## The Golden Ratio

Many buildings and artworks reflect the Golden Ratio: the Parthenon in Greece, and many other classical buildings in Europe. But it is not really known if it was designed that way. Some artists and architects believe the Golden Ratio makes the most pleasing and beautiful shapes.

There is a mathematical ratio commonly found in nature—the ratio of **1 to 1.618**—that has many names. Most often we call it the Golden Section, Golden Ratio, or Golden Mean, but it’s also occasionally referred to as the Golden Number, Divine Proportion, Golden Proportion, Fibonacci Number, and Phi. Now, a Duke University engineer has found the Golden Ratio to be a compelling springboard to unify vision, thought and movement under a single law of nature’s design.

Golden rectangles are still the most visually pleasing rectangles known, according to many, and although they’re based on a mathematical ratio, you won’t need an iota of math to create one.

DesignMantic Blog details how to construct your own golden rectangle: If you want to use a golden rectangle in your own compositions, here’s how you can make that happen without any special tools or mathematical formulas.

- Begin with a square, which will be the length of the short side of the rectangle.
- Then draw a line that divides it in half (forming two rectangles).
- Draw a line going from corner to opposing corner of one of those halves.

Many buildings and artworks reflect the Golden Ratio: the Parthenon in Greece, and many other classical buildings in Europe. But it is not really known if it was designed that way. Some artists and architects believe the Golden Ratio makes the most pleasing and beautiful shapes.

There is a mathematical ratio commonly found in nature—the ratio of **1 to 1.618**—that has many names. Most often we call it the Golden Section, Golden Ratio, or Golden Mean, but it’s also occasionally referred to as the Golden Number, Divine Proportion, Golden Proportion, Fibonacci Number, and Phi. Now, a Duke University engineer has found the Golden Ratio to be a compelling springboard to unify vision, thought and movement under a single law of nature’s design.

Golden rectangles are still the most visually pleasing rectangles known, according to many, and although they’re based on a mathematical ratio, you won’t need an iota of math to create one.

DesignMantic Blog details how to construct your own golden rectangle: If you want to use a golden rectangle in your own compositions, here’s how you can make that happen without any special tools or mathematical formulas.

- Begin with a square, which will be the length of the short side of the rectangle.
- Then draw a line that divides it in half (forming two rectangles).
- Draw a line going from corner to opposing corner of one of those halves.

- Rotate the top point of that diagonal line downward until it extends your square.
- Finish off the rectangle using that diagonal length as a guide for the long side of your golden rectangle. It’s that simple.

## Visual Points of Interest Inside a Golden Rectangle

Any square or rectangle (but especially those based on the golden ratio) contain areas inside it that appeal to us visually as well. Here’s how you find those points:

- Draw a straight line from each bottom corner to its opposite top corner on either side. They will cross in the exact center of the format.
- From the center to each corner, locate the midway point to each opposing corner.

Many artists have subsequently taken this idea and used it to plan their painting compositions. Leonardo DaVinci was probably the most famous artist to use the Golden Ratio in his paintings. Georges Seurat also used it in “The Bathers at Asnières”.

Note that in Da Vinci’s “The Annunciation” the brick wall of the courtyard is in golden ratio proportion to the top and bottom of the painting:

Even the fine details of the emblems on the table appear to have been positioned based on golden proportions of the width of the table.

**The Golden Section** was used extensively by Leonardo Da Vinci. Note how all the key dimensions of the room, the table and ornamental shields in Da Vinci’s “The Last Supper” were based on the Golden Ratio, which was known in the Renaissance period as The Divine Proportion. The lines showing Da Vinci’s intricate use of the Divine proportion were created using PhiMatrix golden ratio design and analysis software.

## The Fibonacci Sequence

Around 1200, mathematician Leonardo Fibonacci discovered the unique properties of the Fibonacci Sequence. This sequence ties directly into the Golden ratio because if you take any two successive Fibonacci numbers, their ratio is very close to the Golden ratio. As the numbers get higher, the ratio becomes even closer to 1.618. For example, the ratio of 3 to 5 is 1.666. But the ratio of 13 to 21 is 1.625. Getting even higher, the ratio of 144 to 233 is 1.618. These numbers are all successive numbers in the Fibonacci sequence.

