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Everything about Discrete geometry
Branch of geometry that studies combinatorial properties and constructive methods
Discrete geometry and combinatorial geometry are branches of geometry that study combinatorial properties and constructive methods of discrete geometric objects. Most questions in discrete geometry involve finite or discrete sets of basic geometric objects, such as points, lines, planes, circles, spheres, polygons, and so forth. The subject focuses on the combinatorial properties of these objects, such as how they intersect one another, or how they may be arranged to cover a larger object. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Discrete geometryA 5-minute orientation
- Skim a recent paper: Modeling of magnetic cilia carpet robots using discrete differential geometry formulationInfluential work since 2022
- Pick up a classic book: Handbook of discrete and computational geometryThe most-reprinted book on the subject
- Read the landmark paper: Extremal problems in discrete geometryCited 301 times
- Go sideways: CombinatoricsA closely related topic
- Go sideways: Algebraic combinatoricsA closely related topic
🏆 Landmark papers (most cited)
Extremal problems in discrete geometry
Shape‐Up: Shaping Discrete Geometry with Projections
Discrete scale axis representations for 3D geometry
A Glimpse into Discrete Differential Geometry
Discrete Riemannian geometry
On organizing principles of discrete differential geometry. Geometry of spheres
Discrete hyperbolic geometry
The discrete Green Theorem and some applications in discrete geometry
🆕 Influential since 2022
Modeling of magnetic cilia carpet robots using discrete differential geometry formulation
A Tutorial on Simulating Nonlinear Behaviors of Flexible Structures With the Discrete Differential Geometry Method
Impedance Control on Arbitrary Surfaces for Ultrasound Scanning Using Discrete Differential Geometry
DisMech: A Discrete Differential Geometry-Based Physical Simulator for Soft Robots and Structures
A discrete differential geometry-based numerical framework for extensible ribbons
📚 Books worth reading
Handbook of discrete and computational geometryJoseph O'Rourke, Jacob E. Goodman · 1997
Geometric Aspects of Functional AnalysisBo'az Klartag · 2012
Discrete geometryAndras Bezdek · 2003
Research Problems in Discrete GeometryPeter Brass, William O. J. Moser · 2005
Elementary Differential GeometryBarrett O'Neill · 1966
Geometric methods and optimization problemsV. G. Bolti͡anskiĭ, V. Boltyanski · 1998
Mathematical essays in honor of Gian-Carlo RotaGian-Carlo Rota, Bruce Eli Sagan · 1998
Forbidden Configurations in Discrete GeometryDavid Eppstein · 2018
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
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