As far as the mathematical theorems refer to reality, they are not sure, and as far as they are sure, they do not refer to reality.
—
Albert Einstein (1879–1955)
Exercise 1.24.
As far as the mathematical theorems refer
to reality, they are not sure, and as far as they are sure, they do not refer
to reality.
—Albert Einstein (1879–1955)
Exercise 1.24. Show the matrix model for Fano’s Geometry is isomorphic to the two models given in Section 1.2.
points lines A, B, C, D,
E, F, GADB, AGE, AFC, BEC,
BGF, CGD, FDE
| P1 | P2 | P3 | P4 | P5 | P6 | P7 | |
| l1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 |
| l2 | 1 | 0 | 0 | 0 | 0 | 1 | 1 |
| l3 | 1 | 0 | 0 | 1 | 1 | 0 | 0 |
| l4 | 0 | 1 | 0 | 1 | 0 | 1 | 0 |
| l5 | 0 | 1 | 0 | 0 | 1 | 0 | 1 |
| l6 | 0 | 0 | 1 | 1 | 0 | 0 | 1 |
| l7 | 0 | 0 | 1 | 0 | 1 | 1 | 0 |
Set up a 1-1 correspondence between the points and lines by assigning A to 1 to P1, B to 3 to P2, C to 5 to P4, D to 2 to P3, E to 4 to P6, F to 6 to P5, and G to 7 to P7. (You should check that the lines also correspond.)
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© Copyright 2006 - Timothy Peil |
