FB_init

Wednesday, November 26, 2008

How Not To Feel Pain At The Dentist

Before my last visit to the dentist, I wanted to know the number of the tooth that was hurting. I found out that there was a certain Universal Numbering System . Great! When I got there, I told him that number 3 was hurting. Well, it happens that the Universal system is not so universal. They told me that tooth was number 16. I was confused, because I thought that if it were number '16', the maximum would be 18 since there are 2 teeth after it, and 18 x 2 = 38, but we only have 32 teeth. So I knew something was wrong with the notation. In fact, they told me that this "Universal" system is used in the U.S. but the rest of the world uses the FDI World Dental Federation notation.

"Universal":

Permanent Teeth
upper left upper right
16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
lower left lower right


FDI:
upper right upper left
18 17 16 15 14 13 12 11 21 22 23 24 25 26 27 28
48 47 46 45 44 43 42 41 31 32 33 34 35 36 37 38
lower right lower left

(As you can see, right and left are mirrored in the tables)

Since I like Math, I began to search for an injective function from the Universal number to the FDI. So let's begin.

The FDI divides the teeth in quadrants. The quadrant may be given by



So we multiply it by 10 to shift the number left



Sometimes the numbers increase in the quadrant, other times they decrease. So we need to alternate by quadrant:



For odd quadrants let's pick the constant 8. And for even quadrants, the constant zero:



Now let's have something varying up and down:



Now to get the unit in the FDI system, from 1 to 8, we use the expression:



So, for the final formula we have:



Next time you go to the dentist, just try to reconstruct the formula to take your mind off the pain.

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