Phi (Φ) was described by Johannes Kepler as one of the "two great treasures of geometry." (The other is the Theorem of Pythagoras.) Phi appears in many basic geometric constructions. 3 lines: Take 3 equal lines. Lay the 2nd line against the midpoint of the 1st. Lay the 3rd line against the midpoint of the 2nd. The ratio of AG to AB is Phi, the Golden Ratio. (Contributed by … [Read more...]
Logo Design using the Golden Ratio
Phi is often applied in product logos. From Renaissance artists of the 1500's to graphic artists of today, phi is recognized for its ability to give a sense of aesthetic appeal in balance and harmony of design. Product logos represent an image that must make a positive and memorable impact on the conscious and subconscious minds of consumers, so it is no surprise to find phi … [Read more...]
Product Design and Marketing applications of the Golden Mean
Phi is used in the design of many consumer products. Phi has been used to bring beauty, balance and harmony to some of the world's greatest art and architecture. It is also used to add style and appeal in the marketing and design of everyday consumer products. The applications are endless, but are illustrated by a few of the products below. Click on the image for a … [Read more...]
Aston Martin, James Bond and the Golden Ratio
What do James Bond, Aston Martin and the Golden Ratio have in common? James Bond, also known as 007, drove an Aston Martin DB5 in the movies GoldFinger and GoldenEye, and Aston Martin is now boasting its application of the Golden Ratio in the design of its latest DB9 and Rapide S automobiles. The Aston Martin Rapide S is described as: "Breathtaking Proportions - The ‘Golden … [Read more...]
Golden Ratio in Art Composition and Design
"Without mathematics there is no art," said Luca Pacioli, a contemporary of Da Vinci. Just as the Golden Section is found in the design and beauty of nature, it can also be used to achieve beauty, balance and harmony in art and design. It's a tool, not a rule, for composition, but learning how to use it can be a great Art 101 lesson on laying out a painting on a canvas. For … [Read more...]
Phi in the 23rd Century – Design of Star Trek’s USS Enterprise
Artists and designers have used for the golden ratio for elegance, balance and aesthetics in design since at least the Renaissance, and possibly even as far back as ancient Greece and ancient Egypt. If the vision of Gene Roddenberry for Star Trek continues on course, the design of future starships will also be based on the unique and timeless proportion of Phi, 1.618, the … [Read more...]
Seurat and the Golden Ratio in Art Composition
Georges Seurat (1859–1891) was a French Post-Impressionist painter, who according to Wikipedia, "is noted for his innovative use of drawing media and for devising the technique of painting known as pointillism." It continues, "His large-scale work A Sunday Afternoon on the Island of La Grande Jatte (1884–1886) altered the direction of modern art by initiating … [Read more...]
The Golden Ratio in Art Composition – Seurat Gallery
Seurat as the Creator of Pointillism As discussed on page 1 of Georges Seurat and the Golden Ratio in Art Composition, Seurat "is noted for his innovative use of drawing media and for devising the technique of painting known as pointillism.” Seurat and the Golden Ratio Seurat is also said by one art expert to have "attacked every canvas with the golden ratio." Some have … [Read more...]
Botticelli, The Birth of Venus and the Golden Ratio in Art Composition
"The Birth of Venus", painted by Sandro Botticelli between 1482 and 1485, is one of the most famous pieces of the 15th century Italian art. It is based on Ovid's Metamorphoses, a classic of Latin literature, and portrays Venus, the goddess of love, positioned between the Hora of spring, her handmaid, and Zephyros, god of the wind whose breath creates the blowing wind. "The … [Read more...]
Is the Nautilus shell spiral a golden spiral?
Nautilus shell spirals may have phi proportions, but not as you may have heard. The Nautilus shell if often associated with the golden ratio. There is a fair amount of confusion, misinformation and controversy though over whether the graceful spiral curve of the nautilus shell is based on this golden proportion. Some say yes, but offer no proof at all. Some show examples of … [Read more...]
