Golden Rectangles. Phi, 1.618, the Golden Ratio and Fibonacci series in life, art, design, beauty, mathematics, geometry, stock markets, theology, cosmology and more. Cosmology and Phi. Geometry and Geometric Constructions related to Phi. Phi or Φ, which is 1.618 0339 887 …, 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. Art and applications of Phi, the golden ratio. “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 those with a deeper understanding yet, the golden ratio can be used in more elegant ways to create aesthetics and visual harmony in any branch of the design arts. As you’ll find in the examples below, it has been used by some of the greatest artists the world has known. Oddly enough, you may also find critics who say that the golden ratio cannot be found in art at all. Leonardo da Vinci The Golden Section was used extensively by Leonardo Da Vinci. Design and Composition using PhiMatrix Golden Ratio Software. Easily apply the timeless aesthetics and natural appeal of the Golden Ratio to your creative works in art, architecture, graphic design, logos, product design, photo cropping, and more.
“Without mathematics there is no art,” observed Luca Pacioli, author of “The Divine Proportion.” Mathematics is the foundation of the universe, guides our perception and gives us a sense of what is natural and beautiful. PhiMatrix was inspired by the same realization, and now makes it easy for artists driven by the creativity of the right brain to easily apply mathematical principles of design that are driven by the left brain. Great for any kind of design work Invaluable aid to aesthetics. Product logos and design based on Phi. 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 proportions in many logos of major companies. The Phi grid proportions are provided by PhiMatrix software. See other examples of logos and design at the PhiMatrix site. Note: The logos presented on this page are for illustration purposes only of principles of graphic design and are do not imply in any way an endorsement of, or affiliation with, this web site or its affiliate web sites by the companies shown. Architecture based on Phi. Its use started as perhaps early as with the Egyptians in the design of the pyramids.
Marketing and product design and Phi. 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 larger version. The gauge shown here was developed by Dr. Photo contest awards swept by Golden Ratio shown by PhiMatrix Golden Ratio Software. Photo Composition techniques with PhiMatrix Golden Ratio Software. PhiMatrix can be used to crop a photo to highlight key elements with golden ratio proportions to give a better sense of balance and composition.
This is illustrated in the two tutorials below. Cropping using the Phi grid. Human Beauty and Phi. “Beauty is in the phi of the beholder.”
It has long been said that beauty is in the eye of the beholder and thought that beauty varies by race, culture or era. The evidence, however, shows that our perception of physical beauty is hard wired into our being and based on how closely one’s features reflect phi in their proportions. The Golden Ratio appears extensively in the human face, as demonstrated in a 2009 university study on attractiveness and as illustrated by the video below of Florence Colgate, Britain’s “Most Perfect Face” of 2012, : The image analysis shown in the video was done withPhiMatrix Golden Ratio Design and Analysis Software But let’s take a deeper look yet at beauty through the eyes of medical science.
A template for human beauty is found in phi and the pentagon Dr. Click on the image below to watch an independently-created Youtube video showing the Marquardt Beauty Mask being applied in Photoshop with rather amazing results: The Math Behind the Beauty. By M. Bourne Jessica Simpson What has mathematics got to do with beauty? Actually, a lot. Physical attraction depends on ratio. Our attraction to another person's body increases if that body is symmetrical and in proportion.
Scientists believe that we perceive proportional bodies to be more healthy. Leonardo da Vinci's "Vitruvian Man", showing the golden ratio in body dimensions Leonardo da Vinci's drawings of the human body emphasised its proportion. 1.618 Phi, The Golden Ratio, God Creator of Heaven and Earth. Donal Duck in Mathmagic Land (Golden Rectangle) Life, its design and Phi, the Golden Ratio and Fibonacci series. “All life is biology.
All biology is physiology. All physiology is chemistry. All chemistry is physics. All physics is math.” Dr. The Golden Rectangle - math word definition. The Golden Rectangle From Latin: rectus "right" + angle A rectangle with its sides in the 'Golden Ratio' or 1 : 1.618...
Golden Ratio. The Idea Behind It Have a try yourself (use the slider): Beauty.