Perpendicular Bisectors and Pizza Delivery

I had a pizza craving. I was torn between ordering in and going to the place to get a bite. I order from Domino’s Pizza as their minimum amount for free delivery is lower than in other pizza places. 

I have never actually been to Domino’s Pizza in Kaiserslautern. A quick web search, and I realized there are two pizzerias in town owned by Domino’s Pizza. 

It was evident that a convenient choice would be the closest one. Then I boarded the next train of thought. Who delivers the pizza to my apartment? (See Figure 1) The perpendicular bisector of the line joining the two Domino’s pizza places would be the invisible divider between the areas to which the respective places delivered! I lived in the area covered by the parallel lines (also parallel to the bisector), passing through the two pizza places. It is essential to realize that the argument is still valid if you lived outside this zone.

Let’s say business is booming, and the owner decided to add a third pizzeria in town. You again need to draw perpendicular bisectors to define these pizza delivery zones (See Figure 2). Notice that no matter where the owner opens the third pizzeria, the three perpendicular bisectors always meet. The point of intersection is called circumcenter. The only exception is when the three pizza places are in a straight line. You can verify this for yourself if you follow the link https://www.mathopenref.com/trianglecircumcenter.html

Figure 2

To find pizza delivery zones for a higher number of pizza places, one has to draw perpendicular bisectors between each pair of points. Crystallographers use a similar concept in Physics to construct what is known as a Wigner-Seitz cell (See Figure 3, Image credits: Wikipedia).

Oh, I finally never ordered that pizza. As my thoughts drifted towards healthy living, I prepared a salad and had it for supper.

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