PPT Slide

(t+2) = 1

(t+2) = T + 2

2 2

(t+2) = T + 4 T + 4

3 3 2

(t+2) = T + 6 T + 12 T + 8

4 4 3 2

(t+2) = T + 8 T + 24 T + 32 T + 16

5 5 4 3 2

(t+2) = T + 10 T + 40 T + 80 T + 80 T + 32

6 6 5 4 3 2

(t+2) = T + 12 T + 60 T + 160 T + 240 T + 192 T + 64

7 7 6 5 4 3 2

(t+2) = T + 14 T + 84 T + 280 T + 560 T + 672 T + 448 T + 128

8 8 7 6 5 4 3 2

(t+2) = T + 16 T + 112 T + 448 T + 1120 T + 1792 T + 1792 T + 1024 T + 256

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Notes:

It turns out that the coefficients of the equation (t+2)**n tell us how many points, lines, squares, cubes, tesseracts, and in general how many sub-cubes there are in any N-space cube.