem of isometries in space and the modern definition of symmetry, emphasizing the complexities of determining symmetries in 3D objects.

Curves and Isometries

Explores curves, isometries, Bezier curves, and the Frenet coordinate system.

Wigner Theorem; Translation Symmetry

Explores the Wigner theorem, translation symmetry, eigenstates, and wave functions in quantum physics.

Geometric Transformations in R2 and R3

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

Symmetry in Modern Space

Explores the classification and practical applications of symmetries in 3D space, emphasizing user-driven determination of object symmetries.

Translations: Isometries and Compositions

Explores translations as compositions of reflections and their properties in preserving orientation, including the special case of identity.

Rotations: Isometries and Axes

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

Group Theory: Basics

Covers the basics of group theory, including sets, applications, and examples like permutations and rotations.

Moment of Inertia: Solid Rotation

Covers the concept of moment of inertia for solid rotation and its independence from movement and reference frame choice.