Discrete geometry | Packing problems
The packing constant of a geometric body is the largest average density achieved by packing arrangements of congruent copies of the body. For most bodies the value of the packing constant is unknown. The following is a list of bodies in Euclidean spaces whose packing constant is known. Fejes Tóth proved that in the plane, a point symmetric body has a packing constant that is equal to its translative packing constant and its lattice packing constant. Therefore, any such body for which the lattice packing constant was previously known, such as any ellipse, consequently has a known packing constant. In addition to these bodies, the packing constants of hyperspheres in 8 and 24 dimensions are almost exactly known. (Wikipedia).
Close Packing Crystal Structures
A description of the two types of crystal structures created from close-packed planes.
From playlist Atomic Structures and Bonding
What 2D Shape Has Maximum Area? What 3D Shape has Maximum Volume?
#shorts Of all 2D shapes with the same perimeter, which has the maximum area? Of all DD shapes with the same surface area, which has the maximum volume? https://mathispower4u.com
From playlist Math Shorts
Chemistry - Liquids and Solids (28 of 59) Crystal Structure: Density of the Unit Cell: Face Centered
Visit http://ilectureonline.com for more math and science lectures! In this video I will calculate the % volume of the molecules in a face centered cubic.
From playlist CHEMISTRY 16 LIQUIDS AND SOLIDS
Measurements of Similar Solids
More resources available at www.misterwootube.com
From playlist Measuring Further Shapes
Prisms (1 of 3: Review of Composite Shape's Area and Perimeters)
More resources available at www.misterwootube.com
From playlist Measuring Basic Shapes
Three space-filling shapes hiding in the structure of diamond
Diamond is an arrangement of carbon atoms called the diamond cubic structure. As well as the cubes there are two other space-filling shapes that are found within it. In the unit cell I say "three more inside". It should of course be "four more inside". https://en.wikipedia.org/wiki/Diamo
From playlist Geometry
Multiple Phase Transitions in a System of Hard Core Rotors on a Lattice (Lecture 1) by Deepak Dhar
INFOSYS-ICTS CHANDRASEKHAR LECTURES MULTIPLE PHASE TRANSITIONS IN A SYSTEM OF HARD CORE ROTORS ON A LATTICE SPEAKER: Deepak Dhar (Distinguished Emeritus Professor and NASI-Senior Scientist, IISER-Pune, India) VENUE: Ramanujan Lecture Hall and Online DATE & TIME: Lecture 1: Monday, D
From playlist Infosys-ICTS Chandrasekhar Lectures
Introduction Sphere Packing problems by Abhinav Kumar
DISCUSSION MEETING SPHERE PACKING ORGANIZERS: Mahesh Kakde and E.K. Narayanan DATE: 31 October 2019 to 06 November 2019 VENUE: Madhava Lecture Hall, ICTS Bangalore Sphere packing is a centuries-old problem in geometry, with many connections to other branches of mathematics (number the
From playlist Sphere Packing - 2019
Role of Intrinsic Inhomogeneities in Active Systems by Shradha Mishra
PROGRAM STATISTICAL BIOLOGICAL PHYSICS: FROM SINGLE MOLECULE TO CELL ORGANIZERS: Debashish Chowdhury (IIT-Kanpur, India), Ambarish Kunwar (IIT-Bombay, India) and Prabal K Maiti (IISc, India) DATE: 11 October 2022 to 22 October 2022 VENUE: Ramanujan Lecture Hall 'Fluctuation-and-noise' a
From playlist STATISTICAL BIOLOGICAL PHYSICS: FROM SINGLE MOLECULE TO CELL (2022)
Chemistry - Liquids and Solids (30 of 59) Crystal Structure: Two Types of Dense Packing
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain the 2 types of dense packing in a crystal structure.
From playlist CHEMISTRY 16 LIQUIDS AND SOLIDS
Hannah Alpert (9/24/20): Combinatorial models of disk configuration spaces
Title: Combinatorial models of disk configuration spaces Abstract: The space of all arrangements of n disjoint disks of radius r in a polygon is hard to get our hands on. In order to approximate its geometric and topological properties, we'd like to replace it by a combinatorial model. Th
From playlist AATRN 2020
S. Hersonsky - Electrical Networks and Stephenson's Conjecture
The Riemann Mapping Theorem asserts that any simply connected planar domain which is not the whole of it, can be mapped by a conformal homeomorphism onto the open unit disk. After normalization, this map is unique and is called the Riemann mapping. In the 90's, Ken Stephenson, motivated by
From playlist Ecole d'été 2016 - Analyse géométrique, géométrie des espaces métriques et topologie
This shows a 3d print of a mathematical sculpture I produced using shapeways.com. This model is available at http://shpws.me/q0PF.
From playlist 3D printing
Exactly solved models by R. Rajesh
DATES Friday 01 Jul, 2016 - Friday 15 Jul, 2016 VENUE Ramanujan Lecture Hall, ICTS Bangalore This advanced level school is the seventh in the series. The school is being jointly organised by the International Centre for Theoretical Sciences (ICTS) and the Raman Research Institute (RRI). T
From playlist Bangalore School On Statistical Physics - VII
Multiple Phase Transitions in a System of Hard Core Rotors on a Lattice (Lecture 3) by Deepak Dhar
INFOSYS-ICTS CHANDRASEKHAR LECTURES MULTIPLE PHASE TRANSITIONS IN A SYSTEM OF HARD CORE ROTORS ON A LATTICE SPEAKER: Deepak Dhar (Distinguished Emeritus Professor and NASI-Senior Scientist, IISER-Pune, India) VENUE: Ramanujan Lecture Hall and Online DATE & TIME: Lecture 1: Monday, D
From playlist Infosys-ICTS Chandrasekhar Lectures
What are the names of different types of polygons based on the number of sides
👉 Learn about polygons and how to classify them. A polygon is a plane shape bounded by a finite chain of straight lines. A polygon can be concave or convex and it can also be regular or irregular. A concave polygon is a polygon in which at least one of its interior angles is greater than 1
From playlist Classify Polygons
Renaud COULANGEON - Lattices, Perfects lattices, Voronoi reduction theory, modular forms, ... 1
Lattices, Perfects lattices, Voronoi reduction theory, modular forms, computations of isometries and automorphisms The talks of Coulangeon will introduce the notion of perfect, eutactic and extreme lattices and the Voronoi's algorithm to enumerate perfect lattices (both Eulcidean and He
From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory
Working with arrays is fundamental to efficient use of Wolfram Language and appears in almost any computation. The basic representation for an array is a nested list, but there are other representations such as PackedArray, SparseArray and structured arrays that are more effective for some
From playlist Wolfram Technology Conference 2022
Battery Management System Development in Simulink
Model and simulate algorithms for a battery management system (BMS) using Simulink® and Stateflow®, including: - Supervisory logic - Monitoring current, voltage, and temperature - State-of-charge (SOC) estimation - Limiting power input and output for thermal, overcharge, and overdischarge
From playlist Battery Management Systems
Review: Perimeter of Basic Figures
From playlist Measuring Basic Shapes