Sacred Geometry
8 This topic may come as a complete surprise, but once you start to learn more about some of the surprising features of certain numbers and geometry, you ll start to realise that there is much more to it than meets the eye.
2If you have read the contemporary novel by Dan Brown, The Da Vinci Code, then you will have some familiarity with many of the following topics. 3Though it's a fictional story, many concepts of sacred geometry and numbers are portrayed with reasonable accuracy.
4Mathematics already has a profound elegance to it, but to the spiritual seeker, you can find a bizarre array of repetitions and coincidences that point to a divine power once you start to see beyond the surface. 5Could these things point to a single Creator, or do they just reflect a natural state of things that gravitate in a certain direction without a planned design? 6Either approach is just as intriguing.
7This succinct quote from Dr. Stephen Marquardt sums up the nature of mathematics and how it creates the foundation of all living things:
“All life is biology. All biology is physiology. All physiology is chemistry. All chemistry is physics. All physics is math.
The Fibonacci Series
8One of the foundational concepts in sacred geometry is the Fibonacci series. 9Without overburdening you with the mathematics, it is a sequence of numbers in which each digit is the sum of the two previous numbers. lOIn other words:
1,1,2,3,5,8,13,21,34,55,89 ...
11At first glance, it simply looks like a pattern of numbers, but there is a greater depth to this pattern to the point where it is almost uncanny.
12If you create a set of squares, each measuring a Fibonacci number on a side, it looks like this:
13And if you then draw a curve through each square, you get this spiral:
14This spiral is remarkable because it is seen throughout nature, created with amazing mathematical accuracy. 15Many spiralled sea shells create this pattern, and you can also see it in the arrangement of seeds in a sunflower head, the shape of a flowering artichoke and how a fern will unfurl itself. 160n a much larger scale, spiral galaxies form this design with their arms.
17A spiral created with Fibonacci numbers is very similar, but not identical, to another mathematical spiral known as the golden spiral. 18The differences are not relevant here, but please be aware of the two variations.
19Though the series is interesting in itself, I encourage you to look further into the wonders created by the mathematics.
Golden Ratio
20Also known as the Divine Proportion, this figure is symbolised by the Greek letter phi (φ). 21Numerically, the ratio is 1.61803... (the number is irrational and continues indefinitely) and this proportion is also seen throughout nature, and has been involved in many great works of art and architecture over the centuries. 22Explaining this is going to be a little tougher than the Fibonacci series, but as long as you understand the general idea, you'll be fine. 23Here is a graphic representation:
24A divided line that is in the Golden Ratio will have its segments (a and b in this case) proportional to each other, as the total length is in proportion to a. 25To put that another way, b times 1.61803 equals a, and a times 1.61803 equals the sum a+b.
26It is related to the Fibonacci series in that the ratio between each number in the sequence is in a Golden Ratio when compared to the previous number (or at least, very close to phi). 27If you look at the Fibonacci numbers given in the previous section, 89/55 = 1.618618 and 34/21 = 1.619047 which shows a clear relationship to phi though it is not exact.
28What is special about this ratio is that we are inexplicably drawn to it and it seems to represent an ideal form of beauty, which is why it appears so frequently in art. 29We also see phi very frequently in the facial structure of an attractive person.
Art and Architecture
30Many large and enduring architectural constructions have prominent examples of the Golden Ratio within their designs, though it is not something you will consciously be aware of. 31The great pyramids of Egypt, the Greek Parthenon, the Great Mosque of Uqba and the cathedral of Notre Dame are just a few examples. 32Paintings have also been found to include many instances of the Golden Ratio, most notably the works of Leonardo Da Vinci. 33In fact, he warrants another section all on his own below.
34Were these ratios worked into both artwork and buildings intentionally or is the human mind simply drawn toward these mysterious proportions without a conscious thought?
35To wax religious for a moment, you can even find phi in the Bible. 36The measurements given in the book of Exodus for the Ark of the Covenant (the chest to hold the original Ten Commandment tablets) are two and a half cubits long, a cubit and a half wide and a cubit and a half high . 37The ratio between length and the other two sides is 1.666, which is close to phi. 38The measurements given for the construction of Noah s Ark is 50 by 30 cubits, which also yields a ratio of 1.666. 39Even if you don t consider that close enough to phi, it is still curious that the measurements would be so closely related to each other in proportions. 40Is this evidence of a connection between the two arks ?
The Human Body
41This ratio exists in the human body – in more than one place. 42You can find examples of phi within the form of the face; people who are considered attractive are more likely to have their facial ratios closer to phi. 430ne example is the distance from the top of your head to the tip of your chin in relation to the width of your face (not including ears). 44It also exists in the ratio between the distance from the tip of your nose to the bottom of your chin and the distance from the centre of your lips to the bottom of your chin. 45There are too many possible ratios of phi to list without a long series of diagrams.
46Beyond the face, the distance from your elbow to the tips of your fingers is in the Golden Ratio with the distance from your elbows to your feet (when your arms are hanging naturally at your sides). 47That s not to say that all bodies are built in the same proportions, but the commonalities are remarkable.
Elsewhere in Nature
48Just as the Fibonacci series is seen in nature, you can find further examples of phi as well. 49The most dramatic one is within a beehive. 50For any thriving population of wild bees, the relation between the male and female bees is almost always 1.618 (with the females in the higher quantity of the two). 51You simply have to wonder about the way the universe works in order for this kind of precision to be found in what should be more random occurrences.
Leonardo Da Vinci
52You can t have a discussion of sacred geometry without mentioning Leonardo Da Vinci. 53Though his writings didn't mention the concept at all, it is found throughout his work.
54His most famous painting, the Mona Lisa, is a prime example of the Golden Ratio. 55Her face can be framed in a perfect Golden Rectangle, which is a two-dimensional version of the line segment shown above (where the long side is a+b and the short side is simply a). 56You can also see phi in the proportion of her head and neck when compared with her torso, as well as the ratio of distances between her chin and bottom lip and then her chin to the tip of her nose. 57They are the same ratios as mentioned above with regard to the perfect shape of the human face.
58Without some complex diagrams, there are too many examples to list. 59Suffice it to say, the Golden Ratio is well represented in this famous painting. 60Could this be why we find it to be so enigmatic?
61The Last Supper is another good example of the Golden Ratio. 62Many elements within the painting conform to these proportions, mostly in how the people are arranged with respect to the central figure of Jesus, and the positioning of the table within the room.
63You can also see a clear study in Golden Ratios in Da Vinci s Vitruvian Man drawing (a male figure with arms and legs outstretched, within a circle and a square). 64The entire purpose of this piece is to describe the proportions of the human form, though Da Vinci doesn t explicitly mention any specific ratios or mathematical constants. 65Though this piece is not specifically drawn with phi in mind, it does tie in nicely with Da Vinci s interest and knowledge of ratios and natural proportions.
66And while we are on the subject of Leonardo Da Vinci, it should be made clear that many of the claims about him in the above mentioned book, The Da Vinci Code, are inaccurate. 67Further, the evidence is not conclusive as to whether or not he was ever part of a secret society. 68Even so, when you see the many mathematical aspects of his work, you can t help but wonder what else was going on in the mind of this great man.
A Divine Force?
69Numbers alone might not inspire too much spirituality in some people, but others see the hand of a deity or divine energy in the universality of these concepts.