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