A Geometric Structure
We will consider a structure for creating a configuration of lines and
points (a graph).
Conditions for a Geometric Structure
-
Each line will have exactly three points.
-
Any two lines will have exactly one point in common.
-
Any two points determine a unique line.
-
There are at least two lines.
Here are two examples:
Notice that each structure has 7 lines and 7 points!
| C |
E |
G |
|
|
G |
B |
C |
| B |
D |
G |
|
|
G |
D |
F |
| A |
F |
G |
|
|
G |
A |
E |
| A |
D |
E |
|
|
C |
E |
D |
| B |
F |
E |
|
|
D |
A |
B |
| A |
B |
C |
|
|
C |
A |
F |
| D |
F |
C |
|
|
B |
F |
E |
Interesting....these were the same arrangements used for the chord
and committee stuctures.
But the question we have now is:
Are there any of these geometric
stuctures that have more or less than 7 lines made from 7 points?
That is, is there some special
relation between these geometric structures and the number 7?