Geometry: Solving Equations and Topological Transformations

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Explores the historical evolution of geometric instruments and the transition to modern CAD software for architectural design.

Explores the intrinsic geometry of regular surfaces and isometric transformations, including spheres and cylinders.

Explores volume calculation of revolution bodies using mathematical formulas and inequalities.

Covers higher order methods for solving equations iteratively, including fixed point methods and Newton's method.

Explores ellipses, conic sections, Kepler's laws, and geometric reconstruction in architectural modeling.

Covers vector spaces in R2 and R3, including planes and lines.

Explains the geometric definition of planes in space and how to determine their equations.

Covers the principle of virtual work and how to determine correct signs and calculations.

Covers the properties and operations of complex numbers and their applications.

Explores geometric transformations, invariant properties, and mean relationships in modern geometry.