Lectures related to Pythagoreanism

Triangle Geometry: Special Lines (Part 2)

Explores triangle bisectors, locus of equidistant points, and incenter intersection.

Orthogonality and Least Squares

Introduces orthogonality between vectors, angles, and orthogonal complement properties in vector spaces.

Orthogonality, Triangle Inequality, Pythagorean Theorem

Explores orthogonality, triangle inequality, and the Pythagorean theorem in vector spaces.

Orthogonality and Least Squares Method

Explores orthogonality, dot product properties, vector norms, and angle definitions in vector spaces.

The 3 Branches: Geometric Means & Constructibility

Delves into ancient geometric means, transformations, and projective geometry's birapports.

Pythagorean Theorem

Introduces the Pythagorean theorem, explaining its geometric significance and applications in calculating areas.

Functions: Elementary Functions

Covers elementary functions like tan(x), sin(x), and cos(x) along with trigonometric identities and Pythagorean theorem.

Triangle Relations: Cosine and Sine Laws

Explores the Cosine and Sine Laws in triangles, highlighting their applications and potential pitfalls.

Orthogonality and Scalar Product

Explores orthogonality, scalar product, and orthonormal bases in vector spaces.

Quadratic Best Approximation

Explores the best quadratic approximation in Euclidean spaces, emphasizing least squares.

Orthogonality and Least Squares Method

Covers orthogonal vectors, unit vectors, and the Pythagorean theorem in R^m.

Orthogonality and Subspaces

Explores orthogonality, vector norms, and subspaces in Euclidean space, including determining orthogonal complements and properties of subspaces and matrices.

Orthogonal Bases in Vector Spaces

Covers the concept of orthogonal bases in vector spaces and Pythagorean theorem applications.

Orthogonality and Inequalities

Explores symmetrical bilinear forms, the Pythagorean theorem, inequalities, and orthogonal matrices.

Orthogonality and Least Squares Method

Introduces orthogonal vectors, scalar product, Euclidean norm, Pythagorean theorem, and unit vectors.

Norms and Orthogonality

Explores norms, orthogonality, and the Pythagorean theorem in vector spaces.

Orthogonal Families and Linear Combinations

Explores orthogonal families, vector orthogonality, and linear combinations in vector spaces.