Question

Fano's Geomety: prove each point is on exactly three lines

Answer 1

Axiom1: There exists at least one line
Axiom 2: There are exactly three points on each line
Axiom 3: Not all points are on the same line
Axiom 4: There is exactly one line on any two distinct points
Axiom 5: There is at least one point on any two distinct lines

Answer 2

Model

Answer 3

I feel your pain. even I have to prove something only it deals with functions :(

Answer 4

Proof: by theorem 2 we know there exists exactly 7 points and 7 lines. By axiom 3 there are three points to each line. Thus there can only exists three lines on each point. QED

Answer 5

dose that work as a proof

Answer 6

probably not :(

Answer 7

@wio do you know this?