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Table 2 Calculation of the center of resistance the tooth apex in models (Average bold areas) according to the calculations obtained from coding C++ 

From: An expansion to the Nägerl’s theory of proportionality in reduced alveolar bone height models: a 3D finite element analysis

Points

Length of root in heathy model (apicoincisal) [mm]

Length of root in 3 mm alveolar bone loss (apicoincisal) [mm]

4.5 mm alveolar bone loss (apicoincisal) [mm]

1

0

0

0

2

0/48959

0/48959

0/48959

3

0/97919

0/97919

0/97919

4

1/4688

1/4688

1/4688

5

1/9584

1/9584

1/9584

6

2/448

2/448

2/448

7

2/9376

2/9376

2/9376

8

3/4272

3/4272

3/4272

9

3/9167

3/9167

3/9167

10

4/4063

4/4063

4/4063

11

4/8959

4/8959

4/8959

12

5/3855

5/3855

5/3855

13

5/8751

5/8751

5/8751

14

6/3647

6/3647

6/3647

15

6/8543

6/8543

6/8543

16

7/3439

7/3439

7/3439

17

7/8335

7/8335

7/8335

18

8/3231

8/3231

8/3231

19

8/8127

8/8127

8/8127

20

9/3023

9/3023

9/3023