Bring4th

Yes, I know 3/14 is considered pi day, but 7/22 is a better approximation. So happy pi day, v.2!

As students of the Law of One, I wonder if we might also consider calling this "archetype day," because maybe there's a relationship between the 22 archetypes, 7 each of mind, body, and spirit, and pi (~22/7).

In the context of the archetypes, Ra mentions the ankh, or crux ansata, several times. They say it contains mathematical relationships in coded form (55.14). Surely one of those relationships is the relationship between the circumference of a circle and its diameter, and maybe that's hinting at the relationship between the archetypes (22) and the densities (7).

Just some thoughts for the day... 7:22 is one of those numbers that always makes me happy when I notice it, much like 11:11 is for some.

I wonder if there is a phi day. The phi ratio has had much more importance in the geometry of everything than even pi.

Anyway, thanks for the reminder.

Though this topic would probably better fit in olio.

Why thank you! Nobody ever mentioned this holiday to me before now. What a lovely surprise! May you receive at least Pi times as many blessings of happiness as you share today.

(07-22-2010, 11:51 AM)βαθμιαίος Wrote: [ -> ]Yes, I know 3/14 is considered pi day, but 7/22 is a better approximation. So happy pi day, v.2!

Don't mean to burst your pi pie but they're actually the same in terms of approximation because 22/7 is 3.142857... so it's only good to two decimal places since pi is 3.14159...

From what I've read on the day, Europeans celebrate it on 7/22 because they tend to put the day before the month whereas in North America we put the month first, so our pi day for them would look like 14/3 and thus wouldn't be very pi-like, hehe. For them 22/7, even though a fractional approximation, is actually their best way of representing it.

Quote:As students of the Law of One, I wonder if we might also consider calling this "archetype day," because maybe there's a relationship between the 22 archetypes, 7 each of mind, body, and spirit, and pi (~22/7).

In this case, I would vote that it be March 8th, because March 7 is 3/7 (3x7 archetypes) plus 1 (The Fool/Choice) would make 3/7 become 3/8

Quote:In the context of the archetypes, Ra mentions the ankh, or crux ansata, several times. They say it contains mathematical relationships in coded form (55.14). Surely one of those relationships is the relationship between the circumference of a circle and its diameter, and maybe that's hinting at the relationship between the archetypes (22.) and the densities (7).

It IS quite interesting to me that the closest fractional approximation for pi is 22/7 which is another way of saying 3 and 1/7 (3x7 archetypes plus Choice). I haven't really looked into the ankh and its ratios but I have with the relationship between the Major Arcana and pi, so here's the brief explanation of my findings thus far.

Another way of seeing the makeup of a circle is to consider it in terms of "pi radians". For those who aren't familiar, a radian is an alternative way of measuring angles in a circle (instead of degrees) and is about equal to 57.2957 degrees. It's found by making a section where the arc length of the circle is the same length as the radius of the circle.



So what's the big deal with radians? Well, a circle is made up 6.28 radians, or in other words two pi radians because 6.28/2 = 3.14 = pi



The hexagon is the first regular polygon where it's radius is equal in length to its outer edges....a pentagon has larger edge vs. radius and a heptagon has a larger radius vs. edge, but the hexagon sits smack dab in the middle of them and has a perfect 1:1 ratio:



This relationship is seen by placing 6 circles around a center one of equal size and a variant on that idea is of overlapping circles such as in the "seed of life":



Considering all of the above we can see that a radian is just 2.7042 (60 - 57.2957) degrees smaller in its internal angles than one of the 6 equilateral triangles in the hexagon, and this is why there is the extra 0.28 in 6.28 radians of a circle.

The hexagon is a natural construction of circles, but what's so interesting about it is that it contains a central of equal size circle by default, and as explained above it's the only regular shape that can do so (5 circles could only fit perfectly around a smaller inner circle and 7 circles could only fit perfectly around a larger inner circle). Another interesting thing to consider is that 6 is the first "perfect" number and these are quite rare; perfect number being one whose divisors (except the number itself) add up the number, so for 6 this would be 1+2+3, the next perfect number being 28 with 1+2+4+7+14 = 28. Also, 6 is both 1+2+3 and 1x2x3...

Anyway, my main point in all of this is that the perfect ratio relationships of the hexagon are a kind of geometric constant of the universe (like pi), and I believe that this relates to the nature of Logos in that 7th density is the source of all the other densities and could be seen to revolve around it as in a hexagon made of circles. Also, in this light, in terms of chakras the 7th exists as a summary of the balances between the main 6 below it and so is similar to the stationary middle circle. This is also, IMhO, a reflection of the sevens seen throughout not only the Ra material but also so many other mystical/spiritual systems, 7 is cosmological number.

The archetypal mind is a natural part of the Logos and from what Ra says the most advanced and widely used system is that of the Major Arcana with 3 groups of 7 (or 7 groups of 3) which all tie into the 22nd Fool/Choice archetype. So, it's interesting that the circle, which naturally contains the Logoic hexagon (and thus the hidden 7), has the pi ratio inherent to it and pi's simplest fractional approximation is 22/7 which relates to the archetypes.

I hope that isn't too confusing. I know a lot of people are math-phobic (me too, to a certain extent) but it really is crucial to understanding the relationships that we see all around us

/:idea:

(07-22-2010, 12:05 PM)Gemini Wolf Wrote: [ -> ]I wonder if there is a phi day. The phi ratio has had much more importance in the geometry of everything than even pi.

It looks like there is, but there is some disagreement about what day it's on: http://www.goldenratio.org/phi_day.html

(07-22-2010, 02:26 PM)Questioner Wrote: [ -> ]Why thank you! Nobody ever mentioned this holiday to me before now. What a lovely surprise! May you receive at least Pi times as many blessings of happiness as you share today.

That's the spirit!

(07-22-2010, 03:13 PM)Poffo Wrote: [ -> ]Don't mean to burst your pi pie but they're actually the same in terms of approximation because 22/7 is 3.142857... so it's only good to two decimal places since pi is 3.14159...

Thank you Poffo, for your interesting post. Lots to think about. At the risk of quibbling, I will point out that 3.142857 is closer to 3.14159 than is 3.140000. Not by a lot, I'll grant you, but 22/7 is a slightly better approximation.

(07-22-2010, 03:13 PM)Poffo Wrote: [ -> ]The archetypal mind is a natural part of the Logos and from what Ra says the most advanced and widely used system is that of the Major Arcana with 3 groups of 7 (or 7 groups of 3) which all tie into the 22nd Fool/Choice archetype. So, it's interesting that the circle, which naturally contains the Logoic hexagon (and thus the hidden 7), has the pi ratio inherent to it and pi's simplest fractional approximation is 22/7 which relates to the archetypes.

I agree. It's fascinating and intriguing. Thank you for the hexagon graphic. I hadn't realized that a hexagon contains seven circles.

(07-22-2010, 10:25 PM)βαθμιαίος Wrote: [ -> ]

(07-22-2010, 03:13 PM)Poffo Wrote: [ -> ]Don't mean to burst your pi pie but they're actually the same in terms of approximation because 22/7 is 3.142857... so it's only good to two decimal places since pi is 3.14159...

Thank you Poffo, for your interesting post. Lots to think about. At the risk of quibbling, I will point out that 3.142857 is closer to 3.14159 than is 3.140000. Not by a lot, I'll grant you, but 22/7 is a slightly better approximation.

Yeah, you're right, but just barely! I'll be eating humble pie for dessert I always enjoy a good quibble

Quote:I agree. It's fascinating and intriguing. Thank you for the hexagon graphic. I hadn't realized that a hexagon contains seven circles.

You're welcome Look at any hexagonal lattice (beehive, tiling, clothing pattern,...) and you'll see this 6-around-1 quality stand out. I think it's a prime example of "beauty" in simple math.

Also of note is the fact that the hexagon in 2 dimensions represents what would be a cube in 3d, so what is 7 circles as the 2d hexagon is actually 8 spheres as a cube; 7 plus the octave. Number and archetype are tightly weaved.

/:idea:

(07-24-2010, 01:40 AM)Poffo Wrote: [ -> ]Also of note is the fact that the hexagon in 2 dimensions represents what would be a cube in 3d, so what is 7 circles as the 2d hexagon is actually 8 spheres as a cube; 7 plus the octave. Number and archetype are tightly weaved.

Can you explain further, or find a graphic illustrating this? How does a 2-D hexagon represent a 3-D cube?

I can help with that one.

A 3D cube as represented in a 2D flat picture:


A simplified picture of a 3D cube, using a single line to represent each edge of the cube, but with hidden lines removed (not being able to see through solid faces):


Just the outline of a cube, edges only, as if you connected a bunch of sticks to make a wireframe outline:


And without any contrast between the edges closer to us and those farther away:


Trace around the outside of that image: six sides, but with a variety of lengths and angles.

Notice that if we look at the cube directly on one of its corners, the perimeter outline is a hexagon:


A hexagon by itself:


So when we see a hexagon in a flat image, we have to ask, is it supposed to represent a flat hexagon, or the outline of a cube as seen from one corner of the cube?

(07-24-2010, 01:13 PM)βαθμιαίος Wrote: [ -> ]Can you explain further, or find a graphic illustrating this? How does a 2-D hexagon represent a 3-D cube?

I was just in the middle of my reply as I previewed it and saw that Questioner had just answered! Thanks Q.

/:idea:

Thanks, guys. What about this, then: "what is 7 circles as the 2d hexagon is actually 8 spheres as a cube; 7 plus the octave."

How do you fit 8 spheres into a cube -- two layers of four?

(07-24-2010, 01:50 PM)βαθμιαίος Wrote: [ -> ]Thanks, guys. What about this, then: "what is 7 circles as the 2d hexagon is actually 8 spheres as a cube; 7 plus the octave."

How do you fit 8 spheres into a cube -- two layers of four?

Exactly!

There are numbers in math called Figurate numbers, and this basically means that a specific number of similar units (like circles or spheres) can be arranged into a specific geometric shape without any left units over or missing. One of the simplest examples of this is the square numbers:

1, 4, 9, 16, 25, 49, ... All are _x_ , 1x1, 2x2, 3x3, ...

The cube numbers then are just the next dimensional level of the squares:

1, 8, 27, 64, 125, 216, ... All are _x_x_ , 1x1x1, 2x2x2, 3x3x3, ...

So the cube of 8 is composed of twice the square number 4, and the Rubik's cube is just a 3x3x3 = 27 micro cubes making up the whole macro cube.

Now, another set of figurates is the Centered Hexagonal, and 7 (as we've already seen) is the second of these:

1, 7, 19, 37, 91, 127, ...

If we bring that 7 (2d hexagon) into 3d it becomes 8. The 8th sphere of the cube is hidden behind the central circle in the 2d hexagonal structure of the seed of life below.:



So if you had a model cube made of 8 smaller cubes (or spheres) and aligned it so it looked like a regular hexagon, you would only see 7 while the 8th would be hidden behind the one directly facing you.

/:idea:

What a cool thread. Thanks everyone!