The term “phi” was coined by American mathematician Mark Barr in the 1900s. Phi has continued to appear in mathematics and physics, including the 1970s Penrose Tiles, which allowed surfaces to be tiled in five-fold symmetry. In the 1980s, phi appeared in quasi crystals, a then newly discovered form of matter.

Phi is more than an obscure term found in mathematics and physics. It appears around us in our daily lives, even in our aesthetic views. Studies have shown that when test subjects view random faces, the ones they deem most attractive are those with solid parallels to the Golden ratio. Faces judged as the most attractive show Golden ratio proportions between the width of the face and the width of the eyes, nose, and eyebrows. The test subjects weren’t mathematicians or physicists.

As with pi (the ratio of the circumference of a circle to its diameter), the digits go on and on, theoretically into infinity. Phi is usually rounded off to 1.618. This number has been discovered and rediscovered many times, which is why it has so many names — the Golden mean, the Golden section, divine proportion.

The Egyptians supposedly used it to guide the construction of the Pyramids. In the Great Pyramid of Giza, the length of each side of the base is 756 feet with a height of 481 feet. The ratio of the base to the height is roughly 1.5717, which is close to the Golden ratio. The fictional character, Harvard symbologist Robert Langdon, tried to unravel its mysteries in the novel *The Da Vinci Code*.

## Sacred Geometry

This is an ancient science and sacred language, considered by some to be a key to understanding the way the Universe is designed. It is the study of shape and form, wave and vibration, and moving beyond third dimensional reality. It is the language of creation, which exists as the foundation of all matter, and it is the vehicle for spirit. It has been called the “blueprint for all creation,” the “harmonic configuration of the Soul,” the “divine rhythm which results in manifest experience.”

Sacred geometry ascribes symbolic and sacred meanings to certain geometric shapes and certain geometric proportions. It is associated with the belief that God is the geometer of the world. The geometry used in the design and construction of religious structures such as churches, temples, mosques, religious monuments, alters and tabernacles has sometimes been considered sacred. The concept applies also to sacred spaces such as temenoi, sacred groves, village greens, and holy wells, and the creation of religious art.

The belief that God created the universe according to a geometric plan has ancient origins. Plutarch attributed the belief to Plato, who wrote “God geometrizes continually”. In modern times the mathematician **Carl Friedrich Gauss** adapted this quote, saying “God arithmetizes”.

As late as **Johannes Kepler** (1571–1630), a belief in the geometric underpinnings of the cosmos persisted among some scientists.

## The Roots In Nature

According to **Stephen Skinner**, the study of sacred geometry has its roots in the study of nature, and the math principles at work therein. Many forms observed in nature can be related to geometry; for example, the chambered nautilus grows at a constant rate and so its shell forms a logarithmic spiral to accommodate that growth without changing shape. Also, honeybees construct hexagonal cells to hold their honey. These and other correspondences are sometimes interpreted in terms of sacred geometry and considered to be further proof of the natural significance of geometric forms.

Geometric ratios, and geometric figures were often employed in the design of Egyptian, ancient Indian, Greek and Roman architecture. Medieval European cathedrals also incorporated symbolic geometry. Indian and Himalayan spiritual communities often constructed temples and fortifications on design plans of mandala and yantra.

**The golden ratio,** which is equal to approximately 1.618, can be found in various aspects of our life, including biology, architecture, and the arts. But only recently was it discovered that this special ratio is also reflected in nanoscale, thanks to researchers from the U.K.’s Oxford University. Their research, published in the journal Science on Jan. 8, examined chains of linked magnetic cobalt niobate (CoNb2O6) particles only one particle wide to investigate the Heisenberg Uncertainty Principle. They applied a magnetic field at right angles to an aligned spin of the magnetic chains to introduce more quantum uncertainty. Following the changes in field direction, these small magnets started to magnetically resonate.