Mathematical chess problems | Parametric families of graphs
In graph theory, a knight's graph, or a knight's tour graph, is a graph that represents all legal moves of the knight chess piece on a chessboard. Each vertex of this graph represents a square of the chessboard, and each edge connects two squares that are a knight's move apart from each other.More specifically, an knight's graph is a knight's graph of an chessboard.Its vertices can be represented as the points of the Euclidean plane whose Cartesian coordinates are integers with and (the points at the centers of the chessboard squares), and with twovertices connected by an edge when their Euclidean distance is . For an knight's graph, the number of vertices is . If and then the number of edges is (otherwise there are no edges). For an knight's graph, these simplify so that the number of vertices is and the number of edges is . A Hamiltonian cycle on the knight's graph is a (closed) knight's tour. A chessboard with an odd number of squares has no tour, because the knight's graph is a bipartite graph and only bipartite graphs with an even number of vertices can have Hamiltonian cycles. All but finitely many chessboards with an even number of squares have a knight's tour; Schwenk's theorem provides an exact listing of which ones do and which do not. When it is modified to have toroidal boundary conditions (meaning that a knight is not blocked by the edge of the board, but instead continues onto the opposite edge) the knight's graph is the same as the four-dimensional hypercube graph. (Wikipedia).
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
From playlist 3d graphs
Platonic graphs and the Petersen graph
In this tutorial I show you to construct the five platonic graphs and the Peterson graph in Mathematica and we use some of the information in the previous lectures to look at some of the properties of these graphs, simply by looking at their graphical representation.
From playlist Introducing graph theory
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
On a 3x3 grid, four knights are placed on the corners. Can you get the knights in opposite corners to swap positions, using only legal chess moves? Give it a try before watching the solution. Puzzle solution is from "Algorithmic Puzzles" by Anany Levitin and Maria Levitin, a wonderful co
From playlist Math Puzzles, Riddles And Brain Teasers
Graph Theory: 03. Examples of Graphs
We provide some basic examples of graphs in Graph Theory. This video will help you to get familiar with the notation and what it represents. We also discuss the idea of adjacent vertices and edges. --An introduction to Graph Theory by Dr. Sarada Herke. Links to the related videos: https
From playlist Graph Theory part-1
Learn how to graph the parent graph of a quadratic equation in standard form using a table
👉 Learn the basics to understanding graphing quadratics. A quadratic equation is an equation whose highest exponent in the variable(s) is 2. To graph a quadratic equation, we make use of a table of values and the fact that the graph of a quadratic is a parabola which has an axis of symmetr
From playlist Graph a Quadratic in Standard Form | Essentials
From playlist 3d graphs
Bruno Courcelle: Recognizable sets of graphs: algebraic and logical aspects
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Mathematical Aspects of Computer Science
This is Lecture 17 of the CSE373 (Analysis of Algorithms) course taught by Professor Steven Skiena [http://www3.cs.stonybrook.edu/~skiena/] at Stony Brook University in 2016. The lecture slides are available at: https://www.cs.stonybrook.edu/~skiena/373/newlectures/lecture15.pdf More inf
From playlist CSE373 - Analysis of Algorithms 2016 SBU
Bob Bosch - Connecting the Dots - CoM Dec 2021
If someone gives us a collection of points, how should we connect them? Should we try to pair them up? Should we try to join them together to form a single loop? Should we try something else? And once we’ve decided on the rules we’re going to follow, how should we go about trying to achiev
From playlist Celebration of Mind 2021
Robert Bosch - Figurative Subgraphs - G4G13 Apr 2018
Given a graph (a collection of dots and line segments connecting certain pairs of dots) and a target image, we form subgraphs that look like the image.
From playlist G4G13 Videos
Can You Solve The Knight On A Chessboard Riddle? Math Olympiad Problem
Alice and Bob are playing a game. Alice starts by placing a knight on the chessboard. Then they take turns moving the knight to a new square (standard chess rules apply: the knight moves in an "L" shape). The first player who cannot move the knight to a new square loses the game. Who wins
From playlist Math Puzzles, Riddles And Brain Teasers
Jeremiah Farrell - Puzzles and Games for the Blind - CoM Apr 2021
My presentation will describe several items I have had success with for blind students all over the United States. I discuss ideas which teachers of the blind can implement, because of the use of tactile props, different shapes replacing traditional colored pieces, and so on. Many classica
From playlist Celebration of Mind 2021
Stanford Lecture: Don Knuth—"Hamiltonian Paths in Antiquity" (2016)
Computer Musings 2016 Donald Knuth's 23rd Annual Christmas Tree Lecture: "Hamiltonian Paths in Antiquity" Speaker: Donald Knuth About 1850, William Rowan Hamilton invented the Icosian Game, which involved finding a path that encounters all points of a network without retracing its steps.
From playlist Donald Knuth Lectures
Stanford Lecture: Don Knuth—"Hamiltonian Paths in Antiquity" (2016) (360 Degrees)
Computer Musings 2016 Donald Knuth's Christmas Tree Lecture (360 degrees): "Hamiltonian paths in Antiquity" Speaker: Donald Knuth About 1850, William Rowan Hamilton invented the Icosian Game, which involved finding a path that encounters all points of a network without retracing its step
From playlist Donald Knuth Lectures
Simple Definition of Petersen Graph | Graph Theory
We introduce the Petersen graph via a combinatorial definition using subsets. This definition of the Petersen graph is easy to understand and useful for proving various results about the graph. #GraphTheory A Petersen graph's vertices can be labeled by all two element subsets from a five
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)
Princess in the Castle | A puzzle with a visual solution | 3blue1brown SoME1 submission
A math puzzle made easy with a fantastic visualization! This video was uploaded as part of the 3Blue1Brown Summer of Math Exposition (SoME1) Contest. Link to contest: https://www.3blue1brown.com/blog/some1 For discussion on extensions, see: https://checkmyworking.com/misc/princess-castl
From playlist Summer of Math Exposition Youtube Videos
Learning how to graph and determine characteristics of a quadratic using vertex formula
👉 Learn how to graph quadratics in standard form. A quadratic equation is an equation whose highest exponent in the variable(s) is 2. To graph a quadratic equation, we make use of a table of values and the fact that the graph of a quadratic is a parabola which has an axis of symmetry, to p
From playlist Graph a Quadratic in Standard Form | ax^2+bx+c