Packing Geometric Objects With Optimal Worst Case Density Information Guide

  1. Overview of Packing Geometric Objects With Optimal Worst Case Density
  2. Main Features
  3. History
  4. Deep Dive
  5. Final Thoughts

Overview of Packing Geometric Objects With Optimal Worst Case Density

Packing Geometric Objects with Optimal Worst-Case Density Update
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Main Features

Packing Circles In Squares (and other shapes with optimal worst-case density) Update
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History

Full Square packing is weird. Update
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ETR-completeness of various geometric packing problems
ETR-completeness of various geometric packing problems
Spectral Bounds and SDP Hierarchies for Geometric Packing Problems
Spectral Bounds and SDP Hierarchies for Geometric Packing Problems
Packing Squares Inside The Smallest Square Possible
Packing Squares Inside The Smallest Square Possible
Packing irregular polygons with holes
Packing irregular polygons with holes
How to Optimally Pack a Container | 2D Knapsack
How to Optimally Pack a Container | 2D Knapsack
The Insane World of Polygon Packings
The Insane World of Polygon Packings
The Geometry of Optimal Packing
The Geometry of Optimal Packing
Critical Densities for Packing and Covering of and by Disks
Critical Densities for Packing and Covering of and by Disks
Calculating the optimal sphere packing density: with oranges
Calculating the optimal sphere packing density: with oranges
pack geometry
pack geometry
H  Cohn The Mathematical Packing Problem I July 6
H  Cohn The Mathematical Packing Problem I July 6

Deep Dive

Data is compiled from public records and verified media reports.

Last Updated: September 22, 2026

Final Thoughts

Full The Surprising Complexity of Packing Shapes Guide
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Summary

Created by Purdue University MA 325 students. This is a research video about the following paper: arxiv.org/abs/2004.07558 Appeared at FOCS 2020. Frank Vallentin, University of Cologne Semidefinite Optimization, Approximation and Applications ... Credit for the Mathematics shown in this video goes to Erich Friedman and David Ellsworth, whose work you can find here! In this video, I'll be talking about the 2D knapsack problem, which is an extension on the classic knapsack problem. I start by ... Let me show you some surprising things about how squares and other polygons fit into different spaces! 0:00 - Homemade ... Seminar talk in Szeged on March 10, 2021. the corresponding video I made with Steve Mould for his channel. youtu.be/O3RsDIWB7s0 Thomas Hales's proof ... Exactly so what we want to look at each fixed dimension to maximize the

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