PPT-Section 1.2: Finding Euler Circuits

Math for Liberal Studies When does a graph have an Euler circuit This graph does not have an Euler circuit This graph does have an Euler circuit When does a graph have an Euler circuit. N. etworks and Graphs. Euler Paths and Circuits. Can You draw this figure without lifting you pencil from the paper?. The original problem. . A resident of Konigsberg wrote to Leonard Euler saying that a popular pastime for couples was to try to cross each of the seven beautiful bridges in the city exactly once -- without crossing any bridge more than once.. . 1707-1784 . Leonhard Euler was born in Basel, but the family moved to . Riehen. when he was one year old and it was in . Riehen. , not far from Basel, that Leonard was brought up. Paul Euler, his father, had some mathematical training and he was able to teach his son elementary mathematics along with other subjects.. By Katherine Voorhees. Russell Sage College. April 6, 2013. A Theorem of Newton. Application and significance . A Theorem of Newton derives a relationship between the roots and the coefficients of a polynomial without regard to negative signs.. When an Euler path is impossible, we can get an approximate path. In the approximate path, some edges will need to be retraced. An . optimal approximation. of a Euler path is a path with the minimum number of edge . = number of vertices – number of edges + number of faces. Or in short-hand,. . . = |V| - |E| + |F|. where V = set of vertices. E = set of edges. F = set of faces. of a series of preparatory lectures for the Fall 2013 online course MATH:7450 (22M:305) Topics in Topology: Scientific and Engineering Applications of Algebraic Topology. Target Audience: Anyone interested in . 24-28 October 2016. 11. Graphs and Trees 1. . Graphs: Definitions. . Trails, Paths, and Circuits Matrix Representations Isomorphisms. 1. . . Graphs: Definitions . Trails, Paths, and Circuits Matrix Representations Isomorphisms. Lesson Plan. Euler Circuits. Parking-Control . Officer Problem. Finding Euler Circuits. Qualifications: Even Valence and Connectedness. Beyond Euler Circuits. Chinese Postman Problem. Eulerizing. a Graph. , Paths, . and Schedules. Euler and . Königsberg. Terminology. Network – a group or system of interconnected people or things. Graph – a mathematical structure consisting of vertices and edges. Vertices – points on a graph that may represent locations, people, or anything of interest. Exploration. Is it possible to draw this figure without lifting your pencil from the paper and without tracing any of the lines more than once?. Leonard Euler. This problem is an 18. th. century problem that intrigued Swiss mathematician Leonard Euler (1707-1783).. Task 1. 17/04/17. Remember to follow @. HuttonMaths. T. his term we will take a look at some of the most famous and notable Mathematicians to have ever lived.. You will hopefully be able to learn a lot about the Mathematicians. . 1. Learning Objectives:. Know how to use graphs as models and how to determine efficient paths.. Modeling with graphs. Euler circuits. Degrees of vertices and Euler’s Theorem. Chapter . 7 Graph Theory. ” Graphs. Math for Liberal Studies. The Story So Far. Consider this graph. Does it have an Euler circuit?. The Story So Far. We count up the degree of each vertex, and find that B and E have degree 3. Ide. . dasar. . penggunaan. . teknik. . numerik. . untuk. . menyelesaikan. . persoalan. . fisika. . adalah. . bagaimana. . menyelesaikan. . persoalan. . fisika. . dengan. . karakteristik.