The Fellowcraft degree relates sequences of 3, 5 and 7 steps.
First we will introduce some visual interpretations of the 3, 5 and 7 steps. Then I will show you a profound relationship from the 345 triangle to these 3, 5 and 7 steps.
Look closely at the numbers to make sure you don't end up confused. Also make sure you read Masonic Geometry in the proper order.
You can easily see that the first three steps are related to the first 3 degrees of Freemasonry.
The five are related to the senses and the five orders or architectural columns.
The seven to the liberal arts and sciences.
You can begin to see how the numbers are never just a coincidence, and if you let them, they will show you how to understand them, and what step to take next.
The 53.13° is the source of the 3 and 5 in the sequence of 3, 5, 7 steps.
It's time to let the numbers lead the way, and trust they will reveal some more details.
Thinking outside the box, looking at the 53.13° tells us two very interesting things:
First, it's not just 3, 5, 7 to 9. The sequence actually begins at number 1.
You can see the 1 in 53.13°, where it would need to be. It's not just a coincidence.
Now we have attention on the entire sequence of odd numbers:
1, 3, 5, 7, ultimately to 9.
Secondly, and perhaps even more interestingly, this 53.13° angle in the 3 4 5 triangle reveals that 345 triangles, in this context, come as connected pairs.
It's not just 53.1°, it's 53.13°
There is a symmetry here, surrounding the number 1. What could this extra 3 be?
That last extra 3 is revealing a connection to another 345 triangle that is paired to this one.
The angle on each of these triangles is 53.13°.
Each triangle relates to the other via the 3.13° in the angle.
They are literally connected together with the values of 1 and 3.
They are wrapped around each other in an unseen dimension.
When paired up in this manner, the 3 and 3 sides join together, such that the number 33 becomes prominent as the central axis.
Most readers will be aware that this number is generally recognized as the highest degree conferred by Scottish Rite Freemasonry.
It is interesting how this double headed eagle mirrors the double 345 triangle.
If any of this is correct, we should find the double 345 triangle in other places.
I have studied many Masonic designs and found this hidden double 345 triangle.
My favorite is in this design by George Kenning.
What is amazing is that the double 345 triangles are invisible, but still defined by the objects in the drawing.
Look at how the columns themselves arise from the hyptenuse 5 of the triangles, and how each of the double triangles is associated with one of the ashlars of Freemasonry.
Better still are the endless thoughts that arise from these simple connections. Each of these columns has a number 3 next to it, relating again to the 33, and also relating each triangle to a particular columnal axis.
Here we actually see that the 345 triangle is connecting to the Perfect Ashlar via the Lewis at the location of this angle 53.13°.
I have found this double 345 triangle in many other places as well, and there is clearly a lot more that could be said, but this is merely an introduction. I will leave one final reference here.
The Earth and the Moon
John Michell, in The View Over Atlantis (1969), found the following proportions relating the earth to the moon, prominently featuring the double 3-4-5 triangle surrounding the moon.