2014-2015 | Page 35

COMMENTS ABAUT BELS MATH DAYS... As BELS mathematics teachers, we try to encourage our students to enjoy math with projects, activities and games. We believe that mathematics is much more than just calculation. That’s why we organized the first BELS math days in our school. Hopefully see you next year. Serap HAKTANIR This was the first experience for our school to have a whole week celebrated as math days. There are a wide range of activities including competitions, presentations exhibitions carried out by student group all the time. We wish experience the same valuable days with our lovely students next year too. Reyhan SAĞLAM Pi is known as irrational number that the digits never end or repeat in any way. When you draw a circle with a diameter of 1, then the distance all the way around the edge of the circle will be pi which is 3,14159265… like all the around the world our school celebrated the pi day in 14th of march which resembles the numbers of pi. Thanks to 10th graders students that help to prepare this wonderful math atmosphere all around the school and special thanks to entire Math Department which has a big role in this week. I hope you had a great time. See you in next pi day. Hazal YILDIRIM 10-C Zeynep GÖKALP 10-C Ece VARLI 10-A Gökçe ÇELİK 10-A Hazal YILDIRIM MATHEMATICS DEPARTMENT CHINESE POSTMAN ALGORITHM APPLIED ON MY WAY TO SCHOOL In 1962, a Chinese mathematician who is Kuan Mei-Ko started to think about a postman who is delivering mail to a number of streets such that the total distance walked by postman was as short as possible. (Suffolk County Council) The aim of this idea was minimizing the total distance walked by the postman delivering mail. The issue is based on traversable graphs. A traversable graph is one that can be drawn without taking a pen from the paper and without retracing the same edge. When the conditions are provided, the graph can be used as a template for Eulerian trail. An Eulerian trail is a path which starts and ends at the same vertex and includes every edge just once. (Nuffield Foundation) Thus, if I can transfer the road of my school bus into a map, I may try to find the shortest way to use which prevents the time loss. I will call the vertices as nodes and I will call the edges between nodes as arcs. The shortest route can be found by the help of number of vertices. An Eulerian trail uses all arcs of the graph. For a graph to be Eulerian all the vertices (nodes) must be of even order which means that my school bus should find numbers of ways which are even numbers. Around all students’ houses, there should be even number of roads to apply the Eulerian trail on to my school bus’ route. If there are some odd vertices rather than even vertices such as 2 odd vertices then the graph is said to be semi-Eulerian. A trail can be drawn starting at one of the odd vertices and finishing at the other odd vertex. (Suffolk County Council) To decide the shortest route for my school bus, I will analyze the map of route of the bus. The map is given below in diagram 1. (Google Maps) Diagram 1: Map of the area which contains students’ houses As it can be seen on the map, blue dots are on the houses of 7 students. I will call each house as node and I will label them as e1, e2, e3, e4, e5, e6, e7 and e8. To apply the Chinese postman algorithm on my school bus’ route, I should draw the possible edges between nodes. Then, I will calculate the number of vertices (possible roads) that the school bus can use to reach the nodes (students’ houses). While I am calculating the shortest route for my school bus, I should consider the starting point of the bus. Our school bus takes off from our school, and after taking all students, the bus get backs to school again. Thus, the journeys should start and finish at the same point. To make calculations and draw the edges easier, I will convert the real map to a sketch. Diagram 2 shows the edges, nodes and starting point of journey below. THE CLAPPER 2014 - 2015 35