Lecture

Sphere Geometry: Properties and Projections

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

Explores affinity in geometry, segment construction, ellipses, and circle projections.

Explores true angle magnitude, reflections, isometries, and symmetries in modern geometry, with practical CAD applications.

Covers the missing projection of points on a sphere using principal planes.

Explores ellipse construction using the Dandelin theorem and properties of conics in space.

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

Covers the definitions and properties of a sphere, including its projections and apparent contours.

Explores conformal maps, hyperbolic geometry, and isometric properties of disks.

Explores the classification and practical applications of symmetries in 3D space, emphasizing user-driven determination of object symmetries.

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

Explains the parametric equations of surfaces of revolution generated by curves in space.

Explores geodesics on surfaces, focusing on minimizing distances and properties of paths, with examples like great circles on spheres.

Explores the geometric properties of paraboloids and hyperboloids in architecture, emphasizing their design implications and practical applications.

Covers geodesics, isometries, and map projections, including the famous Mercator projection and its distortions.

Covers velocity, acceleration, dynamics, moments of inertia, and kinetic energy storage systems.

Explains closed surfaces like spheres, cubes, and cones without covers, and their traversal and removal of edges.

Explores conical sections, plane curves, and the perspective of a sphere and a circle.

Covers gyroscopic effects and angular momentum in rotation dynamics.

Explores descriptive geometry concepts related to spheres, including sectioning by planes and intersection with lines.

Explores Gauss's Law applied to spheres, focusing on electric flux and field symmetry.