Lectures related to Pythagorean theorem

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

Explores the cosine theorem in triangles, analyzing side and angle relationships.

Explores elementary operations in geometry, including addition, subtraction, multiplication, and division of segments and angles.

Delves into normal vectors in calculus, clarifying their role in integrals and parameterization of edges.

Covers the topology of Riemann surfaces and the concept of triangulation using finitely many triangles.

Explores a nonlinear version of Bourgain's Projection Theorem and its diverse applications in mathematics.

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

Explores Euclid's first proposition, ancient symmetria, and Vitruvius' architectural figures.

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

Explores fundamental groups, homotopy classes, and coverings in connected manifolds.

Covers the differentiability of functions of multiple variables and the significance of directional derivatives and gradients.

Explores elementary algebra concepts related to numeric sets and prime numbers, including unique factorization and properties.

Explores curves with Poritsky property, Birkhoff integrability, and Liouville nets in billiards.

Introduces Coq, covering defining propositions, proving theorems, and using tactics.

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

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

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

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