Journal Planetary Triangles: Hypothetical Designs and Uses

[StoatCatcher]

Disclaimer: Everything you're about to see here in this series of posts is more of a theoretical proposal than a tried and true method of harnessing planetary influences. I am posting this here to get some feedback on the ideas presented and to know if my research is onto something.

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Part 1: Building the Triangles​

1.1 The "3x3" Triangle​

In order to build the magic planetary triangles properly let us first consider the design of the magic planetary squares themselves, using the square of Saturn as a stand-in for the basic theory. The square of Saturn, as many of you already know, is built as a 3 by 3 square containing nine smaller squares inside of it with the numbers 1 through 9 inside of each smaller square. The numbers of the square are arranged in the following manner:

What is interesting is that for every single X by X square that contains X² smaller squares it's possible tile together X² equilateral triangles in a similar grid to form a larger triangle that can fit every number of the original square inside of it.

But where do we put all the numbers? The particular arrangement of numbers in the original square has the interesting mathematical property of producing rows, columns and diagonals with three numbers each whose sum is always equal to 15.

• Row A: 4 + 9 + 2 = 15​
• Row B: 3 + 5 + 7 = 15​
• Row C: 8 + 1 + 6 = 15​
• Column A: 4 + 3 + 8 = 15​
• Column B: 9 + 5 + 1 = 15​
• Column C: 2 + 7 + 6 = 16​
• Diagonal A: 4 + 5 + 6 = 15​
• Diagonal B: 8 + 5 + 2 = 15​

I hold that, in order for our planetary triangle of Saturn to be valid, this mathematical grouping of numbers must be respected and emulated in the design. Specifically, we must group the numbers in trios that correspond to those of the magic square and still sum up to 15. I naturally started looking around to see if someone had done this before and found a paper that seemingly described what I was looking for on arxiv:

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. The solution they propose in that paper is that a magic triangle can be defined as a triangle that contains three central lines (horizontal line, upwards slope and downwards slope) that all intersect each other and sum up to 15.

Unfortunately, as you can see in the illustration, this leaves out three numbers at the edges of the triangle that not only won't add up to 15 but are also not one of the valid trios form the original triangle. It's easier to see the unused trio when you transpose their solution back into the magical square like this:

In my opinion this mathematical solution to the problem is not valid for this particular design of magic triangle where we are trying to fit all of the magic trios together. However, keep this idea of building a triangle with three lines of numbers in mind. It's actually going to help us build another type of magic triangle later, and it's going to be mathematically valid one.

But back to the problem of fitting all the nine digits inside this triangle grid we have. I decided to keep looking. Eventually I found what I will politely describe as a "messy" blog by a man named Steven H. Cullinane who seems to be a retired mathematician that posts about various ideas involving geometry, somewhat at random and with little context. But regardless, here's his take on the subject:

Since he seemingly just posts images with no context or explanation for them, at random, I have no idea how he got these solutions in the first place. But regardless, I like his "3x3 Magic Triangle" arrangement. It uses two rows of the square to create two overlapping triangles in the middle that are inside of a larger triangle. And all the numbers that are on opposite sides of the square are also on opposite sides of the triangle. I don't know if there's some deeper math at work here but it does seem to have some intuitive sense to it.

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You might be wondering "What about tracing a sigil by tracing a line from 1 to 9 just like in the square?" and the answer to that question is that the resulting sigil from trying to follow the path of the numbers is...a little underwhelming, actually. I do, however, see a downwards movement that starts at the top and spreads throughout the base of the triangle. This is significant because when we remove the lines and numbers from this triangle we end up with a structure that should be familiar to those who study Pythagorean ideas:

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There's a lot of symbolism with this figure but I just want to focus on the basic idea of energy coming from a singular point (the Monad, God, the One, pure potential) and reaching downwards through the levels of creation until it reaches the multiple points of the manifest world. This makes our planetary triangle act as some sort of circuit that is constantly pulling down the energy of the planet into our material world. Using this idea, we can actually reverse the orders of the numbers to make a triangle that sends energy out rather than receive it.

I'm going to call this particular magic triangle the "3x3" triangle from now on. Everything that I just detailed makes it feel just right to me and it gives interesting ideas for it's use that I'll elaborate on later. I especially like this concept of a planetary symbol that can be used to both receive energy and send energy away. But I'm getting ahead of myself.

I'm going to pause here as this post is already quite long. Do leave your thoughts and feedback below.