Some Ancient Mathematics

Gann was a an expert mathematician

For example:

2 points make a line which is one dimension
3 points make a triangle which is two dimensions
4 points make a tetrahedron which is three dimensions
5 points would therefore be linked to the fourth dimension

When Gann talks about the fourth dimension he is talking about the number 5. 5 is associated with the pentagon which is associated with the golden section, Phi, 1.618...:



Phi is important because 4/Pi ~ Sqrt(Phi) and 4/Pi represents the mathematical relationship that exists when squaring the circle (by length). 4/Pi~1.27 which is approximately 5/4, the musical ratio defining the major third in the diatonic scale. This is also approximated by (1+Sqrt(2))/2~1.207. In the following diagram, the black bold circle would have a diameter of (1+Sqrt(2))/2 if the 2 blue circles had diameters of 1 and Sqrt(2) so the black bold circle approximately circles the square (by area) of the blue square



This diagram contains a LOT of information if you study it carefully

If you square the circle by area then the appropriate number is Sqrt(4/Pi)~1.128 which is approximately 9/8, the musical ratio defining the major tone in the diatonic scale.

The number 5, the pentagon, the vesica, squaring the circle and music are all related, so whenever you come across one of these concepts, chances are, one or some of these other concepts might be related too

There are also links to be found between the dimensions

For example, what we see in 2 dimensions could be a projection of something that really exists in 3 dimensions, like a shadow cast on a wall. The shadow is a 2-dimensional (often skewed) representaiton of what - in reality - is a 3-dimensional object

The picture below shows an icosahedron as 8 triangles. This is a special 2-dimensional projection. In 3 dimensions it takes 20 triangles to form an icosahedron