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GIMNASIO FONTANA MATH – MIDDLE SCHOOL 2010 APPLICATION OF AREAS CELLPHONE NETWORK DESIGN Objectives • • • • Design a cell phone network using polygons. Identify the characteristics of polygons that can be tessellated. Practice and review the area addition concept. To know and recognize statistical data and the poblational distribution of Bogotá

Background The name of cellular phone comes fromthe way how the networks in which this devices work. A cell phone network is composed by coverage cells, each cell has an antenna which is in charge of all the cell phones on that area, what means that the a cell phone on that area connects to the network through that antenna.
Fig. 1

This is an image from the Wikimedia Commons. Author: Andrew pmk

In Fig. 1 is shown the most popular way oforganizing the cells of a mobile phone network. However, this pattern or shape of the cell is drawn deliberately by the network designer; in this case (Fig. 1) the pattern used is a regular hexagon. In Fig. 2 are shown the parts of a cell phone network antenna, if you notice, the six antennas in the upper side are the ones in charge of making the pattern, and the circular antenna is in charge ofconnecting this cell with another. Therefore, it is possible to draw the pattern that the designer wants.

Fig. 2 Image from Flikr, CC

Cuando se diseña una red de telefonía celular es importante la cantidad aproximada de usuarios que estarán conectados simultáneamente a cada antena y la idea es minimizar el número de antenas garantizando el servicio para todos.

Description If you could seea cell phone network from the sky, it would look very similar to a beehive (Fig. 1), every antenna has a cell and it is in charge of the mobiles on that area, a cell phone can only be connected to a unique antenna, so, the idea is to tessellate the patterns of every antenna. When you are designing a mobile network is important to take into account the approximate number of users that will beusing their cell phones at the same time in the same cell. The idea is to minimize the number of cells ensuring a quality service for all the users. In this exercise you will work to a new cell phone company that is going to start operations in Bogotá, they hired you to design a part of the network that they are going to employ. The aim of the company is to ensure to all Bogotá’s citizens service atthe same time and the communication will be perfect, unlike Comcel and Movistar in Christmas and other special occasions. All the antennas has a maximum number of users, for this exercise we will suppose that an antenna (cell) can hold 5000 users simultaneously, and our network can hold all the population that lives on your locality, so the size of the pattern depends of the temporal mean of usersand the restriction of no overlapping with another cell. Methodology • • According to your list number go to the webpage http://www.sdp.gov.co/www/section-2117.jsp, identify your locality, its boundaries, and the population. Then, go to the webpage http://mapas.bogota.gov.co/geoportal/, using the boundaries that you found and the area measuring tool find the area of your locality.

Identifythe minimum number of antennas that you need to use in order to ensure service to all the population in your locality. Calculate the maximum cell area that your antennas will have. Remember that the maximum number of users per cell are 5000.

Usign the grid provided design the pattern that will use your network (Draw at least 4 tessellated figures) and find the exact area of that pattern.From the area found estimate the frequency that your network will use. (Use the chart provided on the appendix A)

Print the map of your locality and using the scale draw the position of the antennas and its patterns.

Worksheet Locality: ______________________________ Population: ___________________________ Borders: North: ____________________________________________________________...
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