Lectures related to Analytical Geometry: Reflection and Symmetry

Orthogonal Projections: Symmetry and Matrices

Explores orthogonal projections, symmetry of matrices, and their applications.

Analytical Geometry: Cartesian Equations

Covers Cartesian equations in analytical geometry, focusing on encoding line directions and unique equations.

Analytical Geometry: Rotation and Center

Explores rotation in analytical geometry, including center coordinates and fixed points.

Explores reflection and rotation composition in analytical geometry, including finding centers and solving fixed point systems.

Analytical Geometry: Oriented Angles

Explores oriented angles in analytical geometry, discussing unit vectors, trigonometric functions, matrix representations, and rotations.

Analytical Geometry: Symmetry of Vectors

Explores the symmetry of vectors with respect to a line in Analytical Geometry.

Analytical Geometry: Locus of Points in a Square

Explores the locus of points in a square and angles between them.

Analytical Geometry: Bisectors and Areas

Explores the properties of bisectors and areas in Analytical Geometry.

Analytical Geometry: Intersections and Medians

Covers Analytical Geometry, focusing on intersections and medians, providing step-by-step solutions for various cases.

Analytical Geometry: Normal Equations of Lines

Explores normal equations of lines in the plane through point translation for precision.

Geometric Transformations: Reflections and Translations

Explores reflections and translations in geometric transformations, demonstrating their stability and practical applications.

Analytical Geometry: Cartesian Equations

Explores Cartesian equations for lines in a plane and their parametric descriptions.

Glide Reflection in Analytical Geometry

Explores glide reflection in analytical geometry, emphasizing fixed points and reflection matrices.

Symmetry in Modern Geometry

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

Analytical Geometry: Coordinates and Midpoints

Covers coordinates, midpoints, and abscissa in analytical geometry, providing practical problem-solving examples.

Isometries & Orientation in Modern Geometry

Explores true angle magnitude, reflections, isometries, and symmetries in modern geometry, with practical CAD applications.

Geometric Properties of Dot Product

Covers the geometric properties of the dot product and its algebraic aspects.

Linear Algebra: Applications and Definitions

Explores linear algebra concepts, mappings between sets, unique element matches, and reciprocal functions.

Symmetry in Modern Space

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

Symmetry in Modern Geometry

Explores symmetry in modern geometry, focusing on isometries, reflections, rotations, and translations, emphasizing the importance of 180-degree rotations.