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Related lectures (27)

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Self-Avoiding Random Walks

Explores self-avoiding random walks and their mathematical models, emphasizing the importance of paths that are self-avoiding.

Discrete Variables: Geometric Properties

Covers the geometric properties of discrete variables in geographic information systems, focusing on shape, location, and size indices.

Implicit Surfaces: Regular Points

Explains regular points on implicit surfaces and their relationship with gradients and tangent planes.

Arc Length Approximation

Explores arc length calculation for curves and polygons inscribed in circles using trigonometry and parametric equations.

Quadrature & Rectification

Explores the historical problems of quadrature, pi approximation, angle trisection, and the use of conchoid in architecture.

Polygons & Polyhedra: Regular & Starred

Explores polygons, polyhedra, regularity, and starred configurations in Euclidean geometry, highlighting historical context and limitations.

Regular Polyhedra: Symmetries & Generation

Explores the properties of regular polyhedra, their symmetries, generation, and historical misconceptions.

Geodesic Curves: Minimizing Distance and Constant Speed

Covers geodesic curves parameterized at constant speed to minimize distances between points.

Methods of Integration of Functions in Several Variables

Explores methods of integrating functions in several variables, emphasizing the importance of regular areas and changing variables to polar coordinates.

Implicit Curves: Analysis & Regular Points

Covers implicit curves, regular and critical points, convexity, concavity, and inflection points.