SmartPhone Geometry. Jonathan Choate Groton School [email protected] www.zebragraph.com. WHAT’S COMING?. Why are they called Smart Cell phones? How do you figure out how far you are from home using your latitude and longitude?
In order to serve the most customers the average cellsize is roughly 10 square miles. Each cell can service approximately 70-80 users at once because - Each cell is alloted 832 frequencies or channels - 42 channels are used for control issues- 790 are available for voice and data transmission.- Cell phones are duplex devises and need 2 frequencies per user unlike walkie talkies.
- 395/7 is roughly 76 so for each cell there are 76 sets of frequencies so each cell can handle 76 users at once.
- In a 7 cell cluster, 532 people can be handled.
Cell Area =
Let Ru = Distance between two cells with same set of
frequences. Using the law of cosines, you get
Let Rc be the cluster radius. Rc = AB =AD=DE and AE = Ru,
Therefore, C = 7
This shows that the possible cluster configurations contain i2 + j2 +ij cells where i and j are the displacements used to get to the nearest cell that can have the same set of frequencies.
9 + 4 + 6 = 19
<PCG = your latitude
R is the radius of the Earth
R = 3,959 Miles
Z= GP = R sin(lat)
X= PQ = PC sin(long)
Y = CQ=PC cos(long)
Activity 2. How do you calculate the distance between two points on the surface of the Earth given their latitude and longtitude? How far are you from home?
Tower maps can be found at http://www.towerco.com
Method 1: Trilaterization
2. Reflect G about the angle bisector of angle BAC creating point G1. Create ray AG1 and hide the angle bisector.
3. Repeat for vertices B and C, creating
rays BG2 and CG3.
4. Rays AG1, BG2 and CG3 are concurrent at the Symmedian point S
Activity 4: Construct the Vornoi Regions for the five towers shown on the diagram below.
equidistant from F and D form a parabola.
Step 1. Open a file and select the graph option. Plot the points which represent the tower locations
Step 2. Construct a vertical line with a movable point D. Through D construct a
horizontal line. This will serve as a movable Directrix.
Step 3. Create the function which will plot the parabola with the upper most tower point and plot it.
Tracking GPS Sattelites
Cell and Cluster Design Information
Some Interesting Problems
Best GPS Information
Tower Location Maps