Concept

Sphere packing

Related lectures (27)

Covers the basics of linear algebra, including minimizing costs and optimal packing strategies.

Explores the crystal packing of conjugated molecules, discussing shapes, structures, and packing arrangements in the solid state.

Crystal Packing of Conjugated Molecules

Explores the shapes and crystal structures of conjugated molecules, discussing packing arrangements, polymorphism, and the impact of substituents on crystal packing.

Supramolecular Organisation: Solid State

Explores the supramolecular organization of π-conjugated molecules in the solid state, covering crystal structures and packing preferences.

Extremal Lattices

Explores extremal lattices, emphasizing bounds on shortest vectors and unique modular forms.

Sphere Packing

Covers the concept of sphere packing and its significance in time shifts and Nyquist criterion.

Solid-Solid Interfaces: Grain Boundaries and Surface Energy

Explores grain boundaries, surface energy, geometry parameters, and micelle formation.

E8 Lattice Optimality

Delves into the construction and optimality of the E8 lattice as the densest sphere packing in dimension eight.

Excitonic Coupling in Electron-rich Systems

Explores the excitonic coupling in electron-rich systems and the formation of neutral solitons in poly(acetylene) due to chemical oxidation.

Supramolecular Organisation in Solid State

Explores supramolecular organization in the solid state, covering pi-conjugated molecules' shapes, crystal structures, and intermolecular interactions.

Geometric Surfaces: Paraboloid and Hyperboloid Concepts

Covers the geometric properties of hyperbolic paraboloids and hyperboloids, focusing on their construction and curvature characteristics.

Ceramic Materials: Structures and Properties

Explores atomic bonds, crystal structures, and polymorphism in ceramics, highlighting the importance of atomic size in crystal packing.

Geometric Surfaces: Paraboloids and Hyperboloids in Architecture

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

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Lattices, Minkowski's Theorem

Explores lattices, Minkowski's Theorem, and properties of symmetric convex sets.

Vertex Operator Algebras: Conformal Vectors and Virasoro Algebra

Explores conformal vectors, Virasoro algebra, and Heisenberg vertex algebra in the theory of vertex operator algebras.

Sphere Geometry: Properties and Projections

Explores sphere properties, projections, and symmetry, including apparent contours and missing projections of points.

Tactical Configurations: Rödl Nibble

Explores tactical configurations, covering the minimal size of subsets needed to cover element sets and the concept of K-sets and base points.

Graph Surfaces and Sphere in Spherical Coordinates

Covers graph surfaces with an example of a surface defined by a parametric equation.