Another Geometric Structure
We will consider a structure for creating a configuration of triangles
and their vertices.
Conditions for a Geometric Structure
-
Any two triangles will exactly one point in common.
-
Any two points determine a unique triangle.
-
There are at least two triangles.
Here are two examples:
Notice that each structure has 7 triangles and 7 vertices!
| 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... the question we is still:
Are there any of these geometric
stuctures that have more or less than 7 triangles made from 7 vertices?
That is, is there some special
relation between these geometric structures and the number 7?