Smallest finite projective Plane



The smallest finite projective plane and most important object is the Fano plane, which consist of 7 points and 7 lines.  In a drawing, the lines should look like circles.  But such a drawing is impossible, even in other dimensions.  Just one line can be drawn like a circle and the others must be just straight point connectors.  Every such line/circle connects exactly 3 points.


There are 3 known Fano Plane drawings.  Each drawing has a triangle outside and the single small circle inside.



1. The mathematical drawing of the Fano Plane

Obviously this picture has 7 points, 6 straight point connectors, and 1 circle, i.e. these point combinars are 6 lines.



2. All-seeing Eye on 1 US $ Bill


A basic Fano-like drawing is also used on the 1 US $ bill, on top of a beheaded pyramid and should mean an all seeing eye,





The eye surroundings above and below together (2 semi-circles) have a meaning of a single circle.  The enclosed eye just means the central dot.  If all existing points are connected by lines, one gets to 7 points and 7 lines, so the drawing becomes a Fano plane.



3. The Deathly Hallows in Harry Potter, Volume 7


The Fano plane is also used in the movie Harry Potter volume 7, the Deathly Hallows.



In this drawing the point in the center must be added and finally all points and lines must be completed.



The Fano Plane in the 2nd Matrix


The programmer for the 2nd of 4 matrix programs was Gitler.  As his system became more and more life-destructives, he was able to convince his gang that all living parts would be based on whatever kind of Fano planes.


As life is infinite within 7 dimensions, no living part was hurt after his invention.  So the Allah-adores were fucked off.