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Rodin aerodynamics - Free-Energy Devices

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Here is a fragment, with rows and columns numbered:<br />

1 2 3 4 5 6 7 8 9 1 1 1 1 1 1 1 1 1 1<br />

0 1 2 3 4 5 6 7 8 9<br />

1 6 6 9 3 3 9 6 6 9 3 3 9 6 6 9 3 3 9 6<br />

2 5 1 2 4 8 7 5 1 2 4 8 7 5 1 2 4 8 7 5<br />

3 2 1 5 7 8 4 2 1 5 7 8 4 2 1 5 7 8 4 2<br />

4 9 6 6 9 3 3 9 6 6 9 3 3 9 6 6 9 3 3 9<br />

5 7 5 1 2 4 8 7 5 1 2 4 8 7 5 1 2 4 8 7<br />

6 4 2 1 5 7 8 4 2 1 5 7 8 4 2 1 5 7 8 4<br />

7 3 9 6 6 9 3 3 9 6 6 9 3 3 9 6 6 9 3 3<br />

8 8 7 5 1 2 4 8 7 5 1 2 4 8 7 5 1 2 4 8<br />

9 8 4 2 1 5 7 8 4 2 1 5 7 8 4 2 1 5 7 8<br />

1<br />

0<br />

3 3 9 6 6 9 3 3 9 6 6 9 3 3 9 6 6 9 3<br />

1<br />

1<br />

4 8 7 5 1 2 4 8 7 5 1 2 4 8 7 5 1 2 4<br />

1<br />

2<br />

7 8 4 2 1 5 7 8 4 2 1 5 7 8 4 2 1 5 7<br />

1<br />

3<br />

9 3 3 9 6 6 9 3 3 9 6 6 9 3 3 9 6 6 9<br />

1<br />

4<br />

2 4 8 7 5 1 2 4 8 7 5 1 2 4 8 7 5 1 2<br />

1<br />

5<br />

5 7 8 4 2 1 5 7 8 4 2 1 5 7 8 4 2 1 5<br />

1<br />

6<br />

6 9 3 3 9 6 6 9 3 3 9 6 6 9 3 3 9 6 6<br />

1<br />

7<br />

1 2 4 8 7 5 1 2 4 8 7 5 1 2 4 8 7 5 1<br />

1 1 5 7 8 4 2 1 5 7 8 4 2 1 5 7 8 4 2 1<br />

8<br />

1<br />

9<br />

6 6 9 3 3 9 6 6 9 3 3 9 6 6 9 3 3 9 6<br />

Imagine the surface of the torus as a matrix, starting at the element t1 1, which is in the<br />

upper left corner: a 6. The first subscript is the row, and the second is the column.<br />

For the 8154 torus, the following conditions hold:<br />

t1 x = e [30]<br />

where t1 x refers to the first row of the matrix.<br />

(Taking e1 as the first element of the matrix is arbitrary. We could have taken any<br />

element in e, d, or b as the first element, and still have been able to construct the<br />

following formulae. You can see this is so because e1, d1, and b1 all appear in the first<br />

column in some row (look at rows 14 and 18 for d and b.) In fact there is no reason to<br />

start with the first element of either of these three series, since there is a row starting with<br />

41

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