Sphere, Cone, and Paraboloid

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Related lectures (30)

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Intrinsic Geometry of Regular Surfaces

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

Descriptive Geometry: The Sphere

Explores the definitions, properties, and symmetry of spheres, including tangent planes and section circles.

Surface Normals: Vector Analysis

Explains surface normals for parametric and implicit surfaces, focusing on vector analysis and examples with spheres.

Surface Integrals: Regular Parametrization

Covers surface integrals with a focus on regular parametrization and the importance of understanding the normal vector.

Descriptive Geometry: The Sphere

Explores the properties and sections of a sphere, including symmetry, tangent planes, and circle projections.

Gaussian Curvature and Geodesics

Explores the derivative of curve lengths, fixed-end deformations, geodesics, surface point typologies, and sphere parametrization.

Parameterized Surfaces: Definition and Examples

Covers the concept of parameterized surfaces in 3D space with examples like cylinders and spheres.

Shells I: Mechanics of Slender Structures

Covers linear and membrane theories of pressure vessels, differential geometry of surfaces, and the reduction of dimensionality from 3D to 2D.

Circular motion: Concepts and Calculations

Explores circular motion concepts, centripetal force, velocity, and acceleration in different coordinate systems, with a focus on auto racing and Formula 1 tire physics.

Internal Transport: Mass Balance and Maxwell-Stefan Equation

Explores internal transport phenomena, focusing on mass balance and the Maxwell-Stefan Equation in single pores.