A Euclidean graph (a graph embedded in some Euclidean space) is periodic if there exists a basis of that Euclidean space whose corresponding translations induce symmetries of that graph (i.e., application of any such translation to the graph embedded in the Euclidean space leaves the graph unchanged). Equivalently, a periodic Euclidean graph is a periodic realization of an abelian covering graph over a finite graph. A Euclidean graph is uniformly discrete if there is a minimal distance between any two vertices. Periodic graphs are closely related to tessellations of space (or honeycombs) and the geometry of their symmetry groups, hence to geometric group theory, as well as to discrete geometry and the theory of polytopes, and similar areas. Much of the effort in periodic graphs is motivated by applications to natural science and engineering, particularly of three-dimensional crystal nets to crystal engineering, crystal prediction (design), and modeling crystal behavior. Periodic graphs have also been studied in modeling very-large-scale integration (VLSI) circuits. (Wikipedia).
Rotating graph of graph with four critical points
From playlist 3d graphs
Graph Theory: 05. Connected and Regular Graphs
We give the definition of a connected graph and give examples of connected and disconnected graphs. We also discuss the concepts of the neighbourhood of a vertex and the degree of a vertex. This allows us to define a regular graph, and we give some examples of these. --An introduction to
From playlist Graph Theory part-1
What are Connected Graphs? | Graph Theory
What is a connected graph in graph theory? That is the subject of today's math lesson! A connected graph is a graph in which every pair of vertices is connected, which means there exists a path in the graph with those vertices as endpoints. We can think of it this way: if, by traveling acr
From playlist Graph Theory
Graph of x^2 + 6xy + 5y^2 rotating
From playlist 3d graphs
What are Cycle Graphs? | Graph Theory, Graph Cycles, Cyclic Graphs
What are cycle graphs? We have talked before about graph cycles, which refers to a way of moving through a graph, but a cycle graph is slightly different. A cycle graph is what you would get if you took the vertices and edges of a graph cycle. We can think of cycle graphs as being path gra
From playlist Graph Theory
The Definition of a Graph (Graph Theory)
The Definition of a Graph (Graph Theory) mathispower4u.com
From playlist Graph Theory (Discrete Math)
Hodge Theory, between Algebraicity and Transcendence (Lecture 3) by Bruno Klingler
DISCUSSION MEETING TOPICS IN HODGE THEORY (HYBRID) ORGANIZERS: Indranil Biswas (TIFR, Mumbai, India) and Mahan Mj (TIFR, Mumbai, India) DATE: 20 February 2023 to 25 February 2023 VENUE: Ramanujan Lecture Hall and Online This is a followup discussion meeting on complex and algebraic ge
From playlist Topics in Hodge Theory - 2023
On some geometry-grounded problems involving PDEs, Dynamics, and discretization - Dmitri Burago
Workshop on the h-principle and beyond Topic: On some geometry-grounded problems involving PDEs, Dynamics, and discretization Speaker: Dmitri Burago Affiliation: Penn State University Date: November 5, 2021 Abstract: I use the same title for different talks, changing the selection of top
From playlist Mathematics
How to Find Periodic Orbits and Exotic Symplectic Manifolds - Mark McLean
Mark McLean Massachusetts Institute of Technology; Member, School of Mathematics October 15, 2012 I will give an introduction to symplectic geometry and Hamiltonian systems and then introduce an invariant called symplectic cohomology. This has many applications in symplectic geometry and
From playlist Mathematics
Bruno Klingler - 1/4 Tame Geometry and Hodge Theory
Sorry for the re upload due to a technical problem on the previous version Hodge theory, as developed by Deligne and Griffiths, is the main tool for analyzing the geometry and arithmetic of complex algebraic varieties. It is an essential fact that at heart, Hodge theory is NOT algebraic.
From playlist Bruno Klingler - Tame Geometry and Hodge Theory
Dmitri Burago (9/16/22): A Mozaic from Geometry, Dynamics, PDEs, and maybe more
I give very different talks under the same title, this leaves me flexibility. I never know in advance what I want to talk about:) I am going to begin with some unsolved problems, which, in my opinion, deserve more attention than they receive. For some problems, there are partial solutions
From playlist Vietoris-Rips Seminar
Let’s graph y = 3sin(2x) + 2 – amplitude, period, shifts (Trigonometry | Pre-Calculus)
How to graph a sin function to include the amplitude, period, and shifts. Pre-Calculus: https://tabletclass-academy.teachable.com/p/tabletclass-math-pre-calculus For more in-depth math help check out my catalog of courses. Every course includes over 275 videos of easy to follow and unde
From playlist Pre-Calculus / Trigonometry
Find the SIN (60 degrees) Without a CALCULATOR
TabletClass Math: https://tcmathacademy.com/ How to find the sin of a number without a calculator. For more math help to include math lessons, practice problems and math tutorials check out my full math help program at https://tcmathacademy.com/ Math Notes: Pre-Algebra Notes:
From playlist Pre-Calculus / Trigonometry
Jacob Tsimerman - An introduction to O-minimal structures: tameness of the real exponential
This is the first talk in the Minerva Mini-course, Applications of o-minimality in Diophantine Geometry, by Jacob Tsimerman, University of Toronto and Princeton's Fall 2021 Minerva Distinguished Visitor.
From playlist Minerva Mini Course - Jacob Tsimerman
Graph Theory FAQs: 01. More General Graph Definition
In video 02: Definition of a Graph, we defined a (simple) graph as a set of vertices together with a set of edges where the edges are 2-subsets of the vertex set. Notice that this definition does not allow for multiple edges or loops. In general on this channel, we have been discussing o
From playlist Graph Theory FAQs
Writing a Sinusoidal Equation Given Max and Min (Example 2)
Learn how to write the sinusoidal equation given a max and min for a graph in this video math tutorial by Mario's Math Tutoring. We go through an example given the points (-1,2) and (1,-4) and go through the steps to write both a cosine and sine equation to model the graph. We discuss fo
From playlist PreCalculus
What are Irregular Graphs? (and why they are boring) | Graph Theory
What are irregular graphs? After learning about regular graphs, this is a natural question to ask. Irregular graphs are the opposite of regular graphs, which means that irregular graphs are graphs in which all vertices have distinct degrees. Equivalently, a graph is irregular if and only i
From playlist Graph Theory
From playlist 3d graphs
Spectral geometry on metric graphs - Lior Alon
Short Talks by Postdoctoral Members Topic: Spectral geometry on metric graphs Speaker: Lior Alon Affiliation: Member, School of Mathematics Date: September 22, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics