Sacred Geometry Text Image

Charles Gilchrist Mandala: Gallery #11

The Golden Mean Rectangle and The Phi Ratio - Part 2

(Fig. 1) A New Painting

#SG1101: 1.6180339 (State II): acrylic painting by Gilchrist © 2009

Author's note: since we created Gallery #11 and our interview #11 part one, Charles has created another major painting celebrating the Golden Mean Rectangle. This wonderful work is entitled, 1.6180339. It is a painting panel measuring 36 '' by 22.25" (Phi Ratio proportions) covered with deep and rich acrylic glazes.

A beautiful rich print is now available of this important Gilchrist Mandala. Charles personally creates and signs these prints. The watercolor paper size is 19 inches by 13 inches. The price is $59.95, plus $14.00 insurance, shipping, and handling anywhere in the continental USA..

The low wholesale price is:
One print - only $59.95 - plus $14.00 I/S/H
This print is shipped flat
See (Order Form)

An Interview With The Artist by Leslie Page - Number 11 Part 2


L.P. "It's beautiful Charles. Tell us about this painting, 1.6180339. Of course the title is the Phi Ratio to nine places, the Golden Mean proportions of the painting, but there's obviously a lot more going on in this piece."

C.G. "That's true, Leslie. This is a contemplative Mandala, based on Sacred Geometric Principles
(Fig. 1). The painting is designed as a cipher, a riddle. All the clues necessary to solve the puzzle can be discovered within the painting, but it would take a great deal of concentration to crack the code, and some additional understanding would really help."

L.P. "I don't know about that, Charles. It feels tremendously mysterious to me. I wouldn't even know where to start.

C.G. "You are very capable of understanding this riddle, Leslie. The key to any cipher is to begin with what you know and let that lead you. What do you recognize?"

L.P. "That makes sense. Yes, what is the first thing I recognize? The Golden Mean Rectangle is obvious, even dominate. The spiral is very beautiful, the way it ratchets around. And the colors are very satisfying Charles.... rich, organic."

C.G. "Thank you Leslie. That is a very good place to start and The Golden Mean - Phi Ratio is precisely what we've been talking about (interview 11 part one). What else do you see?"

Leonardo's man

L.P. "Leonardo's man is an obvious element (Fig 2 - below). I see the square and a number of circles in various sizes, but I have no idea what’s going on there. That's very interesting, mysterious.... even confusing."

C.G. "Try this, Leslie. When you don't see anything you recognize, just turn your eye somewhere else within the Painting."

L.P. "All right. Moving to the right I see a Flower Of Life, no, there's more. It's a dissolving veil, the FOL within a dissolving Nature's First Pattern
(Fig. 3 - below)."

The FOL and Nature's First Pattern

Detail - Fig 3

C.G. "Excellent Leslie. Believe it of not, you just demonstrated the entire process. If you continued to investigate this Mandala from known to unknown to known, you would eventually get the message. But I'm going to give you some hints that will speed the process.

The First Key

"The first Key? This Mandala is layered with three, superimposed Sacred Geometric Formulas. Each formula stands on its own as an unchanging geometric principle but, in this arrangement, each forms additional empirical geometric relationships to one another. These direct relationships prove the inseparable nature of Sacred Geometric principles. All of the archetypes and formulas of Sacred Geometry are omnipresent - omnipotent, interactive principles of this universe."

L.P. OK, I'll bite, three geometric formulas?

Three Sacred Geometric Formulas

C.G. "You already found them all, Leslie. I thought you realized that. They are the Phi Ratio formula (Fig. 4), The Flower Of Life formula with roots in the Nature's First Pattern formula (Fig. 5), and the formula for creating Leonardo’s equal circle and square (Fig. 6)."

L.P. "Now I'm lost again. Could I have another Hint?"


C.G. "Relax, you'll figure this out. Try this one. There is a classic Mandala (a square) that takes up the entire left side of the Golden Mean Rectangle. And the center of this Mandala is extremely important (Fig. 7). All three formulas are centered on that Bindu (the center point)."

L.P. "Yes, I see the Mandala, and I see the square is centered. All those additional lines and circles are also connected to that same center, at least in a symmetrical way. They must be various aspects of the three formulas. All right, now I'm starting to see it a little more clearly. If the center is really important, that little circle in the center must be part of the answer"

The Major Key

C.G. "Very Good, Leslie, and fast. Here is The Major Key. All three formulas share that same small circle at the center (Fig 8). But Let's just take one formula at a time. Where do you want to start?"

Detail - Fig. 8

The Formulas: #1: The Golden Mean - Phi Ratio formula

L.P. "In our earlier conversation (#11 part one) I was struck by the simplicity of the Golden Mean/Phi Ratio formula (Fig. 4) and I really understood that one. Let's start there."

C.G. "Great place to start. You've already perceived the Golden Mean proportions of the panting, and the spiraling rectangles. What else can you see.... relating to Phi?"

L.P. "The number (1.6180339) is strong, hanging just below the square and… I see it now, Charles. The same geometric formula
(Fig. 4 - above), is struck in red on Leonardo’s square (Fig 9 - below). Now I see the little arrows marking the three principle points. Wow, very interesting. I can clearly see the Golden Mean Rectangle - Phi Ratio formula in this Mandala. I must say my confidence is building a bit."

C.G. "That always helps. Now, look back to the FOL you found before, the one on the right side. Look for three blue circles."

The Formulas: #2: The Flower Of Life Formula

L.P. "Yes, I have them, three blue circles. The FOL is three circles high, I remember (Fig 3 - below). Now back to the formula. Wow, tree blue circles (Fig. 10 - below). How simple.... how direct. Why didn't I see that before? The three circles of the FOL are also centered in the Mandala."

Tangent Formulas (#1 and #2)

C.G. "Yes. Now, Leslie, you are very close to an important realization. Look at the geometric relationship between the outer circle enclosing the FOL and the red arc defining the Phi Ratio. They are tangent, they just perfectly touch."

L.P. "Let me look closer. You are right. They are tangent
(Fig 11). Interesting."

C.G. "That tangent proves a direct empirical geometric correspondence between the two formulas because both formulas share that same little circle in the center. I find that to be significant, but Let's discover the third formula so we can begin to tie them all together."

L.P. "Alright. I'm looking at Leonardo’s man in the square, Charles but there are a lot more lines here than were in the original
(Fig. 12 - below)."

The Formulas: #3: Square Equals Circle Formula

C.G. "Leonardo Da Vinci’s “Study Of Human Proportions,” is, in itself, a riddle holding several encrypted messages, including the Sacred Geometric formula that creates a circle and a square of equal perimeters (Fig 13 - Above). In figure 13, the blue circle of the formula equals Leonardo's original circle (the red one. Leonardo hid this important formula in his most famous drawing. This was a very important sacred formula of the ancient master builders. In Leonardo’s time, as before, this secret was not shared openly. In fact it was, as with many other esoteric secrets, guarded with profound zeal. The additional Lines you see are also hidden in Leonardo’s drawing. This 900 parts grid, is suggested by the various hash marks across the body and across Leonardo’s proportional reference line lying just below the square (see Fig 13 - above). Leonardo’s famous masterpiece traces directly to the Dionysian architects and the work of Vitruvius, the ancient and famous Italian master builder (Fig. 14 - below)."

L.P. "Charles, I know these graphics (Figs. 13 & 14) are from your series on Leonardo’s “Study Of Human Proportions.” I remember you telling me about the series but I really had no idea they were so esoteric. I see Fig. 13 (above) illustrates the actual formula and is essentially duplicated in this new painting. I see this now.... very clearly."

C.G. "Exactly! Repetition is a natural aspect of learning Leslie. You look at something a thousand times and then, and suddenly, you finally really see it.

L.P. "Well, I see it now. Better late… as they say. In this case it is the green circles that reveal the formula and the larger circle is tangent to those four green circles. Very interesting, Charles. I am really beginning to get this thing."

Empirical Relationships

C.G. "Now you have the tree basic formulas. See if you can find the empirical relationships between them."

L.P. "All right. If I understand your premise, we are looking for empirical, scientific proof of an interconnected relationship, or relationships, between the three formulas. And the little circle in the center is The Keystone."

C.G. "Exactly! I like your very precise allegory. The small center circle is very much like a conceptual keystone."

L.P. "You say all three formulas share that exactly sized little circle at the center?
(Fig 8 below)"

C.G. "Yes

L.P. "All right. Let's start from what we know. I see the most obvious connection. Leonardo’s formula automatically creates the small circle. It is tangent to the four larger green circles around it. That would firmly connect it to that formula."

C.G. "Correct. One down, two to go."

L.P. "I can see the FOL more clearly now, and I can see NFP in there to. I like the way that NFP is moving through the piece in a very subtle way, stronger at the top, those overlapping circles above the man’s head
(Figs. 8 & 10). I can feel a relationship with the little circle but I can't quite get it. Help me out here, Charles. I almost have it."

L.P. "Yes you do Leslie. There are nine hundred squares in the grid held within Leonardo’s square (thirty units by thirty units), just like the drawing after Vitruvius (Fig. 14 - above). Use that grid Leslie, to measure the little circle."

L.P. "Let's see, the little circle measures six units across the diameter. How interesting. Now I see it. And the blue circles of the FOL formula are exactly twice as large, with a twelve-unit diameter. Wow, fascinating. That is definitely empirical geometry because NFP is a transcendental relationship. It (NFP) naturally magnifies by 1.5 and divides by one half into ever larger and smaller circles, respectively. I've always loved that aspect. This proves a direct relationship between Leonardo’s equal square and circle formula and this FOL formula."

C.G. "Yes, it does Leslie. No question about it. Now let's pull all three formulas together. Connect that little center circle to the Phi Ratio formula, and we'll have it."

L.P. "OK, I'm looking.... still looking. The little center circle is just there.... on its own. I don't see any direct connections to the Phi Ratio formula. It should be there...."

C.G. "Consider this, Leslie. Would you say there is a direct relationship between our little circle and the size of Leonardo’s square?"

L.P. "Yes, of course. That's obvious."

C.G. "Then make this connection. The size of Leonardo’s square is equal to the square of our Phi Ratio formula. In fact, they are the same square....and so....."

L.P. Wow! I see it now. Of course, the squares connect all three formulas. But Charles, I tip my hat to anyone capable of deciphering this Mandala mystery on his own. I'm still not sure it's possible."

C.G. "It's definitely possible. I discovered this reality and I'm just an artist. But I have a question for you, Leslie. Now that you understand this geometry a little more, do you get more out of this Mandala?"

L.P. "Of course, but quite frankly Charles, I don't really think you need to understand the math of these geometries to enjoy this Mandala. I always liked it on its own. But yes, now I appreciate this Mandala on deeper levels. This Mandala is a very serious meditation, for sure. Sum it up for us, Charles."

The Last Word

C.G. "I see Leonardo Da Vinci is the quintessential example of Renaissance Man, and it is obvious he was privy to extremely esoteric information. In his exquisite and famous little drawing 'Study Of Human Proportion,' after Vitruvius, Leonardo was illustrating the esoteric fact that the entire Universe, Including The Human Body, is designed in Sacred Geometry.

This Mandala (1.6180339) is a study in left and right brain thinking, a play between the projective and the receptive. It is a celebration of the beauty and perfection of Sacred Geometric principles, and also backs up Leonardo's understanding with empirical proof of the interrelated realities of three Sacred Geometric Formulas. These three archetypes and formulas of Sacred Geometry are omnipresent, omnipotent, interactive principles of this universe. Sacred Geometry is The Architecture Of The Universe, and the Human Body is an exquisite manifestation of that reality. We are truly made in the image of GOD.

(Fig. 1) The Print

1.6180339: a Fine Arts Print by Gilchrist © 2003

A beautiful rich print is now available of this important Gilchrist Mandala. Charles personally creates and signs these prints. The watercolor paper size is 19 inches by 13 inches. The price is $59.95, plus $14.00 insurance, shipping, and handling anywhere in the continental USA..

The low wholesale price is:
One print - only $59.95 - plus $14.00 I/S/H
This print is shipped flat
See (Order Form)

Additional Gilchrist Paintings related to "The Golden Mean"

#SG1102: Phi And Fibonacci Spirals

#SG1103: Transcendental Golden Mean Rectangle (State II)

#SG1104: Map Of Time

#SG1105: Phi Snake

The low wholesale price is:
One print - only $59.95 - plus $14.00 I/S/H
This print is shipped flat
See (Order Form)

Sacred Geometry Text Image

Sacred Geometry HomeAbout Gilchrist

Sacred Geometry an Introduction
Sacred Geometry Coloring Book

About Mandalas
Charles Gilchrist MandalasEnnis Court Mandalas

Order Form

Copyright © 2012 by Charles Gilchrist
All Rights Reserved, World Rights Reserved
Reproduction in whole or in part in any form or medium without express written permission is prohibited.

Webmaster: swagzSTUDIOZ